Weak flow/viscosity

A corrected and more general analysis of the primary electroviscous effect for weak flows, i.e., for low Pe numbers (for small distortions of the diffuse double layer), and for small zeta potentials, i.e., f < 25 mV, was carried out by Booth in 1950. The result of the analysis leads to the following result for the intrinsic viscosity [rj] for charged particles in a 1 1 electrolyte ... 

As discussed in Section 3.3, viscosity varies as a function of temperature and pressure. For isothermal, uniform-composition flows, viscosity is a constant. For many situations of interest, in which temperature and composition vary over only relatively small ranges, it can be appropriate to consider constant properties. For gases, viscosity is roughly proportional to T0-645—a relatively weak dependence. Moreover there is essentially no pressure dependence. In any case it is instructive to see how the Navier-Stokes equations behave in the limiting case of constant viscosity. 

However, viscometric measurements of dilute polymer solutions in a steady flow are inadequate for this purpose although, as already indicated, viscosity is related to molecular rotation. This has been demonstrated by Zimm s theory ). Zimm considered the kinetics of the motion and deformation of a kinetically flexible polymer chain in a weak mechanical field with harmonic velocity gradient g at frequency v. It has been found that under steady and weak flow conditions... 

It is not easy to measure internal friction processes. For example, the contributions of eqs. (VI. 103, VI. 104) do not show up in the static viscosity for weak flows. This can be understood as follows. To discuss the viscosity increment 5t) due to our dilute coils, we may choose any type of (weak) shear flow. It is then convenient (as noted first hy Kramers ) to choose a longitudinal shear flow, such as the one shown in eq. (VI.6S). In this situation the molecule does not rotate but simply stretches to a certain equilibrium length r (for a given shear rate s). Internal friction is involved only if the chain varies its length (or, equivalently, its conformations). In the present case the length is constant, and there is no dissipation associated with internal friction. 

Strain dependence. Furthermore, in steady shear a strong gel will rupture completely whereas a weak gel will flow, albeit without obeying the Cox-Merz superposition principal. In this case the complex viscosity (r] ) is higher than the flow viscosity ( //). This indicates the presence of weak interactions between the molecules that contribute to the viscosity measured by the non-destructive oscillatory technique but not to the viscosity measured by the destructive flow technique. 

For the wash-coating step, the monoliths are dipped into the colloidal suspension, in a specially lab-made double-wall beaker for a fine control of the temperature. The monoliths are periodically removed and turned over. The final unclogging of the channels is performed under weak flow of argon to remove excess colloidal solution. Beside the composition of the suspension, key parameters are the viscosity, the temperature and the duration of the wash-coating process which must be carefully... 

Solders should flow promptly and smoothly over the surfaces of the parts to be joined. This property depends on the surface tension, viscosity, and adhesive properties of the molten solder. Finally, the color of a solder should match that of the metal employed, and its physical properties should be at least as good as those of the metal, in order for the joint not to be a source of weakness (150). 

It is expected, however, that the Gaussian representation is inadequate in transient elongational flow, even if the chain is only weakly deformed. During a fast deformation, the presence of non-equilibrium effects, like internal viscosity , noncrossability and self-entanglements will stiffen the molecular coil which is now capable of storing a much larger amount of elastic energy than that predicted from Eq. (113). 

While electrical conductivity, diffusion coefficients, and shear viscosity are determined by weak perturbations of the fundamental diffu-sional motions, thermal conductivity is dominated by the vibrational motions of ions. Heat can be transmitted through material substances without any bulk flow or long-range diffusion occurring, simply by the exchange of momentum via collisions of particles. It is for this reason that in liquids in which the rate constants for viscous flow and electrical conductivity are highly temperature dependent, the thermal conductivity remains essentially the same at lower as at much higher temperatures and more fluid conditions. 

Sampling rates for the case of total boundary layer-control can be expected to be nearly independent of temperature, since both the diffusion coefficients in air, and the kinematic viscosity of air are only weak functions of temperature (Shoeib and Harner, 2002). This leaves the air-flow velocity as the major factor that can be responsible for the seasonal differences among sampling rates observed by Ockenden et al. (1998). The absence of large R differences between indoor and outdoor exposures may be indicative of membrane-control, but it may also reflect the efficient damping of high flow velocities by the deployment devices used for SPMD air exposures (Ockenden et al., 2001). 

The 3 1 LDAO/SDS mixture becomes viscoelastic and rheo-pectic when a small amount of NaCl Is added. Its viscosity shows a reversible Increase with time of shearing at constant shear rate. The rheopectic behavior Is probably due to long thread-like micelles that are aligned parallel to the flow In weakly bound clusters, as In the case of cetyltrlmethyl ammonium bromide and monosubstituted phenol mixed solutions (21). 

Compression of a weakly structured food between parallel plates may achieve squeezing flow (Steffe, 1996). When lubricated parallel plates are used, the result is a form of biaxial extension. Biaxial extension may be used to measure biaxial viscosity, which is a reflection of resistance to radial stretching flow in a plane. Lubricated squeezing flow of a semi-solid... 

The measure of a liquid s resistance to flow is called its viscosity. Not surprisingly, viscosity is related to the ease with which individual molecules move around in the liquid and thus to the intermolecular forces present. Substances with small nonpolar molecules, such as pentane and benzene, experience only weak intermolecular forces and have relatively low viscosities, whereas more... 

The intense heat dissipated by viscous flow near the walls of a tubular reactor leads to an increase in local temperature and acceleration of the chemical reaction, which also promotes an increase in temperature the local situation then propagates to the axis of the tubular reactor. This effect, which was discovered theoretically, may occur in practice in the flow of a highly viscous liquid with relatively weak dependence of viscosity on degree of conversion. However, it is questionable whether this approach could be applied to the flow of ethylene in a tubular reactor as was proposed in the original publication.199 In turbulent flow of a monomer, the near-wall zone is not physically distinct in a hydrodynamic sense, while for a laminar flow the growth of viscosity leads to a directly opposite tendency - a slowing-down of the flow near the walls. In addition, the nature of the viscosity-versus-conversion dependence rj(P) also influences the results of theoretical calculations. For example, although this factor was included in the calculations in Ref.,200 it did not affect the flow patterns because of the rather weak q(P) dependence for the system that was analyzed. 

Blends 3 (a,b,c) Rheologically Robust Matrix and Weak Dispersed Components Since PE 1409 is a low viscosity nearly Newtonian polymer melt, its dispersive behavior is uncomplicated and more Newtonian like. Blend 3a forms a small (3-5-pm) droplet dispersion morphology, and Blend 3b is even finer (1-2 pm), becoming, only below 2% concentration, less subject to flow-induced coalescence. The TSMEE-obtained dispersions are finer than those from the TSMEE, with a variety of kneading elements (126). What is noteworthy about these blends is the early stages of the dispersion process, shown on Fig. 11.44, obtained with Blend 3a using the TSMEE at 180°C and 120 rpm. 

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