Apparent wall slip

An apparent slip or lubrication occurs at the wall in the flow of any multi-phase systems if the disperse phase moves away from smooth walls. This arises from steric, hydrodynamic, viscoelastic and chemical forces present in suspensions flowing near smooth walls and constraints acting on the disperse phase particles immediately adjacent to the walls, see [13]. 

The enrichment of the boimdary near the wall with the continuous (and usually low-viscosity) phase means that any flow of the suspension near such a boundary is easier because of the lubrication effect. Because this effect is usually confined to a very narrow layer—with typical thickness of 0.1-10 /an—it so resembles the slip of solids over surfaces that it has historically been described by the same terminology. The restoring effect for all the forces that cause an increase in concentration as particles move away from walls is usually osmotic, and this will always limit the movement of particles away from the walls, thus also limiting the effective slip. 

How do these effects occur When any suspension of particles is placed next to a smooth wall, the original microstructure is locally disturbed. For a simple suspension at rest where the particles are randomly dispersed in space, the concentration of particles undergoes a damped oscillatory variation as one moves away from the wall, see figpre 16, where the concentration is at the maximum packing fraction, so that the effect is enhanced. The new distribution has two effects, first that the variation in concentration does not die out until about five particle radii away from the wall, and secondly that the average particle concentration is zero at the wall and less than average for a small distance away from the wall. 

As well as these static—essentially geometric—effects that produce depletion at the wall, there are also dynamic effects which enhance the phenomenon. The existence of a shear rate and/or a shear rate gradient in the fluid next to the wall (as in a pipe) results in a further movement of particles away from the wall, towards areas of lower shear rates such as the centre of pipes. Solid particles, emulsion droplets and polymer molecules all show this tendency. 

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. 

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Fig.8. Apparent wall slip of a HDPE (Mw=177,800) inferred from the gap dependence of the sliding plate rheometry measurements involving bare steel surfaces, calculated based on the data from HD s paper [37]...

Dogan, N., McCarthy, M. J., and Powell, R. L. 2002. In-line measurement of theological parameters and modeling of apparent wall slip in diced tomato suspensions using ultrasonics. J. Food Scl 67(6) 2235-2240. 

Wein O, Tovchigrechko VV (1992) Rational Viscosimetry under Pressure of Apparent Wall Slip. J J Rheol vol 36 No 5... 

The occurrence of this phenomenon may be tested by comparing the viscosity ftmctions obtained using capillaries of similar length-to-radius ratios, L/R, but of different radii. Any apparent wall slip may then be corrected for and the true viscosity of the fluid determined by extrpolating the results obtained to infinite pipe diameter. In the relation developed by Mooney [1931], apparent wall shear rates obtained for constant length-to-radius ratio are plotted against L/K). 

Jana, S.C., Kapoor, B., and Acrivos, A. (1994) Apparent wall slip velocity coefficients in concentrated suspensions of noncolloidal particles. J, Rheol,... 

In the foregoing analysis we assumed ideal Couette flow V = v(0, rO, 0). For concentrated suspensions, some gels, and polymer solutions, a low viscosity layer can develop near Ae cylinder surfaces (note Figure 10.2.1a). This leads to an apparent wall slip. This slip velocity can be determined by making measurements with two different radii bobs, / and Rz, with cups sized to give the same k (Yoshimura and Prud homme, 1988)... 

It is usually possible to correct this apparent wall slip and determine the true viscosity of the sample by extrapolating to infinite diameter. Apparent wall shear rates measured at constant extrusion pressure (i.e., constant Tw) for a constant L/R are plotted against l/R according to the relation first developed by Mooney (1931)... 

Xanthan gum Tube flow Shear thinning and apparent wall slip... 

Apparently, the slip length diverges when 0. In practice, the shear strain in Eq. (5) will approach zero in such a case, thus leaving the velocity jump finite. Several experimental results on cf have been reported [6, 7], most of them indicating values between 0.8 and 1.0, compatible with rough walls. 

The other approach is to scale up the genuine flow, then add the slip flow for the appropriate pipe diameter. Scale up of the genuine flow can be done as described in Section 3.3 or Section 3.4. In order to assess the flow due to wall slip in the pipe, it is necessary to have information about the variation of vs with tw and dt unless it is assumed that the pipe is large enough for the effect of slip to be negligible. If slip velocity data are available, implying that the apparent fluidity plots are also available, then it would be easier to use these plots directly. 

Not all suspensions will exhibit wall slip. Concentrated suspensions of finely ground coal in water have been found to exhibit wall slip [Fitzgerald (1990)]. This is to be expected because the coal suspension has a much higher apparent viscosity than the water. In contrast, when the liquid is a very viscous gum, the addition of solids may have a relatively small effect. In this case, the layer at the wall will behave only marginally differently from the material in the bulk. 

Three theories were proposed to explain wall-slip (a) adhesive failure at the wall, (b) cohesive failure within the material as a result of disentanglement of chains in the bulk and chains absorbed on the wall, and (c) the creation of a lubricating surface layer at the wall either by a stress-induced transition, or by a lubricating additive. If the polymer contains low molecular weight components or slip-additives, their diffusion to the wall will create a thin lubricating layer at the wall, generating apparent slip. 

Other complex fluids, such as polymer melts, contain no solvent that can serve as a lubricant, and mechanisms for shp at or near a solid surface—and even the existence of wall slip-—are less obvious (Denn 1990). Suspicion that slip may be occurring is aroused by observations of jumps, or abrupt slope changes, in curves of shear stress versus shear rate, or by oscillations in stress or pressure at fixed apparent flow rate, suggesting stick-slip — that is, alternating periods of stick and slip (Benbow and Lamb 1963 Blyler and Hart 1970 Vinogradov et al. 1972 Kalika and Denn 1987 Lim and Schowalter 1989 Piau et al. 1990 Hatzikiriakos and Dealy 1992). But molecular theories of slip for complex fluids such as... 

Capillary rheometry and parallel-plate rheometry use the fact that wall slip will manifest itself as a geometry-dependent phenomenon. That is, wall slip will appear as a geometric effect on apparent rheological properties. In the capillary-rheometer technique, slip will manifest itself as an effect of capillary diameter ( )) on the shear stress (t, ). Wall slip in capillary rheology can be calculated from an analysis that involves the following ... 

D. C. Tretheway and C. D. Meinhart, Apparent fluid slip at hydrophobic microchannel walls, Phys. Fluids 14, L9-L12 (2002) Chang-Hwan Choi, J. A. Westin, and K. S. Breuer, Apparent slip flows in hydrophilic and hydrophobic microchannels, Phys. Fluids 15, 2897-902 (2003). 

The first term in Eq. (17.17) is the flow rate dne to shearing, and the second one is the flow rate dne to slip. The apparent shear rate in case of wall slip is given by the Mooney equation [5] ... 

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