Stress dilatational 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). 

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... 

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. 

Fig. 1 Classes of rheological behavior that can be shown by coal slurries, as they appear when plotted on a shear rate/ shear stress graph. It is desirable for coal slurries to be Bingham plastic or pseudoplastic with yield, as such slurries flow readily at high shear rates (such as during pumping or atomization), while remaining stable against settling at low shear rates because of their yield stress. Dilatant slurries are completely unsuitable for coal slurry applications because they are extremely difficult to pump.

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...

Liquids that follow Newton s law are called Newtonian liquids. In non-Newtonian liquids, the quantity rj, which can be calculated from the quotient, aij/D, also changes with the velocity gradient, or with the shear stress. Newtonian behavior is usually observed for the limiting case D - 0 or Gij - 0. Melts and macromolecular solutions often exhibit non-Newtonian behavior. Non-Newtonian liquids are classified as dilatant, Bingham body, pseudoplastic, thixotropic, or rheopectic liquids. 

Krieger and Choi (1984) studied the viscosity behavior of sterically stabilized PMMA spheres in silicone oil. In high viscosity oUs, thixotropy and yield stress were observed. The former is well described by Eq. 7.41. The magnitude of Oy was found to depend on <(), the oil viscosity, and temperature. In most systems, lower Newtonian plateau was observed for the reduced shear stress value = cti2d / RT > 3 (d is the sphere diameter, R is the gas constant, and T is the absolute temperature). However, when shear stress was further increased, dilatant behavior was observed. Dilatancy was found to depend on d, T, and silicone oil viscosity. The authors reported small and erratic normal stresses. 

Consider the relative change in interfacial area AA/A brought about by an external stress. Dilation leads to dilution of the monolayer which, in turn, results in a rise of the interfacial tension y. Conversely, reducing the interfacial area causes y to decrease. The response of the monolayer to the imposed deformation may be more or less elastic or viscous. Elastic behavior is expected for monolayers in which the amphiphilic molecules are interconnected forming a two-dimensional gel. Also, when the rate of deformation is too high to allow for relaxation back to equilibrium by, for example, adsorption or desorption of amphiphiles to or from the interface, or by reorientation and/or reconformation of the molecules in the monolayer (especially in the case of polymers and proteins), the monolayer responds partly elastically. 

Extracellular matrix mimicry stress—strain behavior and compliance Rather than focusing on texture, one other approach arms to have similar mechanical properties to those of ECM and seems to be crucial in the cell differentiation process, especially since tissues are composed of smooth muscle cells that contract or relax depending on chemical stimuli. It has been observed that loose of vascular tissue contractility leads first to dilated vessels wall, secondly to endothelial cell dysfunction, and finally to atherosclerosis with free lumen dramatic decrease. Consequently, one assumption is to believe that newly formed tissue viability cannot be reached if mechanical properties of the fibrous scaffold do not mimic those of native tissue and particularly the native vascular wall compliance. 

The principle of maximum plastic work[1] is fundamentally important in the plasticity theory. In the case of granular materials, however, the principle has not been clearly explained due to the complexity of their mechanical behaviors. In this paper, assuming a simple condition of stress path and using newly proposed decompositions of stress and strain increment tensors ( which are defined by the stress-dilatancy equation and the condition of stress path),the principle is explained in both 2D and 3D cases. In 3D, the stress-dilatancy equation is introduced in a tensorial form as an extension of the 2D case, and it is shown that the modified associated flow rule proposed by Kanatani [2] is applicable to the case of granular materials. 

To demonstrate that propellants are non-linear materials even at small strains, one need only check the superposition principle experimentally. In the range of small strains below detectable dewetting or volumetric dilatation [6,9-11], most propellants have a relaxation that is independent of strain and in general closely obey the scalar multiplication homogeneity rule. Yet this relaxation modulus cannot be used to accurately predict the response due to other isothermal, low rate, small strain inputs. To demonstrate the inadequacies of linear viscoelastic predictions on solid propellants, laboratory tests where superposition is applicable can be performed. Figure 6.1 illustrates the stress-strain-dilatational behavior of a typical composite propellant. The dilatation-strain behavior is caused by vacuole formation within the microstructure... 

Predictions of the mechanical response of filled elastomers are further aggravated by the phenomenon of strain dilatation. As soon as dilatation commences, the tensile stress lag behind elongation, the degree of dilatation for a given composite being roughly a measure for the deviation from the expected mechanical response. Dilatation increases with particle size and volume fraction of filler—it decreases somewhat if the filler is bonded to the matrix. Farris (16,17) showed that dilatation can account well for the mechanical behavior of solid propellants and his equation ... 

The results of the latest research into helical flow of viscoplastic fluids (media characterized by ultimate stress or yield point ) have been systematized and reported most comprehensively in a recent preprint by Z. P. Schulman, V. N. Zad-vornyh, A. I. Litvinov 15). The authors have obtained a closed system of equations independent of a specific type of rheological model of the viscoplastic medium. The equations are represented in a criterion form and permit the calculation of the required characteristics of the helical flow of a specific fluid. For example, calculations have been performed with respect to generalized Schulman s model16) which represents adequately the behavior of various paint compoditions, drilling fluids, pulps, food masses, cement and clay suspensions and a number of other non-Newtonian media characterized by both pseudoplastic and dilatant properties. 

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