Assignment No-1

Viscosity Measurement

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Rheological behavior

Viscosity- An Introduction & Importance

The viscosity and consistency of the paint determine its capacity to level itself on the surface and not excessively flow, sag or run off during application. Therefore it is of great importance to study different rheological behavior to keep a balance in the formulation of paint with its desired performance properties.

Viscosity is the measure of the internal friction of a fluid. This friction becomes apparent when a layer of fluid is made to move in relation to another layer. The greater the friction, the greater the amount of force required to cause this movement, which is called shear. Shearing occurs whenever the fluid is physically moved or distributed.

The behaviour of fluid between two very large plates

Here, two parallel planes of fluid of equal area A are separated by a distance dx, and the top plate is moving in the x direction with velocity u (or v). Newton assumed that the force required to maintain this difference in speed was proportional to the difference in

speed through the liquid, or the velocity gradient. The Newton’s Law of Viscosity is as follows:

Where:

τ (shear stress) = (F/A) = µ .(dv/dy)µ (viscosity) = τ /(dv/dy)And (dv/dy)is the velocity gradient.

It is a measure of the change in speed at which the intermediate layers move with respect to each other and it has units of per second.

τ describes the shearing which the liquid experiences and is thus called the shearing stress

µ is called the Dynamic Viscosity. Its CGS unit is Poise or dyne.sec.cm-2 and MKS unit is Newton.sec.m-2. There is another term called Kinematic Viscosity which is defined as:

Where:

µ : Dynamic Viscosity of the fluid. ρ : Density of the fluid.v : Kinematic Viscosity.

Role of Rheology in Coatings performance:

Sagging

The sagging of a coating film, when applied to vertical surfaces, is a function of its rheological properties.

It is basically an extreme form of leveling i.e. a wet paint film flows excessively if it is too thin to stay/adhere at a particular area of application after leveling on a vertical wall.

There are two mathematical equations which gives an analysis of sagging. One of which pertains to the rate of sagging i.e.

V=ρGT2/2√

Where

V: Velocity (Cm/Sec)Ρ: Density of coating materialG: Gravitational constantT2: Film thickness (Cm)√: Viscosity

The distance a wet film will sag in given length of time is:

Distance=vt

On doubling the film thickness change in volume of sagged will increase by eight times and given by the following equation:

V=ρGT3/3√

Leveling

Leveling is the ability of a brush out paint to flow out and obliterate the furrows left by the brush bristles.

“Both Sagging and leveling depends on rheological behavior of coating material. A thin paint exhibits severe sagging problem when applied on a vertical wall but if we changes its rheological behavior by making it thixotropic then it does not flow on the other hand a very thick paint does not level on the surface properly but if we incorporate in it pseudo plasticity then it levels properly.”

Viscosity Units:

To express the viscosity of liquid materials following units are used readily:

1. Poise (Centipoises)2. Seconds3. Stokes (Centistokes)

4. Krebs Unit (KU)5. Saybolt Universal Seconds (SUS)

Below is the viscosity conversion chart which correlates these viscosity units with each other.

Temperature dependency of Viscosity:

Viscosity varies considerably on varying temperature. It is mandatory to mention the temp at which viscosity is being measured.

Viscosity is indirectly proportional to the temperature i.e. viscosity decreases on increasing the temperature and vice versa.

Different Rheological Behaviour

We can classify the rheological behavior as follows:

1. Newtonian Fluids 2. Non-Newtonian Fluids

a. Plastic fluidsb. Pseudoplastic fluidsc. Dilatant fluidsd. Thixotropic fluidse. Rheopectic Fluids

Newtonian Fluids

Fluids for which the shearing stress is linearly related to the rate of shearing are designed as Newtonian Fluids. A Newtonian fluid is represented graphically in the figure below.

The linear variation of shearing stress with rate of shearing strain

The consistency of viscosity with varying shearing rate.

What this means in practice is that at a given temperature the viscosity of a Newtonian fluid will remain constant regardless of which Viscometer model, spindle or speed we use to measure it.

Non-Newtonian Fluids

Fluid for which the relationship τ/(du/dy) is not constant. In other words, when the shear rate is varied, the shear stress doesn't vary in the same proportion (or even necessarily in the same direction). Thus, the experimental parameters of Viscometer model, spindle, speed etc. all have an effect on the measured viscosity of a non-Newtonian fluid. This measured viscosity is called the apparent viscosity of the fluid and is accurate only at the same parameters.

Psuedoplastic Fluids

This type of fluid will display a decreasing viscosity with an increasing shear rate, as shown in the figure below. Probably the most common of the non-Newtonian fluids, pseudo-plastics include paints, emulsions, and dispersions of many types. This type of flow behavior is sometimes called shear-thinning.

Dilatant Fluids

This type of fluid will display a increasing viscosity with an increasing shear rate; see the figure below. Although rarer than pseudoplasticity, dilatancy is frequently observed in fluids containing high levels of deflocculated solids, such as clay slurries, candy compounds, corn starch in water, and sand/water mixtures. Dilatancy is also referred to as shear-thickening flow behavior.

