On the no-slip boundary condition

Abstract

It has been argued that the no-slip boundary condition, applicable when a viscous fluid flows over a solid surface, may be an inevitable consequence of the fact that all such surfaces are, in practice, rough on a microscopic scale: the energy lost through viscous dissipation as a fluid passes over and around these irregularities is sufficient to ensure that it is effectively brought to rest. The present paper analyses the flow over a particularly simple model of such a rough wall to support these physical ideas.

Hydrodynamic permeability of aggregates of porous particles with an impermeable core

“…The viscosities (1)   and (2)   are, in general, different. Eq (19) reduces to the Stokes equation for large permeability k  ( (2) 2 (2) (2)…”

“…Using stream functions and eliminating the pressures from both Eqs (18) and (19) and using definitions (23) we arrive to the following fourth order partial differential equations for stream functions:…”

“…As the amount of slip is small enough for macroscopic flows, the Navier boundary condition is practically indistinguishable from the no-slip condition in the most cases on the macroscopic scale for smooth surfaces. Richardson [19] has shown that for а general Newtonian fluid flow in the immediate neighborhood of а rough solid wall the no-slip boundary condition is the relevant macroscopic boundary condition, in the sense that deviations between the results for no-slip and infinite slip are of the order of the slip length, which is unknown in the case of rough surfaces. In the case of micro or nano scale problems, the difference between the solutions for no-slip and infinite slip is of an order comparable to the dimensions of the flow, and that is they are of a special interest in micro and nanofluidics studies.…”

Apparent Slip Due to the Motion of Suspended Particles in Flows of Electrolyte Solutions

“…The first consists in performing indirect measurements, such as pressure-drop versus flow rate or squeezing rate versus resistance, and then use such measurements to infer a slip length. This procedure is indirect in the sense that it assumes that the flow resembles (2) and then equation (3), or an equivalent, is used to determine λ [7,8,10,12,13,14,15,16,17,18].…”

Effective slip lengths for immobilized superhydrophobic surfaces

“…Our mathematical derivation of the transverse flow solution is similar in spirit to that of Richardson (1973), but we have eschewed his approach based on Taylor series, since, for our class of solutions (1.3), it would require an infinite number of terms. We adopt a more function theoretic approach.…”