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Index

actuation, microscale, 3, 4, 407. See also pumpadvection, chaotic

aggregation. See bubble, aggregation; particle,aggregation; particle, concentration(or trapping); protein, aggregation

assemblyby entropic or excluded volume effects, 45particle. See also particle, aggregation

erasure though AC electro-osmotic flowreversal, 264, 335–336

using AC electro-osmotic flow, 263self or directed molecular assembly, 3

asymmetric (or antisymmetric) solution, 56, 57,62

asymptotic matching, 210–212dipole analysis of infinite prolate spheroids, 174double layer solution to Ohmic bulk solution,

83–85, 204, 206, 258, 259intermediate asymptote, 216–217, 218atmospheric breakdown. See corona discharge;

dielectric breakdownatomic dipole. See dipole, microscopicaveraging, 34, 57

coarse graining, 4, 11, 34charge density and electric force, 11, 14, 30dipole description, 16regularizing integration to remove

singularity, 376. See also singularitycross-sectional, 4, 69, 106ion transport and charge conservation

equations, 241time, 34, 73

electric force, 251–252, 257electro-osmotic slip velocity, 256–257hydrodynamic equations, 261–262product of two harmonic functions, 286

transverse, convection–diffusion equation,118–120

bacteria, 7–8. See also pathogenassembly, 176detection. See detection

differentiation, 401–402discrepancy in classical dielectrophoretic

theory, 288metabolism and growth detection, 180–183.

See also detectionband broadening, 147, 150. See also dispersion,

hydrodynamicbandgap illumination, 174biased reptation, 144, 147. See also

electrophoresisbifurcation

in electrospray data with voltage changes, 358of symmetric and nonsymmetric solutions,

60–62of vortex structures, 338

biharmonic equation. See stream functionbinding interaction, 162biosensor. See detectionbirefringence, 176Bjerrum length, 57–58, 139, 303“blob” theory, 154Bode plot, 163–165. See also Nyquist plotBohr atom, 160Boltzmann distribution, 38, 68. See also

Boltzmann factor; transformation,Boltzmann

azimuthal, 135–137, 138global stability, hydrostatic, 38, 40–41, 72–73in double layer, 76. See also Debye double

layerinappropriate for nonequilibrium

electrokinetics, 156. See electrokinetics,nonequilibrium

no analytical solution for charged particle ofarbitrary geometry, 45

nonuniform, due to electromigration, 137.See also polarization, field-induced doublelayer polarization

Boltzmann factor, 68, 80. See also Boltzmanndistribution; transformation, Boltzmann

boundary condition“bulk-scale,” 83–85

475

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476 Index

constant (or zero) potential, 48constant field, 72, 124, 142

boundary condition (cont.)effective external field condition, 216, 259,

266effective slip, 257far field, 39, 142, 170, 204, 206, 219

elimination of zeroth harmonic mode in DCTaylor cones, 404

impenetrable or ideally polarizable surface.See boundary condition, no-flux

insulated, 207, 271–272, 279. See also surface,insulating

due to double layer screening, 97. See alsoscreening

interfacial, 16, 170between gas and liquid phases, 297, 357electric field or displacement continuity and

jump conditions, 16, 18, 168, 190, 194, 381,425

normal stress jump, 28, 352, 377, 424potential continuity, 194, 195, 353tangential stress balance, 424

kinematic, 28, 382, 425mixed Stern layer, 42, 43, 45no-flux

flow, 97ion, 83, 113, 124, 142, 194, 259solute concentration, 119–120

no-slip, 124, 206, 424suppression of centrifugal force, 399

Robin, 60, 195slip, 88, 97, 113. See also electro-osmosis,

electro-osmotic slipStern layer condition, 56–60, 303–304surface, 48symmetry, 68, 70, 88no-penetration. See boundary condition,

no-fluxboundary layer, 62

Ekman, 399Bretherton equation, 430Brownian dynamics, 154Brownian motion, 401bubble

absence of double layer charging, 295aggregation, 90conducting, due to plasma generation, 295.

See also ion, plasmadisruption of electrospray stability, 351dynamics, endowed by AC induced dipoles,

338field-induced double layer polarization effects,

284. See also polarization, field-induceddouble layer polarization

frequency-dependent attraction (coalescence)and repulsion, 299–300. See alsodielectrophoresis, bubble

generation

circumvented with the use of monoliths, 151,270. See also reaction, electrolytic;reaction, Faradaic

due to increased current or electric inelectrolyte, 93

in DC electrokinetics, 6, 7, 155. See alsoreaction, electrolytic; reaction, Faradaic

suppression through high-frequency ACfields. See electric field, AC

multiphase microchannel flow, 99, 344. See alsobubble, transport in capillaries

spacers, 96train (or slugs), 99, 439–440translation speed. See capillary numbertransport in capillaries, 438–441. See also

bubble, multiphase microchannel flowtrapping, 6

buffer solutionaddition to regulate solution pH and osmotic

pressure, 6, 67–68, 129, 156. See also pHeffect of viscosity on dielectrophoretic mobility,

322–324

capacitorcurrent, 163double layer. See Debye double layer, as

capacitorrelaxation frequency, 446Stern layer, saturation at low frequencies, 304

capillary. See channelcapillary number, 428, 439, 441capillary ridge, 426–428, 429, 431capillary tube bundle, 76, 91–92, 96. See also

channelcell

blood cellage discrimination via dielectrophoresis,

311–321. See also dielectrophoresis,cellular

charge relaxation time, 311–312, 314separation, 399. See also separationshell model, 312, 313–315transport, 99–102

culture, 1dielectric properties, measured by

electrorotation, 327. See alsoelectrorotation

dispersive behavior, 177–178. See alsodielectric, dispersion

electrophoresis. See electrophoresis, cellularencapsulation, 387ion-channel, 177lysis

due to DC penetration current and electricfield, 6. See also protein, denaturing

prevented through use of high frequency ACelectric fields, 7, 251, 402

manipulation. See particle, manipulationmembrane. See membrane, lipid bilayer




Index 477

orientation control, using electrorotation, 327.See also electrorotation

separation, 146, 333. See also separationthin double layers, 129

centrifugation, driven by ionic wind, 394–402channel

bicontinuous pore morphology, 90, 91. See alsochannel, geometry

charged, due to double layer overlap, 66–67.See also Debye double layer, overlap

closed microchannel system, 411. See alsodigital microfluidics; open microfluidicsystem

contracting–expanding, 123–127corner. See singularitycritical size to suppress electrokinetic fingering

instability, 116curved, dispersion effects, 122. See also

dispersion, hydrodynamic entrance effects,71,86,123

exit effects, 123geometry

dispersion effects, 121–122. See alsodispersion, hydrodynamic

effect on electro-osmotic slip, 79, 81. See alsoelectro-osmosis, electro-osmotic slip

load, 90–92microchannel, dimension comparable to Debye

length, 88. See also Debye double layer,overlap

nanochannel or nanopore, 5conductivity gradient, 236critical voltage for flow, 96. See also electric

field, critical (or threshold) fieldcurrent–voltage (I–V) characteristics,

239–250. See also current–voltage (I–V)characteristics

dimension comparable to Debye length,79–81. See also Debye length

electro-osmosis, 86–88. See electro-osmosis,in nanochannels or nanopores

extended polarization. See surface, extendedpolarization

ion depletion and enrichment, 202, 214, 215.See also surface, extended polarization;iondepletion (or diffusion) region; ion,enrichment region

large hydrodynamic resistance, 90. See alsohydrodynamic resistance

overall zero net charge, 87overlapping double layers. See Debye

double layer, overlappermselective, limiting resistance region, 239,

242, 245, 248–250. See also current–voltage(I–V) characteristics; current density,limiting

permselective, Ohmic region, 239, 245, 248.See also current–voltage (I–V)characteristics; Ohmic system (or region)

permselective, overlimiting region. Seeoverlimiting region; current–voltage (I–V)characteristics

optimum size, 90, 93streaming current, 80

packing, 89–90, 130, 150. See also packingfraction

porosity, 93, 94pressure-driven bubble transport, 439–440.

See also bubble, transport in capillaries;flow, pressure-driven

profiling, 122pump, 88, 90–94small channel limit, overlapping double layers,

65–71. See also Debye double layer,overlap

surface charging, 35. See also charge, surfaceT-junction, 197tortuosity, 91typical dimension, 3

charge, 8accumulation. See also charge, buildup

at contact line, 415. See also charge, trappingat critical point, 226, 233at electrode, 256at electrospray meniscus tip, 346, 364, 368,

376at ion-selective granule surface, 201, 220.

See also charge, buildupbalance with conduction current, 260due to conductivity gradient, 295due to electrothermal effect, 281, 283.

See also electrothermal effectdue to interfacial conductivity jump,

239in collapsed layer, 56. See also collapsed

diffuse double layerin diffuse double layer, 302. See also charge,

buildupin double layer. See Debye double layer,

chargingin nanochannels or nanopores, 226, 239in Stern layer, 303, 304. See also ion,

adsorptioninsufficient time in high frequency AC

electrosprays, 370outside double layer with AC fields,

280over several period cycles in nonsymmetric

electrolytes, 170zero in electroneutral Ohmic region, 33

advection, 74. See also current; ion, convectionbasis for electrophoretic separation, 144.