Plastic Fluids

These type of fluids will behave as a solid under static conditions. A certain amount of force must be applied to the fluid before any flow is induced; this force is called the yield value. Tomato ketchup is a good example of a plastic fluid; its yield value will often make it refuse to pour from the bottle until the bottle is shaken or struck. After impact, the ketchup flows out of the bottle. Once the yield value is exceeded and flow begins, plastic fluids may display Newtonian, pseudoplastic, or dilatant flow characteristics.

Ideal plastic substance.

So far we have only discussed the effect of shear rate on non-Newtonian fluids. Some fluids will display a change in viscosity with time under conditions of constant shear rate. These are:

Thixotropic Fluids

As shown in the figure below, a thixotropic fluid undergoes a decrease in viscosity with time, while it is subjected to constant shearing.

Rheopectic Fluids

Rheopectic behaviour is essentially the opposite of thixotropic behaviour, in that the fluid's viscosity increases with time as it is sheared at a constant rate, as shown in the figure.

Both thixotropy and rheopexy may occur in combination with any of the previously discussed flow behaviours, or only at certain shear rates. The time element is extremely variable; under conditions of constant shear, some fluids will reach their final viscosity value in a few seconds, while others may take up to several days.

Rheopectic fluids are rarely encountered. Thixotropy, however, is frequently observed in materials such as greases, heavy printing inks, and paints.

Viscometers

A viscometer (also called viscosimeter) is an instrument used to measure the viscosity of a fluid. For liquids with viscosities which vary with flow conditions, an instrument called a rheometer is used. Viscometers only measure the viscosity under a single flow condition.

Types of Viscometers:

“U-tube” Viscometers (Ostwald or Ubbelohde type)

These viscometers are based on the measurement of the rate of flow of a definite volume of liquid through a capillary of definite bore.

These instruments can be used for the comparison of the viscosities of two liquids.

Various types of glass capillary viscometers.

Rotational Viscometers

Rotational viscometers use the idea that the force required to turn an object in a fluid, can indicate the viscosity of that fluid. The viscometer determines the required force for rotating a disk or bob in a fluid at known speed.

'Cup and bob' viscometers work by defining the exact volume of sample which is to be sheared within a test cell, the torque required to achieve a certain rotational speed is measured. There are two classical geometries in "cup and bob" viscometers, known as either the "Couette" or "Searle" systems - distinguished by whether the cup or bob rotates.

'Cone and Plate' viscometers use a cone of very shallow angle in theoretical contact with a flat plate. With this system the shear rate beneath the plate is constant to a modest degree of precision; a graph of shear stress (torque) against shear rate (angular velocity) yields the viscosity.

Rotational viscometers fall into two main types:

1.    Synchronous (Stepper) Motor / Spring2.    Servo Motor / Digital encoder

The first type uses a stepper motor to drive the main shaft. A spring & pivot assembly rotates on the shaft. The spindle or rotor hangs from this assembly. As the spindle rotates the spring is deflected by the viscosity of the sample under test.

The second type uses a precision servo motor to drive the shaft. The Spindle or rotor is attached directly to the shaft. High speed microprocessors measure the speed from a digital encoder and calculate the current required to drive the rotor at the test speed. The current required is proportional to the viscosity of the sample under test.

A rotating body experiences a viscous drag, or retarding force, the amount of which varies with the speed of rotation. In rotational viscometers, the viscosity is determined by measuring the drag on a spindle rotating in the material. The chief advantages of these instruments are:-

They are simple to use. Continuous measurements can be made at a given rate of shear or stress.

The dependency of viscosity on time can be readily determined.

Yield stresses can be determined.

Examples are the Brookfield Synchro-Lectric, Rheometrics, Stormer, MacMichael, Bohlin, Haake, and Brabender viscometers.

  “Cone & Plate” (Couette type) Viscometer

Stormer Viscometer

This viscometer employs a paddle that measures the viscosity of a fluid based on the resistance to flow while stirring.

Cone & Plate Measurement of Viscosity (Accuracy)

The accuracy of the cone and plate viscometer depends upon the instrument’s ability to hold temperature, accuracy of the cone’s angle; the cone’s setting to the plate and the speed of the instrument.

Other parameters also affect the accuracy and these are listed below.

1) Wear on the cone and plate.

2) Size of sample.

3) Time taken to allow the sample to stabilize on the plate before taking a reading.

4) Cleanliness of cone and plate.

5) Material Nature - Newtonian? high or low viscosity, particulate size.

6) Cone type - lower range cones give higher accuracy.

7) Shear Rate applied to sample.

The achievable accuracy for a cone and plate viscometer across its scale is ± 2% of the full-scale range. e.g. 0-10P the accuracy should be within ± 0.2P.

In practice, the accuracy between the 10% and 90% of the scale is normally ± 0.1P for a 10P scale.

Efflux Viscometers

They usually consist of a metal cup with parallel sides and with an accurately machined orifice at the center of the base.The time for the cup to empty through the orifice is noted and the results expressed in seconds.

