Slip-loop model

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... 

Physically, the hysteresis roots in that fact that the effect of the electric force on the stability of 1D conduction is different in different parts of the diffusion layer. Indeed, this force stabilizes ID conduction in the electroneutral bulk and in the quasi-equUibrium portion of EDL and destabilizes it in the ESC region. The nonlinear flow resulting from this instability reduces concentration polarization and, thus, weakens the hampering effect of the electric force in the bulk in the down way portion of the hysteresis loop. In order to verify this mechanism, a model electroosmotic formulation without electric force term in the Stokes equation was analyzed. As illustrated in Fig. 8, this modification results in shrinking of the hysteresis loop. The bifurcation still remains subcritical and the hysteresis loop still exists owing to the hampering effect of the electric force in the quasi-equilibrium portion of the EDL, implicit in the first term in the electroosmotic slip conditions (21). 

An alternative suggestion," similar to the Rubinstein-Colby model, is to determine the rate of CR self-consistently by an iterative procedure. One can run a single-chain simulation and measure the distribution of release times, then start deleting the slip-links according to this distribution. Since the CR affects the rate of chain diffusion, one should repeat this loop several times to achieve self-consistency. This algorithm should lead to exactly the same results however, it is more difficult to implement, especially for polydisperse systems. In this chapter, we shall use the algorithm described in the previous paragraph. 

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