Shear flow near solids: Epitaxial order and flow boundary conditions

Thompson, Peter A.; Robbins, Mark O.

doi:10.1103/physreva.41.6830

Cited by 737 publications

(723 citation statements)

References 21 publications

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“…Early simulations showed no-slip except near contact lines [94,156]. More recent investigations have reported that molecular slip increases with decreasing liquid-solid interactions [7,35,114], liquid density [95,157], density of the wall [158], and decreases with pressure [7]. The model for the solid wall, the wall-fluid commensurability and the molecular roughness were also found to strongly influence slip [7,14,55,82,151,158].…”

Section: Resultsmentioning

confidence: 93%

Microfluidics: The No-Slip Boundary Condition

Lauga

Brenner

Stone

2007

Springer Handbook of Experimental Fluid Mechanics

591

674

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The no-slip boundary condition at a solid-liquid interface is at the center of our understanding of fluid mechanics. However, this condition is an assumption that cannot be derived from first principles and could, in theory, be violated. In this chapter, we present a review of recent experimental, numerical and theoretical investigations on the subject. The physical picture that emerges is that of a complex behavior at a liquid/solid interface, involving an interplay of many physico-chemical parameters, including wetting, shear rate, pressure, surface charge, surface roughness, impurities and dissolved gas.

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Section: Resultsmentioning

confidence: 93%

Microfluidics: The No-Slip Boundary Condition

Lauga

Brenner

Stone

2007

Springer Handbook of Experimental Fluid Mechanics

591

674

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“…Solutions (14) and (15) should be substituted into boundary condition (13). The latter results in the following equation for the unknown velocity at the interface:…”

Section: Boundary Conditions At Porous/liquid Interfacesmentioning

confidence: 99%

“…An improved understanding of the effect of the fluid-solid interaction on flows over rough solid surfaces has received а considerable attention [13][14][15][16]. Molecular dynamics simulations by Qian et.…”

mentioning

confidence: 99%

Hydrodynamic permeability of aggregates of porous particles with an impermeable core

Deo

Филиппов

Tiwari

et al. 2011

Advances in Colloid and Interface Science

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“…This may be expressed ∆V = L sγ where ∆V is the slip velocity of the fluid at the wall,γ is the rate of shear at the wall and L s is a [Thompson & Robbins 1990] have shown this to be the case under some circumstances. In fact recent work [Thompson & Troian 1997] has shown that, in cases where the shear rate is large, there is a nonlinear relationship between L s andγ.…”

Section: Discussion and A Possible Modificationmentioning

confidence: 99%

Pressure determinations for incompressible fluids and magnetofluids

Kress

Montgomery

2000

J. Plasma Phys.

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Certain unresolved ambiguities surround pressure determinations for incompressible flows, both Navier-Stokes and magnetohydrodynamic. For uniform-density fluids with standard Newtonian viscous terms, taking the divergence of the equation of motion leaves a Poisson equation for the pressure to be solved. But Poisson equations require boundary conditions. For the case of rectangular periodic boundary conditions, pressures determined in this way are unambiguous. But in the presence of "no-slip" rigid walls, the equation of motion can be used to infer both Dirichlet and Neumann boundary conditions on the pressure P , and thus amounts to an over-determination. This has occasionally been recognized as a problem, and numerical treatments of wall-bounded shear flows usually have built in some relatively ad hoc dynamical recipe for dealing with it, often one which appears to "work" satisfactorily. Here we consider a class of solenoidal velocity fields which vanish at no-slip walls, have all spatial derivatives, but are simple enough that explicit analytical solutions for P can be given. Satisfying the two boundary conditions separately gives two pressures, a "Neumann pressure" and a "Dirichlet pressure" which differ non-trivially at the initial instant, even before any dynamics are implemented. We compare the two pressures, and find that in particular, they lead to different volume forces near the walls. This suggests a reconsideration of no-slip boundary conditions, in which the vanishing of the tangential velocity at a no-slip wall is replaced by a local wall-friction term in the equation of motion.

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Shear flow near solids: Epitaxial order and flow boundary conditions

Cited by 737 publications

References 21 publications

Microfluidics: The No-Slip Boundary Condition

Microfluidics: The No-Slip Boundary Condition

Hydrodynamic permeability of aggregates of porous particles with an impermeable core

Pressure determinations for incompressible fluids and magnetofluids

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