Dilatant behavior

In packed beds of particles possessing small pores, dilute aqueous solutions of hydroly2ed polyacrylamide will sometimes exhibit dilatant behavior iastead of the usual shear thinning behavior seen ia simple shear or Couette flow. In elongational flow, such as flow through porous sandstone, flow resistance can iacrease with flow rate due to iacreases ia elongational viscosity and normal stress differences. The iacrease ia normal stress differences with shear rate is typical of isotropic polymer solutions. Normal stress differences of anisotropic polymers, such as xanthan ia water, are shear rate iadependent (25,26). 

Such nonequilihrium surface tension effects ate best described ia terms of dilatational moduh thanks to developments ia the theory and measurement of surface dilatational behavior. The complex dilatational modulus of a single surface is defined ia the same way as the Gibbs elasticity as ia equation 2 (the factor 2 is halved as only one surface is considered). 

A wide variety of nonnewtonian fluids are encountered industrially. They may exhibit Bingham-plastic, pseudoplastic, or dilatant behavior and may or may not be thixotropic. For design of equipment to handle or process nonnewtonian fluids, the properties must usually be measured experimentally, since no generahzed relationships exist to pi e-dicl the properties or behavior of the fluids. Details of handling nonnewtonian fluids are described completely by Skelland (Non-Newtonian Flow and Heat Transfer, Wiley, New York, 1967). The generalized shear-stress rate-of-strain relationship for nonnewtonian fluids is given as... 

In order to prepare the PVAc latexes with Newtonian character or dilatancy behavior, the polymerization... 

Generally applicable mathematical representations of the dilational behavior of propellants have not been developed, as might be expected however, Fishman and Rinde (29) have derived empirical expressions for the formulations which they studied. These relationships give reasonable description of uniaxial behavior over wide ranges of strain, time, and temperature for several testing modes. Equation 1 is representative of one of the generalized expressions for the polyurethane and polybutadiene formulations studied. 

The preceding explanation suggests that all suspensions of solids in liquids should exhibit dilatant behavior at high solids contents. Few data are available for evaluation of this conclusion, as the usual examples of dilatant behavior (starch, potassium silicate, and gum arabic in water) (A3, G3) are not true suspensions. The excellent studies of Daniel (Dl) and Verway and De Boer (V3) have indicated under what conditions more dilute suspensions may also exhibit dilatancy. Some of these factors have been summarized by Pryce-Jones (P6). If Reynolds explanation is a valid one, it should be possible to measure the expansion or dilation of the fluid with increases in shear rate. This has been done indirectly Andrade and Fox (A5) measured the dilation of sand suspensions and arrays of cylinders upon the imposition of localized stresses. 

Experiments with the /3-lg/Tween 20 system were performed at a macroscopic a/w interface at a /3-lg concentration of 0.2 mg/ml [40]. The data obtained relate to the properties of the interface 20 minutes after formation. Up to R = 1, the storage modulus (dilational elasticity) was large and relatively constant, whereas the loss modulus (dilational viscosity) increased with increasing R. As R was increased to higher values there was a marked decrease in the storage modulus (dilational elasticity) and a gradual increase in the loss modulus (dilational viscosity). In summary, the data show the presence of a transition in surface dilational behavior in this system at a solution composition of approximately R = 1. At this point, there is a transformation in the adsorbed layer properties from elastic to viscous. 

A wide variety of nonnewtonian fluids are encountered industrially. They may exhibit Bingham-plastic, pseudoplastic, or dilatant behavior... 

Thixotropic and dilatant behavior of the suspension can be monitored by viscosi-metric measurements as a function of shear rate and the duration of the experiments. Studies with a 25 wt.% suspension of LiChrospher 100, 7 gm in a mixture of dioxane-cyclohexane-n-octanol (45/45/10, v/v/v) have shown that the suspension has rather low thixotropic and pseudo-elastic behavior (Hallmann, 1992). The packing pressure of the axial dynamic column packing technique has a significant influence on the column performance (Tab. 3.13). 

When describing dilatant behavior, the maximum stretch rate, e, in the converging flow at the contraction is a better parameter, but more difficult to be calculated. Instead of the term stretch rate, other authors also used deformation rate (e.g., Chauveteau, 1981) or elongational rate (e.g.. Sorbic, 1991). The shear-thickening viscosity is also called elongational viscosity (often referred to as the Trouton viscosity Sorbie, 1991) or extensional viscosity in the literature. James and McLaren (1975) reported that for a solution of polyethylene oxide (a flexible coil, water-soluble polymer physically similar to HPAM), the onset of elastic behavior at maximum stretch rates was of the order of 100 s and shear rates of the order of 1000 s. In this instance, the stretch rate is about 10 times lower than the shear rate. However, some authors use shear rate instead of stretch rate in defining the Deborah number—for example, Delshad et al. (2008). 

Figure 1. The stress-strain dilatational behavior of three highly filled elastomers...

Figure 3. The stress-strain dilatational behavior of a 63.5 vol % filled elastomer at a series of hydrostatic pressures at a high strain rate...

Fig. 6 Plot of membrane tension t as a function of dilation for a wide range of copolymer amphiphiles as extracted from MD simulations. The computational models, derived from systematic coarse-graining (black symbols), show nearly the same dilational behavior marked by the solid line. The slope of the line, ka, is very close to experimental measurements performed on giant vesicles 0colored symbols). Experimental data for a dimyristoyl phosphatidylcholine lipid membrane are also shown. The point of membrane lysis as observed experimentally for selected lipid and polymersome systems is also shown in the plot with green and red stars, respectively. Reprinted by permission from Macmillan Publishers Ltd Nature Materials, Ref. [85], copyright (2004)...

While many process fluids are Newtonian, some are non-Newtonian (as seen in Figure 9.7). For such cases, it is not sufQcient to use a single value for viscosity to determine the impeller Reynolds number. Concentrated slurries are typically non-Newtonian and particle-size dependent. They are frequently shear-thinning. Dilatant behavior seldom occurs. If the system is simply shear thinning, it is usually possible to describe its rheological behavior with a simple power-law relationship ... 

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