Dilatant flow

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Suspensions with high concentrations of densely packed solids often exhibit dilatant flow behaviour. An example of this is a starch/water mixture (figure 9.20). 

Rheopectic Time-dependent dilatant flow. At constant applied shear rate, viscosity increases. In a flow curve, hysteresis occurs. Clay suspensions. A suspension which sets slowly on standing, but quickly when gently agitated due to time-dependent particle interference under flow. 

A dilatant flow is characterized by the opposite type of pseudoplastic flow in which the apparent viscosity increases with the increase in shear stress (i.e., shearthickening). The empirical equation described for the dilatant flow is similar to Equation (4.84) but the exponent n is greater than 1. This behavior is not common for all pharmaceutical solutions and dispersions but it is exhibited by pastes of small, deflocculated particles (solid content > 50%). There is only a limited amount of fluid that can till the interparticulate voids. 

Figure 8-5 Shearing Stress-Rate of Shear Diagrams. (A) Newtonian liquid, viscous flow, (B) dilatant flow, (C) pseudoplastic flow, (D) plastic flow.

Consider now a polymer sample of current volume V responding by craze plasticity to an imposed current elongational strain rate e, developing a tensile (dilatational) flow resistance until a final fracture strain is achieved as shown in Fig. 1. The specific toughness W or the total deformational energy absorbed per unit volume for this polymer is the area under the stress strain curve, or... 

If the strain derived is entirely due to craze matter production, there will be no significant change in the cross-sectional area A of the part during such (dilational) flow. Then, by definition, the imposed tensile strain rate e must be... 

FIGURE 8.7 Non-Newtonian flow behavior, a Structural viscosity (for high molecular solution). b Dilatant flow (suspension with high concentration), c Viscoplastic with flow limits 1, ideal plastic 2 or 3, nonlinear plastic flow, d 1, thixotropy flow 2, antithixotropy flow 3, viscoelastic flow e rheopexy flow. 

By substituting (6.4.8) into (6.4.4)-(6.4.7), one can find the basic characteristics of motion of a power-law fluid in a circular tube. The results of the corresponding calculations [452, 508] are presented in Table 6.5 and are shown in Figure 6.2. One can see that the velocity profiles become more and more filled as the rheological parameter n decreases. The limit case n -> 0 is characterized by a quasisolid motion of the fluid with the same velocity in the entire cross-section of the tube (it is only near the wall that the velocity rapidly decreases to zero). The parabolic Poiseuille profile corresponds to the Newtonian fluid (n = 1). The limit dilatant flow (n — oo) has a triangular profile, which is characterized by a linear law of velocity variation along the radius of the tube. 

Before a mass of tightly packed particles can flow, it must increase in volume to permit interlocking grains to move past one another. Without such dilation flow is not possible. 

Dilatant Flows Krieger and Choi [1984] smdied the viscosity behavior of sterically stabilized PMMA spheres in silicone oil. In high viscosity oils, thixotropy and yield stress was observed. The former was well described by Eq 7.41. The magnimde of Oy was found to depend on ( ), the oil viscosity, and temperature. In most systems, the lower Newtonian plateau was observed for the reduced shear stress value = Oj d / RT > 3 (d is the... 

Hoffman [1972, 1974], Strivens [1976], van de Ven [1984, 1985], Tomita et al. [1982, 1984], and Otsubo [1994] reported pseudoplastic/dilatant flow of concentrated suspensions of uniform and polydispersed spheres. A dramatic change in light diffraction pattern was systematically observed at the shear rate corresponding to the onset of dilatancy. Van de Ven and his collaborators demonstrated that, depending on concentration and shear rate, the distance between the sliding layers of uniform spheres in a parallel plate rheometer can vary by as much as 10%. 

Ouibrahim and Fruman (47) in 1980 found dilational flow in three distinct flow situations, which each involve an extensional component capillary tube flow, orifice flow, and pitot tube flow. They examined extensively hydrolyzed polyacrylamide (HPAA) and found that the dilatant effect was greatly reduced in the presence of excess salt. This finding was attributed to the effect of the salt ions in screening the charges on the polyelectrolytic HPAA and thus causing the contraction of the highly expanded molecule. 

Typical dilatant flow curves for two concentrations of A-16SG alumina and paraffin wax are shown in Fig. 5. Reynolds approach to dilatancy has some limitations. For example, Reynolds approach specifies hexagonal close pack-... 

Based on viscosity of the samples, the flow of samples is broadly classified into three categories, namely, Newtonian, time independent non-Newtonian and time dependent non-Newtonian. Newtonian fluids show shear stress independent constant viscosity profile where as non-Newtonian fluids show a viscosity profile, which is dependent on the shear force and time. In time independent non-Newtonian fluids, the shear stress does not vary proportionally to the shear rate. The time independent non-Newtonian fluids show mainly three types of flow. A decreasing viscosity with an increase of shear rate is called shear thinning or pseudoplastic flow (Figure 46.12a). An increasing viscosity with an increase of shear rate is called shear thickening or dilatant flow. Some fluids need application of certain amount of force before any flow is induced that are known as Bingham plastics. 

The n value indicates the type of flow behavior. The formulations having n = 1 indicates a Newtonian flow behavior, n < 1 signifies pseudoplastic flow whereas n > 1 indicates a dilatant flow. In general, physical organogels shows n values <1 suggesting pseudoplastic nature of the gels. ... 

Deviations from Newtonian flow can occur when shear stress does not increase in direct proportion to shear rate. Such deviation may be in the direction of thickening (called dilatent flow) and in the direction of thinning (called pseudo plastic). Related to non-Newtonian flow is the behavior of thixotropic liquids when subjected to shear, as explained above. Flow behavior can be represented by the following equation ... 

Flow flo [ME, fr. OEflowan, akin to OHGr flouwen to rise, wash, L pluere to rain, Gk plein to sail, float] (before 12c) v. (1) Resistance to movement by a liquid material and divided rheologically into four categories Newtonian (simple) flow, plastic flow, pseudoplastic flow, and dilatant flow. 

Non-Newtonian liquid Any liquid that exhibits a viscosity which varies with changing shear stress or shear rate thus, any liquid which does not satisfy the requirements for a Newtonian liquid, i.e., that displays plastic, pseudoplastic, or dilatant flow characteristics. Most paints are non-Newtonian liquids. 

Shear thickening n. A rheological flow characteristic evidenced by an increase in viscosity with increasing rates of shear, an increase of flow resistance with agitation. Shear thickening is also known as dilatant flow. 

Two types of flow behaviour can be distinguished, namely Newtonian and non-Newtonian flow. Non-Newtonian flow is further divided into plastic, pseudo-plastic and dilatant flow. 

Fig. 18.6 Rheograms of liquids with Newtonian, plastic, pseudoplastic and dilatant flow behavioiu. Source Recepteerkunde 2009, KNMP...

If the suspension also contains particles smaller than 1 pm (the colloidal fraction of the suspension), these particles will not settle but will continue to be suspended in the liquid so that the liquid above the sediment remains cloudy. The sediment exhibits dilatant flow behaviour. 

Flow behaviour sediment dilatant Flow behaviour sediment plastic... 

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