Slip coefficient

G is a multiplier which is zero at locations where slip condition does not apply and is a sufficiently large number at the nodes where slip may occur. It is important to note that, when the shear stress at a wall exceeds the threshold of slip and the fluid slides over the solid surface, this may reduce the shearing to below the critical value resulting in a renewed stick. Therefore imposition of wall slip introduces a form of non-linearity into the flow model which should be handled via an iterative loop. The slip coefficient (i.e. /I in the Navier s slip condition given as Equation (3.59) is defined as... 

Mooney s method has been modified in various ways to allow for the observation that, with many suspensions, the slip velocity depends on the tube diameter as well as the wall shear stress. Jastrzebski (1967) deduced that, for certain kaolinite-water suspensions, vs was inversely proportional to d Thus a modified slip coefficient Cj may be defined by... 

C.G. Qiu and M.A. Rao, Effect of Dispersed Phase on the Slip Coefficient of Apple Sauce in a Concentric Cylinder Viscometer, J. Texture Studies, 16 179-192 (1989). 

In his original derivation Brock used a value of % for Cs, the thermal slip coefficient. More recent data by Ivchenko and Yalamov (1971) have shown that Cs = 1.147 for complete thermal accommodation. In Brock s equation... 

Aj (cm) resin layer thickness (Figure 2). a slip coefficient. 

In some foods, a thin layer of low-viscosity fluid forms at the solid-fluid interface that in turn contributes to lower viscosity values. The boundary condition that at the solid-fluid interface the fluid velocity is that of the wall is not satisfied. This phenomenon is known as slip effect. Mooney (1931) outlined the procedures for the quantitative determination of slip coefficients in capillary flow and in a Couette system. The development for the concentric cylinder system will be outlined here for the case of the bob rotating and details of the derivation can be found in Mooney (1931). 

Qiu, C.-G. and Rao, M. A. 1989. Effect of dispersed phase on the slip coefficient of apple sauce in a concentric cylinder viscometer. J. Texture Stud. 20 57-70. 

Sokhan and Quirke434 devise a method of computing interfacial friction and the Maxwell slip coefficients (a) by equilibrium MD, in which a is computed from the relaxation time, which itself can be estimated by an exponential fit to the collective velocity autocorrelation function. Their equilibrium method is compared to an NEMD method devised by the authors previously and excellent agreement is found. They study the density dependence of the slip... 

The effect of slip flow can be treated either as an extension of a pure viscous flow or as an extension of a Knudsen flow. The simplest method is by adding an additional term (R/2p) (P/RT) dP/dz to Eq. (9.2), with P being the slip coefficient which is proportional to P. 

Here n is the unit normal to the boundary, u and T are the (continuum) velocity and stress, and P is an empirical parameter known as the slip coefficient. The Navier-slip condition says, simply, that there is a degree of slip at a solid boundary that depends on the magnitude of the tangential stress. We note, however, that it is generally accepted that the slip coefficient is usually very small, and then the no-slip condition (2 123) appears as an excellent approximation to (2-124) for all except regions of very high tangential stress. 

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. 

Then, we attempt to illustrate the effect of increasing the standard deviation on the average values informed as priors for the two coefficients and Bi, now markedly increased to 20%, with the initial guesses provided by the average values of the admissible limits as for the base case. It has been noticed that the convergence of the Markov chains have been affected, especially for the slip coefficients Pv and Pt. For p it is apparent that the bum in period seems to require a larger number of states (around 25,000 in this example). This behavior is also evident from the worst estimated values in Table 5, together with the wider confidence intervals, especially for the slip boundary condition coefficients. 

There are no data available on the effect of WPC density on the slip coefficient. However, it is known that polyethylene of lower density has a better traction than that of a higher density. In other words, HDPE is characterized by a low coefficients of friction, and the higher the density (specific gravity), the lower the static (and dynamic) coefficient of friction. For polyethylene density of 0.915 g/cm, coefficient of friction equals to 0.50 for 0.932 g/cm, it is equal to 0.30, and for 0.965 g/cm, it is equal to 0.10 [3]. 

Strictly speaking, coefficients of friction obtained on wet surfaces cannot be called static coefficient of friction, as by accepted definition there should be nothing between the tested surfaces that might effect the friction, including water. However, as we aim at realistic slip behavior of deck surfaces, which are directly related to safety issues, in this context there is no real difference how to call the obtained values—static coefficients of friction or slip coefficients. In any case we operate with quantitative measurements of slip resistance directly applicable to realistic situations. 

Fumed silica, grades, 146 In rice hulls, 145 Moisture content, 146 Natural, 146 Oil absorption, 146 Particle sizes, 146 Precipitated, 146 Specific gravity, 146 Specific surface area, 146 Synthetic, 146 Silicates, 87, 98, 123 Silicosis, 133 Mica, 133 Silylating agent, 85 Simple beam bending, 225 Single-screw compounder, 568 Sink/float procedure, 212, 216-218 Sisal fiber, 82, 86, 90, 110 Slip at the wall, 667 Slip coefficient, 211, 369-382 Slip enhancer, 381 Slip index, 376 Slip modifier, 381... 

Recently, Hynes et al. [221, 222] have pointed out that continuum models of rotational relaxation become unreliable when the molecule of interest rotates in a solvent comprising molecules of similar size. To improve on the model, they considered a sphere to be surrounded by a first co-ordination shell of solvent molecules. All these were taken as rough spheres, that is hard spheres which reverse their relative velocity (normal and tangential components) on impulsive collision. Of specific interest are CCI4 and SF. The test sphere and its boundary layer is surrounded by a hydrodynamic continuum. To model this, Hynes et al. used linearised hydrodynamic equations for the solvent with a modified boundary condition between solvent and test molecule, which relates the rotational stress on the test sphere to the angular velocity of the sphere. A coefficient of proportionality, 3, is introduced as a slip coefficient (j3 0... 

Slip, Coefficient of Static Friction - 0.27 DuPont Method... 

The curves show that the velocity at the membrane surface (A = 1) is 0 when is 0 as expected. As the slip velocity increases with increasing (f), the wall shear decreases, and the velocity profiles become flatter, approaching those for plug flow [12-14]. The effect of slip coefficient on axial pressure gradient (P) is as follows an increase in (j) results in a decrease in wall shear stress so that P also decreases. In addition, the transition from laminar to turbulent flow at a porous surface occurs at a Re of less than 2000, which is also the case with membrane systems. 

The effect of slip coefficient on concentration polarisation (CP) was mathematically modeled for flat membrane and tubular membrane systems [12,13,15,16]. Lowering of CP due to slip coefficient as a function of product water recovery ( ) for different normalised diffusion coefficients (a) is shown in Figure 6.8. The data show that CP decreases both with and a. Since a is a measure of particle diffusion from the membrane surface to the bulk solution, slip-flow possibly augments diffusive back-transport of particles from the membrane surface to the bulk solution. Thus, the slip-flow velocity model possibly accounts for higher or actual UF/MF flux, which is under-predicted by the gel polarisation model discussed in Chapter 1. 

Derivation of the IP-Based Slip Coefficient A key advantage of a molecular-based scheme such as DSMC is its their accuracy at higher Knudsen numbers [4]. Roohi and Darbandi [4] derived the following relation for viscosity coefficient for the range of 0.1 < Kn < 0.5 using the information preservation (IP) method ... 

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