See also electrophoresis

bound, 40, 169. See also charge density, boundcharge

along interface, 359, 434in Stern layer, 50, 54. See also Stern layerlocal orientation under electric field, 156




478 Index

number density balances charges in doublelayer, 155

polarization in dielectric materials, 156.See also dielectric; polarization

polarization time scale, 161. See alsodielectric, relaxation time

charge (cont.)buildup

in extended polarization layer, 214. See alsocharge, accumulation

at corner geometries, 7. See also singularityat interfaces of ion-selective membranes, 5,

71boundary effects, giving rise to streaming

potential, 123due to transient charging, 201, 202. See also

charge, accumulationpolar, 308. See also charging, polar

bulkrelaxation to interface, 345, 360, 362, 363,

368, 376stabilization of capillary instabilities at high

frequency, 368conduction. See conduction, ionconservation, 10, 32. See also Gauss’ Law;

transport, convective-diffusive equationalong cell surface, 135

convection. See convection, iondrainage

due to drop ejection at contact line,447

due to tangential conduction, 304. See alsodiffuse double layer, tangential conduction

entrainmentin electrospray meniscus, 368–369, 372, 374,

378. See also electrospray; meniscustime scale, 73. See also RC time scale

equilibriation, 21. See also equilibrium,Poisson–Boltzmann

excessdue to tangential convection or surface

reaction at high Péclet numbers, 220in double layer, 47, 54, 73, 76in extended polarization layer, 205. See also

surface, extended polarizationsteric effects in double layer, 268

free, 169. See also charge, mobileabsent in perfect dielectrics, 156. See also

dielectricin field-induced double layer polarization,

156. See also polarization, field-induceddouble layer polarization

immobile, 56, 71induced, 16, 175, 184

atomic surface charge, 315flow generation in thick polarization layer

limit, 215. See also polarization layersaturation, 186, 442injection, 415. See also charge, accumulation;

dielectric, dielectric layer (or coating)

interfacial, 368, 436. See also charge, surface;polarization, interfacial

arising due to permittivity jump, 168conservation, 169, 358. See also charge,

conservationevolution equation, 434in electrospinning, 386. See also charge

density, interfacialinduced, 377. See also charge, inducedresponsible for jump in normal field, 16.

See also boundary condition, interfacialinversion. See charge, reversalleakage into atmosphere, 415line, constant field, 271mobile, 81. See also charge, space; ion,

mobilityassociated with Faradaic polarization, 161.

See also charging, Faradaicin collapsed and diffuse double layers, 50, 53,

55, 56in double layer, 137necessity in dielectric liquid pumps, 20–25

moiety, 136net charge giving rise to momentum transfer in

double layer, 76. See also Debye doublelayer

net charge on dipole, 170. See also dipolepoint, 9, 10, 13, 130redistribution

along contact line, 418along interface, 434

relaxation, 23, 167–168, 177characteristic relaxation frequency. See

frequency, characteristicdue to tangential conduction, 225

relaxation time, 162, 233, 345. See alsodielectric, relaxation time; dipole,relaxation time; diffusion layer, relaxationtime; Debye double layer, relaxation time;polarization, relaxation time

repulsion. See electrostatic, repulsionreversal

due to anticorrelated fluctuations betweencounterions and surface charges, 57–58

due to counterion condensation on colloids,138–139, 325

due to pH reduction, 101. See also pHduring AC electro-osmosis, 254. See also

electro-osmosis, ACnot possible through polyvalent counterion

condensation or adsorption, 63separation, 57, 137, 346. See also charge,

relaxationspace

exact differential, 44generation due to ion injection, 27in double layer, 35. See also charge, mobileresponsible for electric body force, 17, 18, 20,

39. See also charge, mobile; forceelectric




Index 479

role in electrospray conical menisci,354–356

storage, 252. See also Debye double layer, ascapacitor; diffuse double layer, capacitance;double layer, capacitance; ion, adsorption

surfaceacquisition, 35–36, 73balances charge in nanochannel, 66. See also

channel, nanochannel or nanopore; Debyedouble layer, overlap

excess, eliminated by superimposing AC fieldon DC voltage, 361

jet, 347natural, principle behind equilibrium

electrokinetics, 7. See also electrokinetics,equilibrium

near cancellation with counterion charge incollapsed layer, 52. See also collapseddiffuse double layer

nonuniform, due to tangential surfacecurrents, 98, 137. See also ion, tangentialconduction

produces normal surface field in double layer,77

reversal. See charge, reversalrole in double layer charging, 252. See also

Debye double layer, chargingspecifies nanochannel conductance, 247–248.

See also channel, nanochannel ornanopore

total residence charge in electrospray meniscuscone, 375

transfer across interface in extendedpolarization layers, 287. See also extendedpolarization layer

transport. See ion, transporttrapping

in insulating dielectric layer, 415–416. Seealso charge, accumulation; dielectric,dielectric layer (or coating)

in thick double layers. See charge, storageresponsible for contact line pinning,

444charge density

accumulated charge, 280bound charge, 159, 169. See also charge, bound;

charge density, surface polarizationfree, 159, 169. See also charge, spacein electrospray aerosol drops, 347interfacial, 382–383

reduction due to charge trapping and partialscreening, 415. See also charge,accumulation; dielectric, dielectric layer(or coating)

line charge, 11, 359surface charge, 11

at electrospray orifice, 383balances charge in double layer to maintain

electroneutrality, 39. See alsoelectroneutrality

balances volume charge in nanopore, 68. Seealso channel, nanochannel or nanopore;Debye double layer, overlap

compensated by counter-ions in collapsedlayer, 53, 141. See also collapsed diffusedouble layer

dependence on particle size, 290determined from I–V characteristics in

Ohmic region, 247–248difference gives rise to electrophoretic

separation, 130. See also electrophoresisdistribution in electrospray meniscus,

374–375, 377does not affect membrane properties, 311.

See also membraneeffect on apparent viscosity, 126. See also

viscosity, apparentfunction of the particle potential, 56–68imbalance with counterion density in

nonequilibrium cases, 98. See alsoelectrokinetics, nonequilibrium

in Stern layer, 54–55, 303induced, 169. See also charge, inducedrelationship with ζ potential, 102. See also

potential, zeta (or ζ ) potentialtotal, comprising of free and induced charge

densities, 169surface polarization, 158. See also charge

density, bound chargetemperature induced space charge, 281volume charge, 11, 13

around particle, 302as exact differential, 38, 40balances surface charge density in diffuse

double layer, 55bulk distribution in nanopore balances

surface charge, 68convective–diffusive equation, 258. See also

transport, convective–diffusive equationgives rise to electric force, 30imbalance with surface charge density in

nonequilibrium cases, 98in polarized region, 80negligible in diffuse double layer, 304of bulk charges discharging in electrospray

meniscus, 368–369of mobile counterions in diffuse double layer,

74, 77scaling, 281total over all ionic species, 38total, comprising free and bound charge

densities, 159

vanishes in electroneutral Ohmic region, 29.See also electroneutrality

charge residue model, 348charged surface

concentration polarization, 36. See also charge,surface




480 Index

role in the generation of equilibriumelectrokinetic phenomena, 74. See alsocharge, surface

chargingAC, 73, 251–253. See also Debye double layer,

chargingdependence on frequency, 256. See also

frequency, AC fieldin electrowetting, 441–442, 443

charging (cont.)modified model to account for double layer

steric effects, 268. See also steric effectasymmetric, around ion-specific granule, 233capacitive, 184, 217–220, 221, 265. See also

electrode, polarizationdriven by normal diffusion, 293, 295–300. See

also ion, adsorption; charging, normalfield

in dielectrophoresis, 285, 292, 300. See alsopolarization, field-induced dielectricpolarization

mechanism for AC electro-osmotic flow.See electro-osmosis, AC

transient, at low Péclet numbers, 220conductive

in dielectrophoresis, 285, 313. See alsodielectrophoresis; current, conduction;polarization, conductive

convection enhancement, 226DC, 252–253double layer. See Debye double layer, chargingdynamic. See charging, transientFaradaic, 161, 264. See also reaction, Faradaicfield-induced. See polarization, field-inducedincomplete at high frequencies. See screening,

incomplete, at high frequenciesinterfacial. See polarization, interfacialmechanisms for dielectrophoresis, 307. See also

dielectrophoresisnonuniform. See polarization, nonuniformnormal field, 7. See also Debye double layer,

normal chargingpolar

electroneutral sublayer, 227, 231. See alsoion, dynamic superconcentration

in double layer, 231, 305–311. See also ion,dynamic super-concentration

surfaceat poles. See charging, polarrole in field-induced double layer

polarization of nonconducting particles,284. See also polarization, field-induceddouble layer polarization

time, 87transient

due to external DC field, 201–203, 217suppression due to external field screening,

