Fluids, structured yield-stress

When an electric field is applied to an ER fluid, it responds by forming fibrous or chain structures parallel to the applied field. These structures gready increase the viscosity of the fluid, by a factor of 105 in some cases. At low shear stress the material behaves like a solid. The material has a yield stress, above which it will flow, but with a high viscosity. The force necessary to shear the fluid is proportional to the square of the electric field (116). 

Complementing these hydrodynamic issues has been an ongoing effort to examine the rheological properties of blood as well as other body fluids. Blood exhibits shear thinning behavior and appears to have a yield stress owing to the formation of macroscopic structures that incorporate protein-aided bridging of red cells. 

The crystal shape may also impact material properties. The packing arrangement of particles in a food matrix depends to some extent on their size and shape. Furthermore, the distribution of forces applied to a food matrix depends on the arrangement of the particles within the structure. For example, spherical particles in a fluid shear field will roll across each other more easily than irregularly shaped particles, resulting in higher viscosity and yield stress for the system with irregularly shaped particles. 

The concepts of inter-particle bonding, net work structure, and viscous dissipation, as well as texture maps should be applicable to all structured dispersions, such as cosmetics and other consumer products. The vane yield stress test is a versatile test in which a fluid food is subjected to small deformations during the initial stages and large deformations during the latter stages of the experiment. From the former set of linear data, a shear modulus (G) of the sample can be estimated. 

Shear thinning of concentrated suspensions is typical for submicron particles dispersed in a low viscosity Newtonian fluid.At low shear strain rates. Brownian motion leads to a random distribution of the particles in the suspension, and particle collision will result in viscous behavior. At high shear strain rates, however, particles will arrange in layers, which can slide over each other in the direction of flow. This results in a reduced viscosity of the system in agreement with the principles of shear thinning. A pro-noimced apparent yield stress can be found for shear thinning suspensions, if the Brownian motion is suppressed by electrostatic repulsion forces, which result in three-dimensional crystal-like structures of the particles with low mobility. 

Simple classifications of fluids can be made on the basis of their rheological profiles. Figure 3.78 shows the (a) shear stress and (b) viscosity profiles for various systems. From Figure 3.78 one may define the following systems. Newtonian systems have a constant viscosity with respect to shear rate. Dilatant (or shear-thickening) systems have a viscosity that increases with respect to shear rate. Pseudo-plastic (or shear-thinning) systems have a viscosity that decreases with respect to shear rate. Yield-stress materials are materials that have an initial structure that requires a finite stress before deformation can occur. The stress that initiates deformation is defined as the yield stress. 

Experience has shown structured fluids to be more difficult to manufacture, due to the complexity of their rheological profiles. In addition to elasticity, dilatancy, and rheopexy, certain structured fluid compositions may exhibit solid-like properties in the quiescent state and other flow anomalies under specific flow conditions. For emulsions and solid particulate dispersions, near the maximum packing volume fraction of the dispersed phase, for example, yield stresses may be excessive, severely limiting or prohibiting flow under gravity, demanding special consideration in nearly all unit operations. Such fluids pose problems in... 

Sodium silicates are also used to provide the fluid with a yield stress large enough to hold the particles at high water content. The mechanism is completely different from that of bentonite platelets that, having opposite charges on the faces and on the edges, gel the fluid by forming card house structures. Here, sodium silicate reacts with lime or calcium chloride to form a calcium silicate gel. It is this gel that provides the yield stress required to hold the particles. 

In some colloidal dispersions, the shear rate (flow) remains at zero until a threshold shear stress is reached, termed the yield stress (ry), and then Newtonian or pseudoplastic flow begins. A common cause of such behaviour is the existence of an inter-particle or inter-molecular network, which initially acts like a solid and offers resistance to any positional changes of the volume elements. In this case, flow only occurs when the applied stress exceeds the strength of the network and what was a solid becomes a fluid. Examples include oil well drilling muds, greases, lipstick, toothpaste and natural rubber polymers. An illustration is provided in Figure 6.13. Here, the flocculated structures are responsible for the existence of a yield stress. Once disrupted, the nature of the floe break-up process determines the extent of shear-thinning behaviour as shear rate increases. 

One further feature must be mentioned about pharmaceutical suspensions, namely, their desirable rheolt ical properties (7). In practice, a Bingham plastic" behavior is most used a minimum shear stress yield stress) is needed for the suspension to begin to flow. For tower stresses—and, of course, when the system is left undisturbed—the viscosity is so high that the particles will likely remain homogeneously dispersed. According to Falkiewicz (7). thixotropy is another flow characteristic that can be useful, since in thixotropic fluids a finite lime is needed to rebuild the structure after, for instance, shaking it for administration. For this reason, most formulations contain thixotropic flow regulators intended to confer optima viscous flow propertie.s to the suspensions. The reader is referred to Chapter 5 of this book for details. 

Thixotropy is a reversible process and in an immobile state of fluid the continuous, progressive ordering of structure occurs. The one flow curve without hysteresis can be obtained, but the share must continue until the equihbrium is attained. The structure of ordinary tixotropic fluids is totally destroyed at high shear stress. After the shear stress elimination they behave like normal fluids until the stracture is rebuilt. There are also the tixotropic plastic fluids (Fig. 5.5) which do not lose totally the features of plastic fluids which is evident from the stable, however, even low yield stress value. Some suspensions show outstanding features the stracture is formed under the shear stress exclusively and without shear it collapses these fluids show a rheopexy. These properties are appear at moderate shear rate only. 

As many non-Newtonian systems are sufficiently structured to display an apparent yield stress, this requirement would appear to severely restrict the application of what would otherwise appear to be a very useful technique. However, on closer inspection, it has been shown that for a fluid which displays a yield stress, a more general derivation than that reported by Krieger and Maron [1952] may be obtained, and that the restriction of infinite outer boundary (i.e. cup) radius may in fact be eliminated [Jacobsen, 1974]. 

Thus soluble polymer, interacting in a controlled fashion with colloidal particles, can transform both the equilibrium state and the mechanical properties of dispersions. The possibilities range from equilibrium, low viscosity fluids to nonequilibrium, pseudoplastic pastes with high yield stresses. However, substantial ga( still exist in the ability to, for example, (i) create high viscosity equilibrium fluids with prescribed relaxation spectra, (ii) impart a sol-gel transition at prescribed conditions, or (iii) connect explicitly macromdecular structure with rheological behavior. 

Concentrated dispersions may be shear thickening, as opposed to the shear thinning of dilute polymer solutions. Some materials, such as latex paints, tend to form a structure. As the structure breaks down with shearing action, the viscosity decreases. Such materials are thixotropic. Some fluids have a yield stress. A thorough characterization of the rheology may require a number of different measurements. 

---