Viscosity anisotropic particles

Quite specific effects in the flow of dispersions of long fibers are connected with particles orientation in the flow. Indeed, the state of fibers during the flow changes greatly as compared the initial state, so that the material in a steady-state flow is an anisotropic medium. Therefore the viscosity of such a suspension may become independent of a fiber s length [30], The most strong effects caused by a deformation of anisotropic particles should be expected in transient flows, in particular if the particles themselves are flexible and deformed in the flow. 

This is obvious for the simplest case of nondeformable anisotropic particles. Even if such particles do not change the form, i.e. they are rigid, a new in principle effect in comparison to spherical particles, is their turn upon the flow of dispersion. For suspensions of anisodiametrical particles we can introduce a new characteristic time parameter Dr-1, equal to an inverse value of the coefficient of rotational diffusion and, correspondingly, a dimensionless parameter C = yDr 1. The value of Dr is expressed via the ratio of semiaxes of ellipsoid to the viscosity of a dispersion medium. 

In this equation, viscosity is independent of the degree of dispersion. As soon as the ratio of disperse and continuous phases increases to the point where particles start to interact, the flow behavior becomes more complex. The effect of increasing the concentration of the disperse phase on the flow behavior of a disperse system is shown in Figure 8-41. The disperse phase, as well as the low solids dispersion (curves 1 and 2), shows Newtonian flow behavior. As the solids content increases, the flow behavior becomes non-Newtonian (curves 3 and 4). Especially with anisotropic particles, interaction between them will result in the formation of three-dimensional network structures. These network structures usually show non-Newtonian flow behavior and viscoelastic properties and often have a yield value. Network structure formation may occur in emulsions (Figure 8-42) as well as in particulate systems. The forces between particles that result in the formation of networks may be... 

It has been shown experimentally [13] that the viscosity of anisotropic particle suspensions increases proportionally to the square of the ratio between the large and small axes for ellipsoids of revolution when the particles are prolate and increase directly proportional to the... 

If the particles are not spherical, even in the very dilute limit where the translational Brownian motion would still be unimportant, rotational Brownian motion would come into play. This is a consequence of the fact that the rotational motion imparts to the particles a random orientation distribution, whereas in shear-dominated flows nonspherical particles tend toward preferred orientations. Since the excess energy dissipation by an individual anisotropic particle depends on its orientation with respect to the flow field, the suspension viscosity must be affected by the relative importance of rotational Brownian forces to viscous forces, although it should still vary linearly with particle volume fraction. 

The list could be made longer, taking the idea of electrokinetics in a wide sense (response of the colloidal system to an external field that affects differently to particles and liquid). Thus, we could include electroviscous effects (the presence of the EDL alters the viscosity of a suspension in the Newtonian range) suspension conductivity (the effect of the solid-liquid interface on the direct current (DC) conductivity of the suspension) particle electroorientation (the torque exerted by an external field on anisotropic particles will provoke their orientation this affects the refractive index of the suspension, and its variation, if it is alternating, is related to the double-layer characteristics). 

Concerning the causes of the two other principal naechanisms of interaction, solvent immobilization and anisotropic particle form, see e.g. B. E. Hatschek, Kolloid Z., 9, 280 (1912) H. Fikentscher and H. Mark, Kolloid Z., 49, 185 (1929) F. Eirich and H. Mark, Ergeb. exakt, Naturwiss.f 15, 1 (1936) R. Burgers, First Report of Viscosity and Plasticity Amsterdam, New York 1935. 

The intrinsic viscosity of a colloidal dispersion is always positive, even for dispersions such as foams in which the particles are less viscous than the medium. For rigid particles, intrinsic viscosity depends on particle shape (but not on particle size). For emulsions, both interfacial tension and the viscosity of the particles affect intrinsic viscosity. For deformable particles and for small anisotropic particles, the intrinsic viscosity can depend also on shear rate (non-Newtonian intrinsic viscosity). 