201. See also screeningtermination due to tangential convection,

217, 220–221. See also ion, tangentialconvection

chemical potential. See potential, chemicalchromatography

high-performance liquid chromatography(HPLC), 89, 148, 150, 378

mobile phase, 149, 150stationary phase, 148, 150

Clausius–Mossotti factor, 172, 287, 329, 333modified to account for diffuse double layer

tangential conduction, 302–303, 304–305.See also ion, tangential conduction

modified to account for normal capacitivecharging, 298. See also dielectrophoresis,bubble

particle-size dependent, 299co-ion

exclusion from ion-selective granule, 201exclusion from nanochannel, 248. See also

channel, nanochannel or nanoporecollapsed diffuse double layer, 50

conductance, 53, 140–141conduction, 139–140. See also ion, tangential

conductioncontains Stern layer, 53–54convection, 140current flux contribution in nanochannel

electro-osmotic flow, 87. See alsoelectro-osmosis, nanochannel or nanopore

disappearance at large medium conductivities,284

field line penetration, 284–285. See also electricfield, penetration

low-conductivity correction to crossoverfrequency, 288–294. See alsodielectrophoresis

screening due to trapping of large biomolecules,323

screening in weak electrolyte system, 52thickness, 48, 50, 51–52, 53

collision length, 32. See also mean free pathcolloid. See also particle

ability for nanocolloids to store ions and toform dipoles, 294

aggregation, in double layer, 322–324. See alsoaggregation

challenges in microfluidic systems involvingnanocolloids, 3

concentration (or trapping). See particle,concentration (or trapping)

counter-ion condensation on surface, 138–139.See also ion, condensation

crystal morphology. See dielectrophoresis,molecular

differential mobility analyzer, 406difficulty of manipulation with

dielectrophoresis, 174. See alsodielectrophoresis

disordering effects, 325

electrospray ring deposition patterns, 404–406.See also electrospray

nanocolloid manipulation, 2, 5




Index 481

selection of multiple discrete harmonics in DCelectrospraying, 404–406

self-assembly, 294surface functionalization, 325suspension viscosity, 398

colloidal docking. See dockingcolloidal interaction. See particle-particle

interactioncompressibility effects. See electrostrictionconcentration gradient, in diffusion layer,

233concentration polarization. See polarization,

concentrationconducting layer, 50, 136–137conducting liquid. See electrolyteconformal mapping, 192, 419, 426conservation equations, 14, 15, 203.

See also transport, convective–diffusiveequation

contact angle, 409. See also wettingadvancing. See contact angle, hysteresisdynamic condition, 429–431frequency dependence, 443hysteresis, 412–414, 442macroscopic (or apparent), 421

dynamic, 431. See also contact angle,dynamic condition

static (or equilibrium), 421. See alsoelectrowetting, static

microscopic, voltage independent in localcontact line region, 421

receding. See contact angle, hysteresisstatic or equilibrium, 411

contact linedynamic, 409equilibrium (or static)

force balance, 409–410intermolecular interactions, 431, 446. See also

precursor filmmolecular slip, 418. See also slippinning, 412, 443–444pitting of electrode surface. See contact line,

pinningsaturation, 414–417, 422, 442–447

analogy with paramagnetism,417

critical field, 442critical radius, 442

singularity. See singularity, contact linecontinuum mechanics, validity, 4, 14convection layer, 209convection

charge or ion. See ion, convectionhydrodynamic

concentration homogenization, 334in multiscale particle trapping, 270responsible for distortion and instability of

diffusion layer, 233responsible for particle migration and vortex

formation around corners, 190solute, 117–119, 224

time scale, 117corona discharge, 20, 369–370, 394–395. See also

dielectric breakdowncorona wind. See ionic windCoulomb force. See force, electric (or

electrostatic)Coulomb’s Law, 9–10, 13, 359

coarse grained, 11, 20Coulombic fission, 346, 347, 348, 365

absence in AC electrospraying andelectrospinning, 370, 386

counterionequilibriation in double layer, 252in interfacial polarization (double) layer,

346saturation assumption in ion-selective granule,

221critical field. See electric field, critical fieldcritical point gate, 225–226crystal lattice site, 36current, 29–30. See also ion, transport

AC, 7insufficient time to penetrate biological cells,

251balance. See transport, convective–diffusive

equationcapacitive charging, 7, 170, 271. See also

charging, capacitivenormal, in thick diffuse double layers, 291,

293, 300–301, 308charging, 168, 273. See also charging, transientconduction, 167, 170. See also current,

displacement; ion, conductionarising from streaming current, 74assumption of dominance over convection

current in AC electro-osmosis, 257in double layer, 53. See also Debye double

layerinterfacial, 358penetration into ion-selective granule,

221tangential assumption breaks down for large

diffuse double layers, 300convective, 218, 358. See also ion, convectionDC, penetration damages biological cells, 6diffusion, coupling with flow velocity,

125displacement, 167electrospinning jet, 382–383. See also current,

electrosprayelectrospray, 356, 358. See also current,

electrospinning jetenhancement due to gas-phase ionization

effects, 358Faradaic charging, 7. See also reaction,

Faradaic; charging, Faradaic

flux, 30, 87, 155nanochannel or nanopore, controlled by

intrachannel and polarization layerresistances, 245




482 Index

limiting, 215, 243–245. See also current density,limiting

breakdown of electroneutral assumption,245. See also electroneutrality

minimization through electrolyte inelectro-osmotic pump, 93. See alsoelectro-osmosis,

electro-osmotic pumpOhmic. See current, conductionoverlimiting, 235, 236, 249. See also

overlimiting regionpenetration. See electric field, penetration

current (cont.)penetration depth

small for high frequencies, 387. See also RCtime scale, limitation of field-penetrationdepth

enhancement due to tangential convection,219, 221. See also ion, tangentialconvection

into ion-selective granule due to incompletescreening, 201, 203

into membrane to sustain electrolyticreaction, 90. See also reaction, electrolytic

scaling in nanopore, 66–67. See also channel,nanochannel or nanopore; Debye doublelayer, overlap

streaming, 74, 79–81, 96. See also streamingpotential

surface, 95–96, 98. See also current, tangentialtangential. See also current, surface

low conductivity correction to crossoverfrequency, 288. See also dielectrophoresis

negligible for small double layers, 255total, continuous across interface, 169. See also

boundary condition, interfacialcurrent density, 29, 32–33, 168

limiting, 209, 218, 242, 245, 249. See alsocurrent, limiting

thick polarization layer (high field) theory, 215.See also polarization layer

current–voltage (I–V) characteristics, 210–213.See also nanochannel, current–voltage(I–V) characteristics

I–V curves, 193–249pump, 96. See also pump

current–voltage (I–V) scaling, 356

Deborah number, 383, 385Debye double layer, 35, 36

as capacitor, 155, 162, 180, 252, 255–256, 260,293, 361, 443. See also Debye double layer,

chargingas equivalent series RC circuit, 180, 256, 260as surface conducting layer, 177balance with surface charges, 39, 54, 155.

See also electroneutrality

bipolar, around cylinder, 278capacitance, 256, 280, 443

decrease due to Debye double layer stericeffects, 268

dependence on ζ potential, 186, 310enhancement with zwitterion buffer, 281.

See also zwitterionlinear for small potential drop, 264negligible in electrowetting, 411. See also

electrowettingcharge balance, 255charge leakage arrested by Stern layer

adsorption, 309charge storage mechanism through Stern layer

adsorption. See charge, accumulationcharging, 47, 87, 177. See also Debye double

layer, formation and relaxation dynamics;polarization, Maxwell–Wagner

breakdown in classical Maxwell–Wagnertheory, 172. See also dielectrophoresis;polarization, Maxwell–Wagner

by conducting current, 260capacitive, in AC electro-osmosis.

See electro-osmosis, ACconditions, 251–253flux density, 306governing mechanism in AC electrowetting,

441–442, 443, 447charging time, 277. See also Debye double

layer, relaxation timeconcentration around particle, 307conductance, 52. See also collapsed diffuse

double layer, conductance; diffuse doublelayer, conductance; Stern layer,conductance

convective polar charging. See charging, polardiffuse double layer theory. See diffuse double

layerdistortion, 130, 132–133dynamic, 47. See also polarization,

field-induced double layer polarizationeffect on bubble transport, 440–441electric field, 184equilibrium, 47, 76

absence of flow, 39equilibriation time. See Debye double layer,

relaxation timefully developed flow, 252in steady-state ion-specific granule, 207

extended. See surface, extended polarizationformation and relaxation dynamics, 72–73. See

also Debye double layer, relaxation timegas phase, 295, 297governing mechanism in electrokinetic

phenomena, 73–74in concentration polarization layer, 241increased thickness at poles of ion-specific

granule, 231, 345, 363. See also ion,dynamic superconcentration

interfacial. See also polarization layer,interfacial

large shear and viscous dissipation, 6, 78




Index 483

linear theory (Debye-Hückel approximation),45–47. See also Debye-Hückelapproximation

localization of AC current within, 7near-equilibrium, 204nonequilibrium, 184nonlinear effects, 52, 58. See also polarization,

field-induced double layer polarizationnonlinear theory, 47–53normal charging, 277overlap, 65–72, 86, 90, 93, 236. See also

electro-osmosis, in nanochannels ornanopores

allowed for by symmetry boundary condition,124. See also boundary condition,symmetry

counterion concentration, 248in annular films, 441overlap: nanochannel, loss of permselectivity,

