Rheological Properties Shear Stress the force experienced by the liquid is proportional to the area of the upper plate and is defined as the shear stress, σ = F/A (Units = Nm -2 or Pascals [Pa]) Shear Rate the velocity gradient or the rate of change of velocity at which one layer passes over an adjacent layer is the shear rate, (Units = s -1 ) Viscosity this is expressed mathematically as, η = shear stress / shear rate and is the measurement of the resistance to flow of a fluid. Pascal.second (Pa.s) is the basic unit of viscosity, but Poise or centipoise (cp = one hundredth of a Poise) is often used and one cp is equivalent to a millipascal-second, mpa.s. / dy / dx When quoting viscosities the shear rate (or measurement method/equipment used) should be stated together with the temperature at which the measurement was taken.
Rheological Nomenclature What is Rheology? Rheology is the study of how a material deforms during and after a force is applied. Rheology directly affects product handling and flow characteristics. Rheological Classifications There are two types of fluids: Newtonian and Non-Newtonian. Newtonian Fluids These are truly viscous ideal liquids, which means as the shear rate changes the viscosity remains constant (water, oils, solvents). Hence if you double the strain rate you will double the stress required. Non-Newtonian Fluids These fluids are affected by shear and are divided into Power Law Fluids (Pseudoplastic or Dilatant) and Time Dependent Fluids (Rheopectic or Thixotropic). Most polymers are pseudoplastic and thixotropic. Viscosity: A measure of the internal resistance of friction when a material moves against itself. The internal resistance or viscosity is typically measured using a rotating spindle instrument The amount of force needed to turn the spindle (torque) at a selected speed (RPM) is measured. A simple calculation converts this internal resistance to viscosity.
Rheological Nomenclature shear-thinning [pseudoplastic] A decrease in viscosity with increasing shear rate during steady shear flow. shear thinning [pseudoplastic] with yield response viscosity decrease continuously with shear rate once the apparent yield stress has been exceeded. shear-thickening An increase in viscosity with increasing shear rate during steady shear flow. The term dilatant is commonly used in practice to indicate shearthickening,although this usage is strictly incorrect. dilatant A property often associated with suspensions of irregularly shaped particles, in which the liquid exhibits an increase in volume while being sheared. The term is also used in common practice to mean shear-thickening, the increasing resistance to shear with increasing shear rate. It is possible for either of these two effects to exist in the absence of the other. thixotropy A reversible time-dependent decrease in viscosity at a particular shear rate. Shearing causes a gradual breakdown in structure over time. negative thixotropy [anti-thixotropy = rheopetic] A reversible time-dependent increase in viscosity at a particular shear rate. Shearing causes a gradual buildup of structure over time. Bingham plastic (ideal) Obeys the Bingham relation ideally. Above the Bingham yield stress the viscosity is constant and is called the plastic viscosity. Bingham plastic (non-ideal) Above the apparent yield stress the coefficient of viscosity decreases continuously, while the viscosity approaches a constant value with increasing shear rate. Reference : NIST Special Publication 946, Guide to Rheological Nomenclature: Measurements in Ceramic Particulate Systems
Rheological Properties 1. Newtonian 2. shear-thickening 3. shear-thinning 4. shear thinning with yield response 5. Bingham plastic (ideal) 6. Bingham plastic (non-ideal) Reference : NIST Special Publication 946, Guide to Rheological Nomenclature: Measurements in Ceramic Particulate Systems
Rheological Properties Suspensions containing a high concentration of nearly equiaxial particles may show shear thickening. Moderately concentrated suspensions of small, elongated particles may show shear thinning or pseudoplasticity, where the viscosity decreases with increasing shear rate. When the viscosity decreases with time under shear but recovers to its original value after flow ceases, the behavior is known as thixotropic. This type of behavior is more often observed in flocculated suspensions and colloidal gels. When the suspension is sheared, the flocs are broken down leading a distribution of floc sizes. The opposite behavior, when the viscosity increases with shear rate and is also time dependent, is known as rheopectic. In practice, dilatant and rheopectic behavior are often undesirable because at high shear rates the suspension becomes too stiff to flow smoothly. Plastic behavior is desirable for many ceramic forming methods because the suspension will flow under high stress but will retain its shape when the stress is removed after forming.
Influence of Particle Interactions on the Viscosity The interactions between the particles have a dramatic effect on the viscosity of the suspension, for Al2O3 suspensions containing 50 vol% particles which are stabilized with the polyelectrolyte poly(acrylic acid). The viscosity decreases dramatically as the concentration of PAA is increased and, at some critical PAA concentration corresponding to the amount required to form a complete monolayer on particle surface, reaches a low plateau region that is almost independent of the PAA concentration. This dramatic change in viscosity reflects the change from a flocculated suspension at low PAA concentration to an electrosterically stabilized system above the critical PAA concentration. The critical PAA concentration required to achieve monolayer coverage of the particle surface is dependent on the molecular weight. After the critical concentration is reached, further additions of PAA serve mainly to produce excess polymer in the solution, and the viscosity of the suspension starts to increase again at high concentration.