Rheology At the completion of this section the student will be able to: describe Newtonian behaviour; illustrate and explain 3 different kinds of non-Newtonian flow; illustrate and explain time dependent non-Newtonian flow; describe different ways to measure viscosity and different viscometers 5

Questions and Feedback

Hookean materials t shear stress [F’/A] Nm-2 g strain [dx/dr] no units For an elastic or Hookean material, stress is proportional to strain , if you double the tension you double the extension. t shear stress [F’/A] Nm-2 g strain [dx/dr] no units Hooke’s Law (F=kx): t = G g where G is storage modulus (Pa) F’ A dx dr NB. (shear) strain is defined as the flow deformation per unit length

e.g. a rubber band : instantaneous deformation, deformed state lasts as long as the stress is applied, work done is recoverable. Before F During After For an elastic solid (e.g. a rubber band) a stress results in an instantaneous deformation. Once the deformed state is reached there is no further movement, but the deformed state lasts as long as the stress is applied. Suppose we apply a Force F to the upper face of an elastic body and it displaces dx, the work done is Fdx. Upon removal of the force the upper face recoils to its original position. All of the work done on an elastic material is recoverable.

Newtonian Liquids . . t shear stress [F’/A] Nm-2 Newtonian liquids are inelastic liquids in which stress is proportional to the rate of strain. If you double the force you double the velocity gradient t shear stress [F’/A] Nm-2 g rate of strain [dv/dr] sec-1 Newtonian fluid: t = h g where h is viscosity Nm-2sec . F’ A dv dr . NB. dv = dx/dt Velocity gradient= rate of strain is also called the shear rate.

Work done is dissipated as heat and cannot be recovered. F Before During After

Viscoelasticity Viscoelastic materials: a viscoelastic material exhibits viscous as well as elastic behaviour Note: in the rheological sense water is a "viscous" fluid. Normally, however, the term "viscous" is used for fluids with high viscosity

Only partial elastic recovery is observed when the force is removed. Before During After Only partial elastic recovery is observed when the force is removed. A portion of the work done is recoverable and the remainder is lost as heat.

Force (shear stress) Speed (shear rate) Stress = force Strain rate and rate of shear = speed therefore, you are really plotting force v speed or vice-versa Viscosity = 1/gradient.

“Nothing changes viscosity like temperature” 0.0004 0.0008 0.0012 0.0016 0.002 10 20 30 40 Temperature [°C] Viscosity [kg/(m*s)] Viscosity of water as a function of temp. An increase in temperature gives a decrease in viscosity according to the equation: h = Ae(Ev/RT)

Newtonian Flow Newtonian liquids have constant viscosity. There is no change in viscosity with either changing shear stress or shear rate. Pure liquids are examples of Newtonian liquids eg water, castor oil, etc. Newtonian Rate of shear Shearing stress

Non–Newtonian Flow Rate of shear Shearing stress dilatant plastic pseudoplastic Newtonian Materials in which there is not a simple relation between shearing stress and rate of shear are termed Non–Newtonian. Examples of non–newtonian samples are liquid and solid heterogenous dispersions such as colloidal solutions, emulsions, liquid suspensions, and ointments.

Plastic Flow Plastic materials do not flow until a yield stress is exceeded, e.g. thick tomato sauce, toothpaste*. The physical behaviour of fluids with a yield stress is usually explained in terms of an internal structure in three dimensions which is capable of preventing deformation for values of stress less than the yield value. plastic viscosity Newtonian Rate of shear Plastic Shearing stress yield stress Plug flow: Movement of a material as a unit without shearing within the mass

an example of plastic flow optimisation Same formulation, but have changed the solution conditions so that yield stress changes. Note that plastic viscosity does not change. Shear rate, , s-1 g . Shear stress, t, Pa

Pseudoplastic Flow Pseudoplastic materials always flow like a liquid but viscosity decreases as shear rate increases, e.g. mayonnaise. Decrease in viscosity with shear rate may be due to: orientation and disentaglement increasing with shear rate; or solvating layers being sheared away resulting in decreased particle size. Newtonian Rate of shear Pseudoplastic Shearing stress

Dilatant Flow Rate of shear Shearing stress Dilatant fluids are characterised by increasing viscosity with increasing shear rate. Dilatant behaviour is not nearly as common as pseudoplastic behaviour. Dilatant behaviour is sometimes observed in suspensions at high solids content. Dilatant Newtonian Rate of shear Shearing stress

Time Dependent Non–Newtonian Flow Viscosity Time thixotropic If the viscosity decreases with time of shear the materials is thixotropic, if it increases with time of shear it is called rheopectic/dilatant-thixotropic/anti-thixotropic. NB: changes may not be linear as in schematics Viscosity Time rheopectic

Thixotropy Arises from structural breakdown and reaggregation in complex materials in which a loose network connects the sample. At rest or very low shear rates, the 3-D structure provides the system with some rigidity and the material behaves as a gel. Increased stress disrupts the structure and the particles start to align. The material commences flowing and its consistency decreases as shear rate and stress increase. When the stress is decreased or removed, the internal structure starts to reform but with a time lag, as the particles which build the network need time in which to contact each other.

Determination of Rheological Properties If measuring Newtonian fluid, i.e., one that the viscosity does not change with rate of shear, then can use instrument that operates and only one rate of shear (or shear stress), eg, capillary viscometer. But if measuring non–Newtonian fluid then need to use instrument with range of shear rates (or shear stresses), eg, cup and bob, and cone and plate.

Single Point Measurements A measurement made at this shear stress could show many materials to have the same viscosity even though they possess very different properties and behaviour Use for Newtonians only! Viscosity Shearing stress

Capillary Viscometer – only force is gravity The viscosity can be determined by measuring the time required for the fluid to flow between the two marks, A and B, as it flows by gravity through the vertical capillary tube. This time is compared to that for liquid of known viscosity: where h is viscosity, r is density and t is the measured time for each of the liquids, 1 and 2. A B 2 1 t r h =

Cup and Bob Viscometer Stormer instrument: known weights cause bob to turn with known torque (shearing stress) and speed of rotation (rate of shear) is measured. Plot rpm versus mass added. Need to be calibrated with liquids of known viscosity for quantitative use. w

Lets see if you can… determine the rheological behaviour of a material from a graph of viscosity, shear rate, or shear stress (y-axis) versus shear rate, shear stress, or time (x-axis). Shearing stress Rate of shear Viscosity Shearing stress Time Rate of shear