239polarization. See polarization, field-induced

double layer polarizationpossible mechanism for dielectric dispersion,

177potential drop across. See potential, zeta

(or ζ ) potentialquasi-steady equilibrium assumption, 263,

295relaxation time, 47. See also dielectric,

relaxation time; dipole, relaxation timecharacteristic time for double layer

formation, 73, 167, 291, 292. See alsoDebye double layer, formation andrelaxation dynamics; RC time scale

diffusion in gas bubble, 295electrospray charging dynamics, 363. See also

RC time scalereturn to symmetry after double layer

distortion, 132role in electrotation, 329. See also

electrorotationrole in nonequilibrium electrokinetics, 8. See

also electrokinetics, nonequilibrium;polarization, field-induced double layerpolarization

screening. See screeningscreening length. See Debye lengthslip plane, 55, 74, 76, 78tangential conduction. See ion, tangential

conductionthermal gradients in large double layers, 281,

283. See also thermal gradientthickness. See Debye lengthtypical dimension, 76

Debye length, 46. See also screeningaround ion-selective granule surface, 227at corner geometries, 200effect on electroviscous effect, 125–126, 132. See

also electroviscous effectindependent of surface charge, 47

optimum channel dimension forelectro-osmotic flow, 67, 79–81. See alsoelectro-osmosis

pertinent length scale in AC electrowetting. Seelength scale, characteristic

role in extended polarization layer generation,202, 204, 214

weak logarithmic dependence on ζ potential,49. See also potential, zeta (or ζ ) potential

Debye–Hückel approximation, 46, 49. See alsoDebye–Hückel equation; linearization

limitations, 46, 47–48, 65. See alsoDebye–Hückel limit

Debye–Hückel equation, 46. See alsoDebye–Hückel approximation

Debye–Hückel limit, 47–48, 138. See alsoDebye–Hückel approximation

Debye–Hückel theory. See Debye–Hückelapproximation

DEP. See dielectrophoresisdepolarizing factor. See particle, polarizability

(ellipsoid or prolate spheroid)Derjaguin approximation, 57. See also DLVO

theorydetection, 3, 411–412

biological, 1–3, 268, 326integrated dielectrophoretic chip, 329–331.

See also dielectrophoresisvia ionic wind driven microcentrifugation,

398, 399detection threshold, 2, 268explosives, 1optical, 3, 5sample, 145

diagnostic (or genetic) bead, 2–3, 5, 7, 321–327diagnostics, 2–3dielectric

dielectric layer (or coating), 7, 410. See alsoelectrical insulator

minimum thickness, 415nonuniform thickness, 432thickness, 421

dispersion, 162, 166. See also time scale, chargedispersion

dissipation factor. See dielectric, loss tangentdouble layer charging on dielectric surfaces,

253heterogeneous, 17. See also dielectric, mediumideal, 16, 17, 159. See also dielectric, mediuminhomogeneous, 168interface, 156. See also interfaceleaky. See dielectric, Maxwell–Wagnerlinear. See dielectric, idealliquid. See also dielectric, medium

absence of electrospray Taylor cone, 354.See also electrospray; meniscus, conical

cancellation between electric andhydrodynamic pressures, 19

electrokinetic flow, 18, 20–29, 35loss tangent, 167




484 Index

lossy. See dielectric, Maxwell–WagnerMaxwell–Wagner, 165–177, 311, 328medium, 156, 158. See also dielectric, liquid

additional forces due to induced charges, 9storage of capacitive energy, 166

nonideal. See dielectric, Maxwell–Wagnerperfect, 156. See also electrical insulatorpermittivity. See permittivitypolarization. See polarization, field-induced

dielectric polarizationrelaxation mechanism, 177–180relaxation time, 167, 172, 177–180. See also

dipole, relaxation timedielectric (cont.)

solid, 20, 45. See also dielectric, mediumspectroscopy, 177surface, 50, 98

dielectric breakdown, 369, 407, 415dielectric constant, 159. See also permittivity,

relativemembrane, effect on crossover frequency, 318

dielectric polarization. See polarization,field-induced dielectric polarization

dielectrophoresis, 285–311AC electro-osmotic flow enhanced trapping,

334–336advantage of using AC fields, 287bubble, 295–300

double crossover frequency due to normaldiffusive charging, 295–297, 299

cellular, 312double crossover frequency due to internal

fluid conductivity, 311–312, 313, 314,318–321. See also cell, blood cell

effect of membrane permittivity andcytoplasm conductivity on crossoverfrequency, 314, 315–317

conducting Stern and collapsed diffuse doublelayer correction, 288–294

crossover frequency, 172, 280, 287, 335anomalous drop at high medium

conductivity, 305corresponding to distinct relaxation times,

292–294dependence on medium conductivity, 291,

292, 309dependence on particle size, 290–291, 293,

297field dependence, 293, 308increase at intermediate medium

conductivity, 300–305independent of medium conductivity,

289–290, 308, 310low-conductivity correction through

conducting Stern and collapsed doublelayers, 289–290, 310

maximum, 311modification through DNA hybridization,

326. See also DNA, hybridization

DC, inability to generate particle aggregationand vortices around corners, 189–190

dielectric polarization mechanism, 287dielectrophoretic mobility, 174, 176, 294

cells, 311polyelectrolytes, 325

dielectrophoretic velocity, 175–176, 294, 335force, 174, 273, 286–287, 294

localization at stagnation point for trapping,335

relation to electrocapillarity, 423scaling with particle size, 331time-averaged, 286traveling-wave dielectrophoresis, 333

gate, 331integrated chip for bioparticle sorting and

detection, 329–331. See also particle,sorting

mechanism for drawing particles into surfacevortices, 397–398

molecular, 321–327associated time scales, 325colloidal crystal morphology, 324dependence of crossover on DNA

concentration and conformation, 325–326.See also DNA; polyelectrolyte

vanishing dielectrophoretic mobility at lowfrequencies, 322–324

negative, 287positive, 287protein crystal migration, 342. See also protein,

crystallizationthree-dimensional continuous flow, 329–331trap, 176traveling wave, 332–334separation, 176

diffuse double layer, 53–56. See also Debyedouble layer

capacitance, 256, 310dependence on ζ potential, 186when tangential conduction is significant, 309

collapsed. See collapsed diffuse double layerconductance, 52, 140. See also diffuse double

layer, conductanceconduction, 81, 140convection, 140electro-osmotic slip, 73–74, 76. See also

electro-osmosisfield line penetration, 284–285. See also electric

field, penetrationin polarization produced by conductivity

gradients, 287–288relationship to Debye length, 47. See also

Debye lengthrelationship to Maxwell–Wagner dielectrics,

170. See also dielectric, Maxwell–Wagnerrole of space charge in screening external field

around thick layers, 303, 308space charge distribution, 302




Index 485

tangential conduction, 301, 303, 307–309. Seealso ion, tangential conduction

tangential diffusion, 307–308thickness, to allow for tangential conduction,

303. See also ion, tangential conductiondiffusion

diffusion coefficient. See diffusivityion

balance with electromigration underequilibrium conditions, 130, 134. See alsoion, electromigration; equilibrium,Poisson–Boltzmann

limitation to pore transport, 71relationship with ion mobility, 31–32. See also

ion, mobilitylength scale, 106, 110, 136, 215. See also length

scalemolecular, 7, 114, 117normal, 260plasma, 396relaxation time, role in electrorotation,

329solute, 105, 117–122, 147tangential, 141. See also diffuse double layer,

tangential diffusionthermal, 58, 133, 404. See also thermal

fluctuationtime scale, 117, 178, 223, 256, 263

diffusion front, 104, 107–109, 114diffusion layer, 204, 215, 218, 241, 245. See also

polarization layercharging dynamics, 236, 237–238compression/dilation due to convection,

234concentration profile, 243–245electroneutral, 206, 219, 233, 235relaxation time, 239

tangential diffusion, 292, 293thickness, 216, 218

correspondence to convection layer length,209

growth induced through AC forcing, 236independence of field strength and

frequency, 236limited through tangential convection, 219,

221scaling with Péclet number, 217selection of vortex dimension, 233, 236,

239diffusivity

absence in Dukhin scaling, 202, 206. See alsoDukhin (low Péclet number) theory

dependence in electrophoretic velocity in highPéclet number theory, 219

enhancement due to mixing, 223ion, 32

assumption of equal co-ion and counter-iondiffusivities, 105

effective, 32relationship to ion mobility, 30, 31

lysozyme, 339plasma, 295solute, effective, 105, 117–120, 122. See also

diffusivity, ionsurface, 135

digital microfluidics, 5, 411digitated platforms. See digital microfluidicsdilute system, 32, 37dipole, 177, 180

aggregation, 294alignment, 158, 170. See also dipole, orientation

during orientational polarization, 161.See also polarization, orientational

giving rise to torque, 158, 327–328. See alsodipole, torque

in dielectrophoresis, 285, 287, 332. See alsodielectrophoresis

sufficient time with low AC frequencies, 162,167

complex polarizability, 285. See also dipole,polarizability

displacement, 162force, 157, 286induced, 157–158. See also polarization,

field-induced dielectric polarizationdue to rotating electric field. See

electrorotationdue to tangential ion migration in double

layer, 301electrostatic potential, 302giving rise to dielectrophoresis, 335–336, 338.