But these viscometers are unsuited to paints which possess any degree of thixotropy.

Ford Cup No#4 Viscometer

The Ford viscosity cup is a simple gravity device that permits the timed flow of a known volume of liquid passing through an orifice located at the bottom of the cup. Under ideal conditions, this rate of flow would be proportional to the kinematic viscosity (expressed in stokes and centistokes) that is dependent upon the specific gravity of the draining liquid. However, the conditions in a simple flow cup are seldom ideal for making true measurements of viscosity.

Zahn cup Viscometer

A Zahn cup is a viscosity measurement device widely used in the paint industry. It is commonly a stainless steel cup with a tiny hole drilled in the center of the bottom of the cup. There is also a long handle attached to the sides. There are five cup specifications, labeled Zahn cup #x, where x is the number from one through five. Large number cup sizes are used when viscosity is high, and low number cup sizes when viscosity is low.

To determine the viscosity of a liquid, the cup is dipped and completely filled with the substance. After lifting the cup out of the substance the user measures the time until the liquid streaming out of it breaks up, this is the corresponding "efflux time".

Conversion:

One can convert efflux time to kinematic viscosity (cSt) by using an equation for each cup specification number, where t is the efflux time and ν is the kinematic viscosity.

Zahn Cup #1 : ν = 1.1 * (t - 29) Zahn Cup #2 : ν = 3.5 * (t - 14)

Zahn Cup #3 : ν = 11.7 * (t - 7.5)

Zahn Cup #4 : ν = 14.8 * (t - 5)

Zahn Cup #5 : ν = 23 * t

Falling Sphere and Bubble Rise Viscometers

In these instruments, the time required for a sphere of some sort to pass through a liquid is measured. The sphere may be a falling ball or a rising bubble. This method is particularly good for low-shear measurements. Examples are the Hoeppler rolling-ball viscometer and the Gardner-Holdt comparative bubble tubes.

Stokes' law is the basis of the falling sphere viscometer, in which the fluid is stationary in a vertical glass tube. A sphere of known size and density is allowed to descend through the liquid. If correctly selected, it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the tube. Electronic sensing can be used for opaque fluids.

Knowing the terminal velocity, the size and density of the sphere, and the density of the liquid, Stokes' law can be used to calculate the viscosity of the fluid. The technique is used industrially to check the viscosity of fluids used in processes. It includes many different oils, and polymeric liquid solutions.

Stokes' law

Where:

F : frictional force, r : radius of the spherical object, η : fluid viscosity, and v : particle's velocity.

If the particles are falling in the viscous fluid by their own weight, then a terminal velocity, also known as the settling velocity, is reached when this frictional force combined with the buoyant force exactly balances the gravitational force. The resulting settling velocity (or terminal velocity) is given by:

Where:

Vs: particles' settling velocity (m/s) (vertically downwards if ρp > ρf, upwards if ρp < ρf), r: Stokes radius of the particle (m), g: gravitational acceleration (m/s2), ρp : density of the particles (kg/m3), ρf : density of the fluid (kg/m3), and μ: (dynamic) fluid viscosity (Pa s).

Bubble viscometer

Bubble viscometers are used to quickly determine kinematic viscosity of known liquids such as resins and varnishes. The time required for an air bubble to rise is directly proportional to the viscosity of the liquid, so the faster the bubble rises, the lower the viscosity.

The Alphabetical Comparison Method used in the Gardner Tubes uses 4 sets of lettered reference tubes, A5 through Z10, of known viscosity to cover a viscosity range from 0.005 to 1,000 stokes. The Direct Time Method uses a single 3-line times tube for determining the "bubble seconds", which may then be converted to stokes.

Bubble Tubes

A bubble rising in a fluid.

Saybolt Viscometers

They are used to express the fluid’s viscosity, in Saybolt universal seconds or Saybolt furol seconds. The glass capillary viscometers, shown in the figure are examples of the second type of viscometer used.

These viscometers are used to measure kinematic viscosity. Like the Saybolt viscometer, the glass capillary measures the time in seconds required for the tested fluid to flow through the capillary. This time is multiplied by the temperature constant of the viscometer in use to provide the viscosity, expressed in centistokes. The following formulas may be used to convert centistokes (cSt units) to approximate Saybolt universal seconds (SUS units).

For SUS values between 32 and 100:

For SUS values greater than 100:

Rheometers

A Rheometer is a laboratory device used to measure the way in which a liquid, suspension or slurry flows in response to applied forces. Viscometers that can measure fluids with high viscosity or molten polymers are usually called rheometers or plastometers.

It is used for those fluids which cannot be defined by a single value of viscosity and therefore require more parameters to be set and measured than is the case for a viscometer. It measures the rheology of the fluid.

It can be of two types:

a. Shear rheometers (apply shear stress)

Pipe or Capillary Rheometers

Rotational Cylinder Rheometers

Cone and Plate Rheometers

b. Extensional rheometers (apply extensional stress) Acoustic Rheometers

Pulled string Rheometers

Capillary Rheometers

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