Modeling wall slip effects

If it is known that a particular form of relation, such as the power-law model, is applicable, it is not necessary to maintain a constant shear rate. Thus, for instance, a capillary tube viscometer can be used for determination of the values of the two parameters in the model. In this case it is usually possible to allow for the effects of wall-slip by making measurements with tubes covering a range of bores and extrapolating the results to a tube of infinite diameter. Details of the method are given by Farooqi and Richardson. 21 ... 

Kn = 0.01-0.1 Slip flow rarefaction effects that can be modeled with a modified continuum theory with wall slip taken into consideration... 

Development of this model is continuing in our laboratory, and among the aspects still under development are capabilities for transient flows, reactive fluids, free surfaces, and wall slip. Although incorporation of fluid elasticity is desired due to its importance in many polymer melt flows, such a development has proven elusive to a number of well qualified groups in the past several years. At present, it seems prudent to let the theoretical aspects of elastic effects be developed further before attempting their incorporation in a general process model. 

Qiu and Rao (Qiu, C. G. and Rao, M. A. J. Texture Stud., submitted) determined slip coefficients and slip velocities for apple sauce in a concentric cylinder viscometer as well as the effect of insoluble solids content on them. Three concentric cylinder units specified in the theory of Mooney (42.) were employed. Rotational speeds were determined with the different concentric cylinder systems at the same magnitude of torque. Figure 2 shows, for one sample of apple sauce, the shear rates uncorrected and corrected for slip plotted against the shear stress. The magnitudes of the flow behavior index of the power law model (Equation 2) did not change significantly due to correction for wall slip however, the magnitudes of the consistency index increased due to wall slip corrections. 

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. 

There are a number of additional physical phenomena, such as wall slip, electric effects and viscous energy dissipation, which may need to be taken into account. Generally applicable models are not available for some of these effects, particularly wall slip. 

Mathematical modeling of the flow through SSE considers that the screw and the barrel are unwound. The screw is stationary and the barrel moves over it at the correct gap height and the pitch angle. The initial models assumed (i) steady state, (ii) constant melt density and thermal conductivity, (iii) conductive heat only perpendicular to the barrel surface, (iv) laminar flow of Newtonian liquid without a wall slip, (v) no pressure gradient in the melt film, and (vi) temperature effect on viscosity was neglected. Later models introduced non-Newtonian and non-isothermal flows. Present computer programs make it possible to simulate the flow in three dimensions, 3D [39]. 

The result of these combined static and d)mamic depletion effects is an effective lubricating layer at the wall. This can be modelled simply as a particle-free layer of about half a particle-radius wide. Hence the lubricating effect is larger for larger particles, and in this context large particles include floes, so that at low shear rates, slip effects are stronger than at higher shear rates for flocculated suspensions. 

Reply by the Author Any EHL model is only as good as the assumptions made in the analysis. I belieye, howeyer, that the assumptions of no fluid inertia, no yisco-elastic effects, and no wall slip are reasonably accurate for the pure rolling conditions examined here. 

Inner slip, between the solid wall and an adsorbed film, will also influence the surface-liquid boundary conditions and have important effects on stress propagation from the liquid to the solid substrate. Linked to this concept, especially on a biomolecular level, is the concept of stochastic coupling. At the molecular level, small fluctuations about the ensemble average could affect the interfacial dynamics and lead to large shifts in the detectable boundary condition. One of our main interests in this area is to study the relaxation time of interfacial bonds using slip models. Stochastic boundary conditions could also prove to be all but necessary in modeling the behavior and interactions of biomolecules at surfaces, especially with the proliferation of microfluidic chemical devices and the importance of studying small scales. 

So far, the influence of bubble wake on mean bubble velocity i b relative to the column wall has not been mentioned, since Eq. (5-3) has been formulated on the basis of uy,o, which already includes the effect of the wake (although it lacks a correction for wake fraction). In bubbling-bed models (FIO, F12, K24, L5, S18) an upward flow of solid carried by the bubbles and bubble wakes leads to a downflow of solid (that has been assumed uniform) in the remainder of the bed. Then the bubble velocity b relative to bed wall should be smaller than the slip velocity of the bubble Ms relative to emulsion, since the bubble phase is retarded by downflow of... 

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