See also dielectrophoresisjump across interface produces surface

charge, 168. See also charge, interfacialof polyelectrolyte molecule. See

polyelectrolyteparallel or antiparallel, 299–300, 328

microscopic, 16orientation, 161, 167, 339

along polyelectrolyte molecule, 339. See alsopolyelectrolyte

during dielectrophoresis, 338. See alsodielectrophoresis

orientation vector, 157permanent, 158, 160, 325, 338polarizability, 16, 158, 160, 171polarization vector, 158–159, 173, 328potential, 157potential energy, 157relaxation time, 162, 312. See also dielectric,

relaxation time; Debye double layer,relaxation time

reversal, 308. See also charge, reversal;polarization, reversal

rotation, 158, 332. See also polarization,orientational

torque, 158, 161, 327. See also particle, torquedipole moment, 157–158, 160–161, 172,

173effective, 170, 171, 174, 285




486 Index

discrete axisymmetric harmonics. See expansion;meniscus, conical

dispersiondispersion coefficient. See diffusivitydispersivity function, 121–122hydrodynamic, 116–122. See also band

broadeningin curved channels, 122minimization using field-effect ζ -potential

variation, 187minimization with electro-osmotic flow, 76,

89, 131. See also electro-osmosissignificant in composite channels, 131

sample or solutal, 88. See also dispersion,hydrodynamic

dispersion relationshipelectrospray jet instability, 347. See also jetfilm destabilization due to Maxwell pressure, 28instability due to conductivity gradients, 114Rayleigh–Lamb, 361, 363, 364, 402

disturbance. See also fluctuationgrowth rate, 28, 110, 114, 115in viscoelastic filaments, amplified by inertial

effects, 385interfacial. See interface, deformationlinear perturbation, 28, 108, 113, 115long wavelengthmechanical, 351to extended polarization layer thickness,

234wave number, 28, 108, 114, 348. See also

instability, wavelength; fluctuationDLVO theory, 20, 46, 56, 189DNA, 7–8

condensation, 57, 139, 325. See also ion,condensation

dielectrophoretic trapping. Seedielectrophoresis, molecular

diffusion coefficient, 148, 322–324. See alsodiffusivity

encapsulation, 387field-induced polarization due to association or

dissociation, 161. See also polarization,field-induced dielectric polarization

free-draining, 152hybridization, 2, 326identification, 2immobilization and stretching using AC

electro-osmotic converging-stagnationflow, 274–275, 276

ionization and mass spectrometry, 151, 344.See also mass spectrometry, electrosprayionization (ESI-MS)

separation, 147, 152–154. See alsoelectrophoresis, polyelectrolyte

sequencing, 1, 152stretching, 294

through converging flow at stagnation point,274–275

target sequence, 2, 325

trapping concentration, 322Donnan equilibrium relationship, 248. See also

potential, DonnanDorn effect. See sedimentation potentialdouble layer. See Debye double layerdrop, 99, 344–345. See also digital microfluidics

aerosolejection mechanism, 363, 370nanodrops, 348negative charge on drops ejected by AC

electrosprays, 369size, 347, 360

charged during electrospraying orelectrowetting, 347, 348, 446, 447

charging, 446curvature, 439, 446deformation and instability. See instability,

interfacial; interface, deformationdisintegration. See Coulombic fissionejection at electrowetting contact lines, 414,

446–447equilibrium shape, 418merging (or recombination), 438nanodrop formation with electrowetting films,

431–432splitting, 412, 436–438translation, 435. See also drop, transporttransport, 407–408, 411

Dukhin (low Péclet number) theory, 71, 215–217breakdown in Dukhin scaling due to tangential

convection, 220critical electric field limit, 202, 208, 217, 221. See

also Dukhin (low Péclet number) theoryDukhin scaling (thin polarization layer limit),

202–203, 206, 208, 214Dukhin number, 53, 81, 140–141

efficiencymixing, 7

enhancement through fingering instabilities,112

enhancement through superpositioning ofsecondary field, 222, 223

power. See power, efficiencypump, 89, 94–95

electrodeconstant potential, at high frequencies,

257electrical capacitance, 163electric displacement, 16, 158–159, 168electric field, 10, 11–14

electric fieldAC

advantages over DC fields in electrokinetics,5, 7–8

effect on polarized layer thickness, 201penetration of electrolyte to polarize double

layer, 251use for electrophoretic rattling, 223




Index 487

use to suppress bubble generation andelectrolytic reaction, 224, 287

voltage-frequency characteristic, 340–343,370, 396

asymmetric (e.g., traveling wave), 254characteristic field strength, 208critical (or threshold) field

for electrokinetic flow of dielectric liquids,22, 25

for flow in a nanopore, 69–71, 96, 123, 215.See also electro-osmosis, nanochannel ornanopore

linear scaling with ζ potential, 71. See alsopotential, zeta (ζ ) potential

polyelectrolyte chain unfolding, 154. See alsopolyelectrolyte

transition from linear to nonlinearelectrophoresis. See Dukhin (low Pécletnumber) theory, critical electric field limit

DCability to generate nonequilibrium

electrokinetic phenomena, 184. See alsoelectrokinetics, nonequilibrium

disadvantages of use in electrokinetics, 6–7disadvantages of use in electrospraying.

See electrospray, DCdisadvantages of use in protein

crystallization, 339, 343enhancement due to particle concentration, 337existence of singular tangential field at corner,

194. See also singularityfield lines

along electrospray cone, 404attraction to granule surface due to high

conductivity, 200–201, 221attraction to nonconducting surfaces due to

conducting Stern or collapsed layers, 284.See also polarization, field-induced doublelayer polarization

coinciding with streamlines, 6, 97–99, 129. Seealso similarity, field-streamline

dipole, 157during double layer charging, 254, 277in nanowires, 174penetration in thick double layers, 252penetration into curved surface, 86

flux, 12–13focusing

geometric focusing effect in nanochannels,241, 242–243, 245. See also channel,nanochannel or nanopore

to produce thermal gradients, 281. See alsothermal gradient

fringe, at contact line, 415. See also singularity,electric field

induced, 174–175

irrotationality, 12, 22leakage. See electric field, penetration

local enhancement at electrospray meniscus tipdue to plasma polarization, 372. See alsopolarization, gas phase

nonuniform, 285–286, 329normal, in gas phase, 371, 373penetration, 155, 156

across dielectric film, 443at corners or sharp geometries, 184enhancement due to tangential convection,

219, 221. See also ion, tangentialconvection

inability for normal field to penetrate intothin double layers, 252

insufficient time at high frequencies, 304into cytoplasm at high frequency, 313, 315into double layer, 184–185, 201, 277, 284, 291,

292. See also Debye double layerinto ion-selective granule, 203minimization of penetration into liquid with

conducting liquids, 402normal field leakage through corner, 195normal, giving rise to normal capacitive

charging, 294. See also charging, normalfield

slip length condition, 216, 218suppressed by large normal surface field, 292

penetration depth, 7rotating. See electrorotationsingularity. See singularitysurface, 39

balance with normal field at critical point,226

constant, inability to produce nonequilibriumelectrokinetics, 206, 207

enhanced due to thin double layer, 305–306irrelevance in normal AC charging, 252large, implicit assumption in equilibrium

electrokinetics, 155. See alsoelectrokinetics, equilibrium

normal, at conducting gas interface, 295reversal in direction, 272

tangentialinterfacial field of electrowetting film, 426in electrospray jet, 360

electric Rayleigh number, 114electric susceptibility, 16, 160electrical admittance, 166electrical capacitance

bulk, 180–183decrease due to dielectric layer, 411dielectric layer, 411, 417membrane, 312, 318. See also electrical

capacitance, surfacesurface, 303. See also diffuse double layer,

capacitance; Debye double layer,capacitance; Stern layer, capacitance

electrical conductance, 31. See also electricalconductivity

bulk, 53, 81




488 Index

determined from I–V characteristics in Ohmicregion, 247–248. See also electricalconductance, nanochannel or nanopore

in Ohmic region, 248, 249membrane, 312nanochannel or nanopore, 66–67, 247Stern layer. See Stern layer, conductancesurface, 52, 81, 140–141. See also collapsed

diffuse double layer, conductance; diffusedouble layer, conductance; Debye doublelayer, conductance; Stern layer,conductance relationship with Stern layerconductance, 289

electrical conductivity, 30–31, 65–66, 95. See alsoelectrical conductance

bulk, 50, 180. See also ion, conductivity;electrical conductivity, medium

critical, balance between particle and mediumconductivities

electrical conductivity (cont.)cytoplasm, 312, 314, 315–317, 318–321drives electrothermal flow, 253, 280, 283.

See also electrothermal effectelectrothermal scaling, 282. See also

electrothermal effectgradient

instabilities, 103–116introduced by surface curvature, 82produces polarization, 22, 287

medium or solution, 53, 81, 106, 172, 280.See also electrical conductivity, bulk

effect on field-induced double layerpolarization, 284–285. See alsopolarization, field-induced double layerpolarization

membrane, 311alteration through crosslinking, 312, 314.

