Wall-slip effect flow mechanics

The fact that the appearance of a wall slip at sufficiently high shear rates is a property inwardly inherent in filled polymers or an external manifestation of these properties may be discussed, but obviously, the role of this effect during the flow of compositions with a disperse filler is great. The wall slip, beginning in the region of high shear rates, was marked many times as the effect that must be taken into account in the analysis of rheological properties of filled polymer melts [24, 25], and the appearance of a slip is initiated in the entry (transitional) zone of the channel [26]. It is quite possible that in reality not a true wall slip takes place, but the formation of a low-viscosity wall layer depleted of a filler. This is most characteristic for the systems with low-viscosity binders. From the point of view of hydrodynamics, an exact mechanism of motion of a material near the wall is immaterial, since in any case it appears as a wall slip. 

As mentioned previously, additional complications arise when the size of the pores or flow capillaries in the porous matrix in only slightly larger than the polymer molecules themselves. Polymer molecules may then be retained by both adsorption on to the walls of the pores and by mechanical entrapment, thereby leading to partial or even complete blockage of pores and increased pressure drops. The exact cause of the sharp rise in pressme gradient as shown in Figure 5.12 is therefore difficult to pinpoint. The existence of a slip velocity at the wall of the pore may explain many of the observations. However, at present there is no way of assessing a priori whether slip effects would be... 

While experimental evidence indicates that fluid flow in microdevices differs from flow in macroscale, existing experimental results are often inconsistent and contradictory because of the difficulties associated with such experiments and the lack of a guiding rational theory. Koo and Kleinstreuer [6] summarized experimental observations of liquid microchannel flows and computational results concerning chamiel entrance, wall slip, non-Newtonian fluid, surface roughness, and other effects. Those contradictory results suggest the need for applying molecular-based models to help establish a theoretical frame for the fluid mechanics in microscale and nanoscale. 

Many different techniques have been used to either minimize or eliminate this effect. One technique involves the use of a mixing mechanism in the slip reservoir. Another feeds the slip streams through a screen mesh. (This usually only breaks the flow into much smaller streams and produces streaks that are much closer together and harder to see.) The best technique is to use a feed system that does not introduce the problem in the first place. The slip is fed to the reservoir under the surface, not on the top surface. This has been accomplished by the use of a reservoir system like that shown in Figure 4.3. This reservoir also uses a "weir feed system, in which the slip must flow from the first chamber over a retaining wall into the main feed chamber of the doctor blade assembly. The flow down the retaining wall is similar to a waterfall and provides a uniform and... 

In the intermediate range between viscous flow and Knudsen flow, that is, 0.05 pore wall. As a result, the velocity of gas molecules at the wall surface is not zero. This mechanism - combining both viscous flow and Knudsen diffusion - is thus called slip flow. The slip effect is negligibly small when r>> X but becomes significant when r is close to X. A correction has to be applied to the viscous flow with a wall velocity to describe the permeation flux as... 

One of the fundamental assumptions in fluid mechanical formulations of Newtonian flow past solids is the continuity of the tangential component of velocity across a boundary known as the "no-slip" boundary condition (BC) [6]. Continuum mechanics with the no-slip BC predicts a linear velocity profile. However, recent experiments which probe molecular scales [7] and MD simulations [8-10] indicate that the BC is different at the molecular level. The flow boundary condition near a surface can be determined from the velocity profile. In molecular simulations, the velocity profile is calculated in a simitar way to the calculation of the density profile. The region between the walls is divided into a sufficient number of thin slices. The time averaged density for each slice is calculated during a simulation. Similarly, the time averaged x component of the velocity for all particles in each slice is determined. The effect of wall-fluid interaction, shear rate, and wall separation on velocity profiles, and thus flow boimdary condition will be examined in the following. 

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