power-law rheology in the bulk and at the interface: quasi- properties and fractional constitutive...

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Power-law rheology in the bulk and at the interface: quasi-properties and fractional constitutive equations by Aditya Jaishankar, and Gareth H. McKinley Proceedings A Volume 469(2149):20120284 January 8, 2013 ©2013 by The Royal Society

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Page 1: Power-law rheology in the bulk and at the interface: quasi- properties and fractional constitutive equations by Aditya Jaishankar, and Gareth H. McKinley

Power-law rheology in the bulk and at the interface: quasi-properties and fractional constitutive equations

by Aditya Jaishankar, and Gareth H. McKinley

Proceedings AVolume 469(2149):20120284

January 8, 2013

©2013 by The Royal Society

Page 2: Power-law rheology in the bulk and at the interface: quasi- properties and fractional constitutive equations by Aditya Jaishankar, and Gareth H. McKinley

(a) Schematic of a spring-pot as an element that interpolates between a spring (α=0) and a dashpot (α=1).

Aditya Jaishankar, and Gareth H. McKinley Proc. R. Soc. A 2013;469:20120284

©2013 by The Royal Society

Page 3: Power-law rheology in the bulk and at the interface: quasi- properties and fractional constitutive equations by Aditya Jaishankar, and Gareth H. McKinley

Rheological data for ‘highly anomalous’ butyl rubber taken from Scott-Blair et al. [31].

Aditya Jaishankar, and Gareth H. McKinley Proc. R. Soc. A 2013;469:20120284

©2013 by The Royal Society

Page 4: Power-law rheology in the bulk and at the interface: quasi- properties and fractional constitutive equations by Aditya Jaishankar, and Gareth H. McKinley

Interfacial small-amplitude oscillatory shear data of 3 wt% Acacia gum solutions carried out using the DWR. (a) Strain amplitude sweep performed at ω=1 rad s−1.

Aditya Jaishankar, and Gareth H. McKinley Proc. R. Soc. A 2013;469:20120284

©2013 by The Royal Society

Page 5: Power-law rheology in the bulk and at the interface: quasi- properties and fractional constitutive equations by Aditya Jaishankar, and Gareth H. McKinley

The FMM fitted (lines) to interfacial storage Gs′(ω) and loss Gs′′(ω) moduli data (symbols) obtained from (a,b) 3 wt% Acacia gum solutions and (c,d) 50 mg ml−1 BSA solutions.

Aditya Jaishankar, and Gareth H. McKinley Proc. R. Soc. A 2013;469:20120284

©2013 by The Royal Society

Page 6: Power-law rheology in the bulk and at the interface: quasi- properties and fractional constitutive equations by Aditya Jaishankar, and Gareth H. McKinley

Creep compliance for 3 wt% Acacia gum solutions performed at various values of imposed interfacial stress σ0s.

Aditya Jaishankar, and Gareth H. McKinley Proc. R. Soc. A 2013;469:20120284

©2013 by The Royal Society

Page 7: Power-law rheology in the bulk and at the interface: quasi- properties and fractional constitutive equations by Aditya Jaishankar, and Gareth H. McKinley

(a) Experimentally measured values of the interfacial compliance response for 3 wt% Acacia gum solutions (symbols), and the short- and long-time asymptote in the FMM coupled with instrument

inertia.

Aditya Jaishankar, and Gareth H. McKinley Proc. R. Soc. A 2013;469:20120284

©2013 by The Royal Society