See also reaction, cell fixationnanowire or nanotube, 174particle, 140, 172, 280, 311. See also particle,

effective conductivityplasma, 295. See also ion, plasmareduced locally by normal diffusion, 295

electrical conductor, 156–157. See also electrolyteelectrical field-streamline similarity. See

similarity, field-streamlineelectrical impedance, 162–163

AC, 7equivalent RC circuit, 180, 256–266. See also

equivalent circuit, RCparallel RC circuit, 165. See also equivalent

circuit, RCpure ideal capacitor, 163, 178pure resistor, 163sensing, 3, 180

series RC circuit, 164–165. See also equivalentcircuit, RC

spectroscopy, 162–168, 292electrospray, 366

electrical insulator, 99, 156. See also dielectric,perfect

electrical reactance, 163, 180–183frequency response, 181–183

electrical resistance, 31, 66, 156, 163. See alsoelectrical resistivity

bulk, 182–183differential, 245, 249–250in concentration polarization layer, 245, 248intrachannel or intraslot, 240, 242, 245Ohmic, 240, 245–247

tangential, dominant in thick diffuse doublelayers, 301

electrical resistivity, 30. See also electricalresistance

electrocapillarity, 408, 409, 411, 423. See alsoelectrowetting

electrodearray, 281, 317, 326, 330, 332, 340

successive activation, 411–412asymmetric, 254, 268, 281coil or spiral, 7, 275, 295, 333, 401corona, 395dielectric layer. See dielectric layer (or

coating). See also dielectricembedded, 5, 7, 187functionalization, 3. See also surface,

functionalizationgate electrode in field-effect transistors,

186housing, 6. See also membrane, Nafion R©insulated, due to double layer screening at low

frequencies, 257line, in electrowetting, 423–432orthogonal, 254, 275pin-plate, 25plate, in electrowetting, 432–438polarization, 7, 8. See also surface, polarization;

polarizationquadrupole. See electrode, arrayreaction. See reaction, electrochemical;

reaction, electrolyticrotating, 380serpentine. See electrode, coilshielding electrode for field-effect manipulation

of electro-osmotic flow, 186–187, 432wire, 7, 23, 275, 432

electrohydrodynamic atomization.See electrospray

electrokinetic force. See force, electric(or electrostatic)

electrokinetic phenomena of the second kind, 185,200–208

electrokinetic potential. See potential, zeta(or ζ ) potential

electrokinetic slip. See electro-osmosis,electro-osmotic slip; slip

electrokinetics, 2, 4–8, 40AC. See electrokinetics, nonequilibriumequilibrium, 8, 31, 35, 73–74, 141, 155–156




Index 489

interfacial, 7, 344–345. See also interfacenonequilibrium, 8, 156, 251

DC, 184, 201requirement for field-penetration, 207

nonlinear. See electrokinetics, nonequilibriumpreferred method of microfluidic transport, 5

electrolysis, 30, 410electrolyte

concentrationabsence in Dukhin scaling, 202, 206. See also

Dukhin (low Péclet number) theorydependence in electrophoretic velocity in

high Péclet number theory, 219scaling with channel or pore dimension,

66–70. See also channel, nanochannel ornanopore

force on, 18–19, 20internal phase within particle (e.g., cytoplasm),

311polarization, 29. See also polarizationrepresented by a resistor in double layer

equivalent RC circuit, 256, 309requirement for the formation of electrospray

Taylor cones, 354. See also electrospray;meniscus, conical

strong, 47, 67, 134symmetric binary, 31, 32, 36weak, 47, 55–56

electrometer, 408electromigration. See ion, electromigrationelectron cloud, 160electron–hole pair, 161electron

as charge carrier in Stern layer, 304. See alsoStern layer

avalanche, 347, 415mobility, 347, 369. See also ion, mobility

electroneutrality, 33, 54. See also Laplaceequation

global, 39, 66, 79in nanochannels or nanopores wherein double

layers overlap, 86–87, 93local. See electroneutrality, role in the

generation of depletion regionsOhmic region, 206polarized layer asymptote, 215role in the generation of depletion regions, 71,

201–202, 204. See also ion, intermediatediffusion layer

zero net force on liquid, 29, 41electro-osmosis, 74–75, 76–77

AC, 251capacitive charging mechanism, 253–257converging-stagnation flow. See flow,

converging-stagnation; flow, stagnationpoint

enhancement of dielectrophoretic trapping.See dielectrophoresis

flow reversal, 101, 264–268limitation, 280

maximum slip, 275, 335normal double layer charging on ideally

polarizable surfaces, 277slip velocity, 254, 256–263slip velocity, combined electrothermal and

electro-osmotic effects, 281–283. See alsoelectrothermal effect; flow, electrothermal

slip velocity, time-averaged, 262, 263advantages, 89, 116–117around a 90◦ microchannel bend, 190–200conductance enhancement in nanochannel or

nanopore, 248DC

electro-osmotic pump, 6, 79, 88, 89–96.See also pump

flow rate, 88–89velocity profile, 87. See also flow, plug;

velocity profileelectro-osmotic mobility, 131, 135–136,

144electro-osmotic slip, 76–77

independent of channel size, 89electro-osmotic velocity, quadratic scaling with

voltage, 253field-effect flow manipulation, 186flow rate, independent of capillary

cross-section, 440in ion-selective granule pores, 221. See also

electro-osmosis, nanochannel or nanoporeion convection in double layers, 53. See also

ion, tangential convectionnanochannel or nanopore, 65–72, 86–88.

See also electro-osmosis, in ion-selectivegranule pores; ion, transport

flow rate, 87of annular film around bubble, 440of buffer solution in electrophoresis, 129–131,

144. See also electrophoresissecond kind, 94. See also electrokinetic

phenomena of the second kindslip velocity, 74, 76–80

in cylindrical capillaries, 80–81in diffusion layer, 217, 219inverse relation with capillary cross-section,

440nonlinear, 251nonlinear, dependence on overpotential, 221nonlinear, due to field leakage, 196nonlinear, over conducting cylinder, 279–280nonlinear, over ion-selective granule, 206,

208, 218, 219reversal across corner geometry, 194, 195,

196, 199singular, 198typical value, 94variation across channel due to field effect,

187variation with longitudinal ζ -potential

gradients, 100–103, 137–138electrophoresis, 74–75, 128–154




490 Index

apparent mobility (or velocity), 131, 144capillary, 143–154capillary electrochromatography (CEC), 6, 150,

152capillary isoelectric focusing, 149–150capillary isotachophoresis, 149capillary zone, 146–147cellular, 99–102, 133–137DC, 6differential mobility, 144, 147, 149, 150differential partitioning, 148, 150electrophoretic mobility, 128–131, 216. See also

electrophoresis, electrophoretic velocitycellular, 135–136. See also electrophoresis,

cellularDNA, 144. See also DNA, separationend-labeled free solution (ELFSE), 152negative, due to charge reversal, 138

electrophoretic velocity, 128–131. See alsoelectrophoresis, electrophoretic mobility

electrophoresis (cont.)cellular, 134–136. See also electrophoresis,

cellularelectrophoresis of the second kind, 206. See

also Dukhin (low Péclet number) theoryin presence of surface charge migration,

137–138nonlinear field dependence, 185, 206, 219nonlinear, maximum, 206, 207–208, 216–217,

218, 221. See also Dukhin (low Pécletnumber) theory

nonlinear, thick polarization layer theory,215

nonlinear, reduction due to tangentialconvection, 217, 218, 219, 221

elution time, 131, 148, 152end-labeled free solution (ELFSE), 144,

152–154entanglement effect. See electrophoresis, gelforce, 268free-solution mobility, 152gel, 130, 144, 147–148micellar affinity, 149micellar electrokinetic chromatography,

148–149microelectrophoresis, 145particle trapping, 268–270. See also particle,

concentration (or trapping)point charge theory, 128, 130, 138polyelectrolyte, 144, 152. See also

polyelectrolyteread length, 148, 152, 154regulating function, 146–147, 149retards dielectrophoretic motion, 287separation, 129, 130, 131, 143–154. See also

separation, flow or particleenhancement using field effects, 186–187resolution, 148shape independence, 130

size effects, 130, 139, 141, 144, 147

zone, 146–147, 149electrorheological fluid, 4electrorotation, 172, 327–329

velocity, 329electrospinning, 380

AC, 386–392interconnected multistrand fiber networks,

386, 390–391, 392DC, 380–386

axial and radial charge relaxation-time scales,383

encapsulation, 387–389non-Newtonian jets. See jet, non-Newtonianpolymer concentration, 387

electrospray, 345AC, 360–378

AC field superimposed on DC voltage, 361effect of liquid conductivity, 366–368, 369,

370–371, 378low frequency, 363–366spray modes, 366–368, 370charge relaxation time, 345, 360, 362, 368,

372. See also Debye double layer,relaxation time

gas phase, 373liquid phase, 373–374

cone-jet mode. See electrospray, spraymodes

continuous flow. See electrospray, spraymodes

DC, 351spray modes, 348–351

ionization, 348. See also mass spectrometry,electrospray ionization (ESI-MS)

jet. See jetlateral whipping or bending. See jet, instabilitymode (positive or negative), 347oscillating cone-jet mode, 361. See also

electrospray, modesperfect conducting limit, 353, 355pulsating flow. See electrospray, spray modesstability, 351, 354, 366

electrostatic, 8–14attraction, 8. See also force, interaction; force,

van der Waalsbetween particle and wall, 42

between two particles, 45due to negative osmotic pressure gradient,

41, 42. See also pressure, osmoticleading to film collapse, 441like-charge, 56

decoupling from hydrodynamic problem, 257electrostatic interaction, 152, 375, 411

arising from concentration polarization, 36between two charges, 8–10. See also

Coulomb’s Lawbetween particle and wall in confined

geometries, 41, 42force. See force, electric (or electrostatic)repulsion, 8, 44. See also force, interaction




Index 491

at electrospray meniscus tip, 346at electrospray orifice, 383at electrowetting contact lines, 414between particle and wall, 44, 45between trapped particles, 401between two particles, 41, 42capillary pressure compensation, 374–378due to steric effects, 39during ion adsorption, 36. See also ion,

adsorptionoffset by osmotic pressure gradient, 41.