The viscosity of the solvent is constant but the viscosity contribution due to a suspension of large anisotropic particles may depend on the rate of shear. This is in particular true of DNA and the extrapolation of [ ] to zero rate of shear can be obtained by a variety of means [76E1]. 

Shear Thinning Flow. Dispersions showing a decrease in viscosity with shear rate (or shear stress) are described as shear thinning or pseudoplastic. Shear thinning behavior is generally produced by the reversible breakdown of suspension structures or alignment of anisotropic particles due to shear. 

There are no equivalent studies of concentrated anisotropic suspensions. This is because of the tendency of anisotropic particles to form oriented ordered structures such as micro-bundles of fibers. Batchelor [45] has modeled the flow of concentrated suspensions of large parallel fibers. Very large elongational viscosities are predicted. This was extended to suspensions in non-Newtonian fluids by Goddard [46]. 

The apparent viscosity of a shear-thimiing flnid decreases with the shear. This frequent behavior in ceramics is due to the orientation of the particles, particularly anisotropic particles, and of the polymeric chains in the direction of the flow, which reduces flow resistance. This behavior is described by a power law ... 

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). 

Example. A tailings stream from the hot-water flotation process (oil sands) contains 27 % (mass) solids. Estimate the suspension viscosity. Light-scattering analysis indicates that the particles are finely divided and anisotropic with a 10 Tm major dimension and a 0.5 pm minor dimension. Using Eq. 

FIGURE 12J27 Effect of aggregate structure on the viscosity of a semidilute suspension of anisotropic platelet particles [61]. 

Very few data exist for the viscosities or Frank constants of discotic nematics—that is, nematics composed of disc-Uke particles or molecules (Chandrasekhar 1992). One can estimate values of the Leslie viscosities from the Kuzuu-Doi equations (10-20) by setting the aspect ratio p equal to the ratio of the thickness to the diameter of the particles thus /j — 0 for highly anisotropic disks. This implies that R(p) —1, and Eq. (10-20b) implies that the viscosity o 2 is large and positive for discoidal nematics, while it is negative for ordinary nematics composed of prolate molecules or particles. If, as expected, is much smaller in magnitude than 0 2. the director (which is orthogonal to the disks) will tend... 

Figure 13.15 shows the effects of and Af on the zero-shear viscosity r o(relative) for dispersions of infinitely rigid anisotropic filler particles. It is seen that, at any given and Af, T o increases more with fibers than it does with platelets. 

If the particles are strongly anisotropic then, as illustrated in Figure 8.9(a), their rotational motion in the shear field is greatly enhanced. Additional energy is dissipated in maintaining this motion and the viscosity is increased. Since only single particles are concerned in this process, it will increase the intrinsic viscosity above the value of 2.5 for spherical particles. For example, it is calculated that for rods having an axial ratio of 15 the intrinsic viscosity rises to 4.0. 

Assembly of silicon chips onto substrates with anisotropically conductive adhesives uses specialized equipment, initially developed for ffip-chip solder and TAB inner lead bonding. Heat and pressure are transmitted to the adhesive through a thermode attached to a robotic arm or a high-precision linear translator. Equipment requirements are more demanding than for solder assembly, as no self-alignment can occur. A minimum placement accuracy of 0.0005 in. is required. Coplanarity between the substrate and die is critical one study reports maintaining coplanarity to within 0.00004 in. [19]. The pressure required to achieve interconnection depends on the size of the die, the type of conductive particle used, and the viscosity of the adhesive at the bonding temperature. 

Since the direction of the elongated particles does not coincide with the axial direction as a consequence of the spiraling of the streamlines as well as of the perpendicular shear, we find that extensional viscosity can act in an anisotropic way in the plain perpendicular to the axial movement. As long as the molecules are stretched the viscosity used in eq. (2.1) therefore becomes time dependent and its value increases with wall distance.. It can easily be seen from the integration (2.9) of the vorticity equation (2.3) that... 

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