See also pressure, osmoticelectrostriction, 17. See also force, electrostrictiveelectrothermal effect, 14, 253, 280–283

electrothermal velocity, 253electroviscous effect, 88, 122, 132–133

dilute suspension theory, 132electrowetting, 408–438

AC, 441–447advantages over DC, 407force, 443

continuous, 411DC, force, 413, 421. See also force,

electrocapillary; force, electric (orelectrostatic)

departure from perfect conducting limit, 417.See also charge, accumulation; dielectric,dielectric layer (or coating)

distinct to electrocapillarity, 409electrolytes. See electrowetting, ACequilibrium. See electrowetting, staticfilm, 423–432force, unpinning of the contact line, 445on dielectric (EWOD), 411. See also

electrowetting, staticon insulator coated electrodes (EICE), 411.

See also electrowetting, staticperfect conducting assumption, 419spontaneous, 423–438static, 409–410, 411–422

change in macroscopic contact angle, 421drop velocity, 421–422

energy balance, 14, 253, 280energy barrier, associated with contact line

pinning, 444–445. See also contact line,pinning

energy minimizationfree surface, 348Onsager’s principle of minimum energy

dissipation, 40energy

electrical (or electrostatic), 58, 139free

due to Coulombic interactions, 418excess at contact line, 418mixing, 65

kinetic, ion, 354–356potential, 37thermal, 32, 37, 47, 58, 139viscous dissipation, 418

entropic effects, 45, 139equilibrium, 38

adsorption. See isothermdouble layer. See Debye double layer,

equilibriumelectric and capillary stress balance across

interface. See stress balance,electrocapillary

electrochemical, 71electrowetting. See electrowetting, staticforce or flow, 19–20, 40–41, 42ion or charge, 36, 37, 40, 57normal and tangential force balance in

electrospray menisci, 376Poisson–Boltzmann, 19–20, 38. See also

Poisson–Boltzmann equationbetween overlapping double layers, 67–68between two oppositely charged surfaces,

57–60in double layer, 76, 77, 84modified to account for steric effects at high

frequency, 268. See also steric effectosmotic pressure effects, 39–41. See also

pressure, osmoticstability, 233violated by external field penetration, 98, 185,

203, 207static Taylor cone. See meniscus, conicalStern layer. See boundary condition, Stern

layer conditionthermodynamic, 15, 191–193

equivalent circuitcapacitors in series to model dielectric and

double layers, 443capacitors in series to model Stern and diffuse

double layers, 186–249, 256–266, 303RC

capacitive charging, 256Faradaic charging, 266parallel RC circuit, 180, 287, 363series RC circuit. See Debye double layer, as

equivalent series RC circuitRC time constant. See RC time scale

expansion, 83–85. See also linearizationof potential in spherical harmonics, 194, 352,

355, 373, 403extended space charge region, 241, 245. See also

polarization layerextensional thinning and thickening, 383–384extensional viscosity, 383–384

Faradaic dissociation. See ion, dissociationFaraday charging. See reaction, Faradaicferromagnetic liquid, 381fiber

alignment, 381, 391bead suppression due to larger extensional

stress, 391beading, 384–385, 391. See also electrospinning,

non-Newtonian jets




492 Index

composite (core-shell), 389effect of voltage and frequency on thread

characteristics, 391–392elastic recoil, 385. See also fiber, beadingembedded, 388nanoporous surface morphology, 385–386repulsive force due to charge on fiber, 392segments, oppositely charged due to dynamic

charging, 389–390, 392stabilization, 391synthesis. See electrospinning

field-effect transistor analogy, 186field-induced polarization. See polarization,

field-inducedfield-penetration. See electric field, penetrationfilm

annular, 438–439, 441dewetting, 28, 431, 436. See also wettingevolution equation, 28rupture, 28, 431, 435, 436

filtration, 2, 147, 330, 406fixed point

attractor, 268–270, 273hyperbolic. See critical point gate

flow rateelectrokinetic flow around bubble, 440electro-osmotic pumps, scaling with channel

dimension, 89–96. See also electro-osmosislongitudinal variation due to pH gradients, 100.

See also pH, gradientlow in electrokinetic pumps, 6mixed or frustrated flow, 89

flowback flow

due to field leakage around corner, 190, 194,195

imposed by pressure gradients, 91–92,222–223. See pressure, pressure gradient;pressure, pressure-driven

induced by conductivity gradients, 104. Seealso electrical conductivity, gradient

induced by pH gradients, 6, 82–100, 101, 156,222. See also pH, gradient

Batchelor, 398bulk, absent in static electrowetting, 420,

421capillary-driven, 89circulation, 25. See also vortex

AC electro-osmosis, 254due to back-pressure, 88. See also flow, back

flow; pressure, backdue to interfacial shear over cylindrical

microchamber, 395–399due to pH gradients, 6, 99–103. See also pH,

gradienteddy generation due to electroviscous effects,

133. See also electroviscous effect

in nanopores, 69. See also channel,nanochannel or nanopore

continuity (or conservation). See massconservation

converging-stagnationdue to field-penetration at corner, 185for long-range particle trapping, 270, 273,

275–276, 335–336. See also particle,concentration (or trapping)

converging, at corner geometries, 195, 199converging, helical (or spiral), 399Couette, 114, 120diverging, through AC electro-osmotic flow

reversal. See electro-osmosis, ACejection at corner, 185, 195, 199electrohydrodynamically driven air flow.

See ionic windelectrothermal, 281. See also electrothermal

effectextensional or elongational, 384. See also

stress, extensionalfrustrated, 88–89, 92, 99–103, 116imbalance, 98–99inviscid air flow due to ionic wind, 395.

See ionic windirrotational, 6, 98, 155

violation in ion-selective granule, 221mixed. See flow, frustratedpath length, 122plug

advantages, 89, 122contribution in mixed (or frustrated) flow, 89.

See also flow, frustratedflat velocity profile in electro-osmotic flow,

81, 100. See also electro-osmosisPoiseuille

contribution in mixed (or frustrated) flow, 89due to pressure-driven flow, 92, 101. See also

flow, pressure-drivenin electrowetting drop, 421solutal dispersion effects, 76, 117, 120.

See also dispersion, hydrodynamicpotential, 6, 97–98, 99, 155pressure-driven. See also flow, Poiseuille;

pressure, pressure gradientback flow. See flow, back flowdue to pH gradients, 6, 93–100, 101. See also

pH, gradientin mixed (or frustrated flow). See flow,

frustratedlarge pressures required for bubble transport,

439net streaming current, 79, 80. See also

streaming potentialsolutal dispersion effects, 76, 120, 122

quadrupolar, 279radial. See flow, quadrupolarregulation, 3reversal, 99, 101–102

AC electro-osmotic flow. Seeelectro-osmosis, AC

rotation. See also flow, circulation; vortex




Index 493

saddle point, conversion to fixed point, 270, 335separation. See separation, flow or particleshear, 117, 120, 133, 384sheath, 151, 388–389spontaneous (or dynamic), 423

absent in static electrowetting, 421stagnation point

converging AC electro-osmotic flow, 264in converging spiral flow, 399on ion-selective granule surface, 220particle trapping, 270, 272–274, 335. See also

particle, concentration (or trapping)Stokes, reciprocal theorem (boundary integral

formulation), 206, 208, 219streaming around conducting cylinder, 279stretching, 122viscous, 133

fluctuation. See also disturbance; instabilitycontact line, 446correlated, 56–59flow, due to vortex interactions, 223ion concentration, at ejecting pole of

ion-specific granule, 227–228particle aggregate concentration, 337proton, 325thermal, random, 39, 47, 53, 139

fluctuation theory, 56–63. See also couplingtheory; fluctuation

fluctuation-dissipation theorem, 32, 47force

buoyancy, 268, 273capillary, 364–365

dominant stress in polymer molecules, 385electrowetting drop, 442inverse scaling with characteristic dimension,

407stabilizing, 28, 346

centrifugalsuppression in Ekman boundary layer, 399use to generate sedimentation potential, 74used to provide local stagnation force, 268

Coulomb. See force, electric (or electrostatic)dissipative. See viscous dissipationDLVO. See DLVO theoryelectric (or electrostatic), 5, 8, 16, 17–19. See

also stress, Maxwellarising due to space or induced charges, 20,

39. See also charge, induced; charge, space

as body force term in hydrodynamicequation, 77–79. See also conservationequations

AC, 7at boundary, 40coarse graining to produce force density, 20,

30. See also averaging, coarse grainingcontribution to electrothermal effects, 253,

281. See also electrothermal effectDNA, scales with number of bases, 144.

See also DNA

due to charge accumulation at contact line,415, 417, 446. See also charge,accumulation; electrowetting, force

equal to osmotic pressure gradient, 68.See also pressure, osmotic

in double layer, 155, 446. See also Debyedouble layer

in electrophoresis, 128–129. See alsoelectrophoresis

in electrowetting, 442. See alsoelectrowetting, force

net point force at contact line, 420. See alsoelectrowetting, force

on dielectric particle, 303. See also particle,force

on electrospray meniscus, 346. See alsoelectrospray

singular. See singularitytime-averaged, 254, 372. See also averaging,

timeelectrocapillary, 409. See also electrowetting,

forceelectrostrictive, 20. See also electrostrictioninteraction (short-range repulsion or long-range

attraction), 42, 57, 58, 433. See alsoDLVO theory; electrostatic, attraction;

electrostatic, repulsion; force, van derWaals

Kelvin polarization force density, 17. See alsoforce, electric (or electrostatic)

Korteweg–Helmholtz force density, 17, 20Lorentz. See force, electric (or electrostatic)Maxwell. See force, electric (or electrostatic)particle. See particle, forceponderomotive, 17, 284, 424surface, dominance over body forces at small

scales, 344van der Waals, 39, 57, 398, 431, 435. See also

DLVO theory; force, interactionviscous (or drag)

at contact line, 436dominance over body forces at small scales,

344dominance over inertia, 252due to local electro-osmotic flow in double

layer around particle, 132. See alsoelectro-osmosis

in electrowetting drop, 421–422. See alsoelectrowetting

interfacial, 440. See also interfaceon liquid due to charge migration, 20, 128on particle, 268, 294role in jet ejection, 373

free-molecular-flow limit, 4. See also Knudsennumber

free solution, 144, 148, 152–154. See alsoelectrophoresis, end-labeled free solution(ELFSE)

free surface. See interface




494 Index

frequency spectrum: interfacial waves, 348.See also disturbance

frequencyAC field. See time scale, AC forcing

ability to selectively tune fiber morphologiesin AC electrospinning, 385, 391–392.See also electrospinning

advantages of high-frequency operation, 251control of diffusion layer thickness, 209.

See also diffusion layercritical frequency for quasi-steady electrospray

Taylor cone, 362, 366. See alsoelectrospray; meniscus, conical

double layer steric effects at high frequencies,268. See also Debye double layer; stericeffect

existence of threshold for moleculardielectrophoresis, 322–325

in electrospraying, 360–361. See alsoelectrospray

independence of, for AC electro-osmosis dueto Faradaic charging, 265. See alsoelectro-osmosis; reaction, Faradaic

frequency (cont.)operation window, 251–252, 253, 256, 257,

263optimum for electrorotation, 328. See also

electrorotationoptimum for high-frequency AC

electrospraying, 371. See also electrospray,AC

optimum for maximum electro-osmotic slip,252, 255, 256, 260, 275, 335. See alsoelectro-osmosis, slip velocity

optimum for maximum plasma generation,372, 373. See also ion, plasma

optimum for microcentrifugation, 396.optimum for mixing, 224. See also mixingoptimum for protein crystallization, 340–342.

See also protein, crystallizationrelevant time scale in AC electrosprays, 369,

384. See also electrospray, ACuse to control diffusion layer thickness, 238,

239. See also diffusion layeruse to control electrophoretic rattling, 223

characteristiccapacitive charging, 274charge relaxation, 167, 177, 283

crossover. See dielectrophoresis, crossoverfrequency

natural, 363pulsation, in oscillating menisci, 350resonant, 363, 366vibration, 366

frit. See monolith

Gauss Divergence Theorem, 13, 17, 159

Gauss’ Law, 12–14, 33, 159Guoy–Chapman theory, 45

Hamaker constant, 431. See also pressure,disjoining

Hartmann number, 133heat or mass transfer enhancement, 3, 122heating

Joulearising due to ion mobility in double layer, 95due to DC current, 6due to viscous friction on bound charges, 166generation of electrothermal effects, 14, 282,

283. See also electrothermal effectlimitation in capillary

electrochromatography, 151. See alsoelectrophoresis, capillaryelectrochromatography (CEC)

suppression with use of high frequency ACfields, 7, 402

Ohmic, 253, 280Helmholtz plane, 55high Péclet number theory, 208, 217–221. See also

near-equilibrium (low Péclet number)theory

limitations, 221Hückel equation, 129, 130, 134, 136, 138, 143hydrated phase. See ion, hydrationhydration cage, 58, 303, 339–341. See also ion,

hydrationhydrodynamic interaction, 41, 45, 152, 325hydrodynamic resistance. See also pressure,

pressure dropgeneration of electroviscous effect, 123. See also

electroviscous effectsuppression of vortex instability, 235

hydrodynamic shear. See stress, shear

I–V characteristics. See current–voltage (I–V)characteristics

ideal-gas law, 15image effect,induced-charge electrokinetic phenomena, 184.

See also electrokinetics, nonequilibriuminstability

absolute, 114–115, 116capillary. See instability, interfacialconductivity gradient driven, 103–116contact line, 414convective, 115, 116Coulombic, 347. See also Coulombic fissionextended polarization layer. See instability,

vortexfeedback mechanism, 115fingering, 104–105, 107, 111–112, 116hydrodynamic. See instability, interfacialinterfacial, 347, 380–381, 385. See also jet,

instabilityeliminated by superimposing AC fields on

DC voltage, 361kink. See jet, instabilitylong wave, 110, 383. See also lubrication

approximation




Index 495

meniscus, due to Coulombic fission, 346natural frequency of fastest growing

disturbance, 361particle clusters, 336–337Rayleigh. See instability, interfacialspiral (axisymmetric or three-dimensional),

399thermodynamic, 386varicose. See instability, interfacialvortex

analogy to Rayleigh–Bénard instability, 233suppression of diffusion layer growth, 235.

See also diffusion layersurface vortices driven by ionic wind, 396.

See also vortexwavelength, 105, 347. See also disturbance,

wave numberinterface, 344. See also dielectric, interface;

electrokinetics, interfacial; stress, interfacedeformation, 347, 395. See also meniscus,

capillary waveinduced charge, 16–17, 22–23. See also

boundary conditions, interfacialmicroscopic–nanoscopic, 5, 236, 242. See also

asymptotic matchinglarge pressure gradient, 67

net Maxwell stress, 18. See also stress, Maxwellpermittivity jump due to dielectric polarization,

17. See also polarization, interfacialshear, 395, 434, 436. See also stress, shear

interfacial destabilization, 27interfacial phenomena. See interfaceinterfacial polarization. See polarization,

interfacialinterfacial tension. See surface tensionintermediate electroneutral layer. See diffusion

layerion. See also charge

accumulation. See charge, accumulationadsorption

asymmetric, producing oppositely chargedsurfaces, 57

collapsed diffuse layer, 81. See also ion,desorption

due to solvation or hydration effects, 47.See also ion, hydration; ion, solvation

nonspecific, 402, 411responsible for surface charging, 8, 36reversible, 56–64Stern layer, 39. See also Stern layer

accounted for in thick double layertheory, 300

charge storage mechanism, 252gives rise to surface conductance, 140Helmholtz plane, 55–56prevented by charge leakage, 309time scales, 57, 304suppressed with polymer or gel, 147

association, 378equilibrium constant, 59

field induced, 325giving rise to depletion regions, 202giving rise to polarization at ends of

molecules, 161. See also polarization, fieldinduced dielectric polarization

time scale, 57bridging, 58cloud, 129, 178, 201co-ion exclusion. See ion, selectivityconcentration

beyond close packing limit, 268conservation law, 33. See also conservation

equationscritical cutoff, 268critical, for bubble motion, 441enhancement factor, 232. See also ion,

dynamic super-concentrationin Poisson–Boltzmann equilibrium, 46. See

also equilibrium, Poisson–Boltzmannscaling with pore dimension, in double layer,

79. See also Debye double layerconcentration enrichment. See ion, dynamic

superconcentrationcondensation, 138–139, 303

driving like charge attraction, 56reduces current in Stern layer, 54

conduction. See also conducting layer; ion,tangential conduction

flux, electro-osmotic flow in nanochannel, 87.See also electro-osmosis, nanochannel ornanopore

in collapsed diffuse layer, 54. See alsocollapsed diffuse layer

mechanism for charge relaxation inMaxwell–Wagner model, 177. See alsopolarization, Maxwell–Wagner

normal, 288conductivity. See electrical conductivityconservation. See charge, conservationcontamination, due to electrode reactions, 6, 7,

155, 339, 351. See also ion, generation;reaction, electrochemical; reaction,

electrolyticconvection

breakdown in Ohm’s Law, 30, 32. See alsoOhm’s Law

breakdown of thick polarization layer (highfield) theory, 215. See also polarizationlayer, thick polarization layer (high field)theory

contribution to tangential migration aroundion-specific granule, 230

enhancement of field singularities, 200flux, electro-osmotic flow in nanochannel, 87.

See also electro-osmosis, nanochannel ornanopore

gas-phase. See ionic wind

streaming currents in pressure driven flow.See current, streaming




496 Index

depletion (or diffusion) region. See depletedco-ion layer

desolvated gas phase ion, 348desorption, time scale, 57, 303diffusion–electromigration balance, 191, 200,

204–205, 208, 231. See also Péclet number,ratio of tangential electromigration todiffusion

diffusion, breakdown in Ohm’s Law, 30, 32.See also diffusion; Ohm’s Law

disordering effects, 53dissociation

due to large electric fields, 372field induced, 325giving rise to polarization at ends of

molecules, 161. See also polarization, fieldinduced dielectric polarization

kinetics, 354of surface groups, 8, 35partial, effect on charge, 129space charge generation, 21, 354. See also

Onsager’s theorydoping, 354drift velocity. See ion, mobility

ion (cont.)dynamic superconcentration, 225–233ejection at critical point, 226, 231electromigration, 302. See also current, flux;

diffusion, charge (or ion)along cell membrane, 133–137. See also cellbalance with diffusion at isoelectric point,

150dominance of tangential conduction at high

fields, 231enhancement of field singularities, 200flux or flux density, 30, 31–32, 306in diffuse layer, 56. See also diffuse double

layerin electrophoresis, 74, 128–130, 150. See also

electrophoresisin interfacial polarization layer, 169, 346mechanism for AC charging of electrode

surfaces, 7, 8. See also charging, ACnormal flux into double layer, 83, 277, 281,

300. See also charging, normal field; Debyedouble layer

enrichment region, 202, 241. See alsopolarization, concentration

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