Mesoscopic two-phase model for describing apparent slip in micro-channel flows

Abstract

The phenomenon of apparent slip in micro-channel flows is analyzed by means of a two-phase mesoscopic lattice Boltzmann model including non-ideal fluid-fluid and fluid-wall interactins. The weakly-inhomogeneous limit of this model is solved analytically. The present mesoscopic approach permits to access much larger scales than molecular dynamics, and comparable with those attained by continuum methods. However, at variance with the continuum approach, the existence of a gas layer near the wall does not need to be postulated a priori, but emerges naturally from the underlying non-ideal mesoscopic dynamics. It is therefore argued that a mesoscopic Lattice Boltzmann approach with non-ideal fluid-fluid and fluid-wall interactions might achieve an optimal compromise between physical realism and computational efficiency for the study of channel micro-flows.PACS numbers: 47.55. Dz,47.55.Kf, 47.11+j, 83.50.Rp, The microscopic physics underlying fluid/solid interactions is fairly rich and complex, for it depends on specific details of molecular interactions as well as on the micro-geometrical details of the boundary. However, on a macroscopic scale, these details can often be safely ignored by assuming that the net effect of surface interactions is simply to prevent any relative motion between the solid walls and the fluid elements next to them. This is the so-called "no-slip" boundary condition, which forms the basis of mathematical treatments of bounded flows as continuum media [1]. No-slip boundary conditions are extremely successful in describing a huge class of viscous flows. Yet, the evidence is that certain classes of viscous flows do slip on the wall. Recent advances in microfluidics experiments [2,3], as well as numerical investigations [4,5,6,7,8], have identified the conditions which seem to underlie the validity of the no-slip assumption. Namely: (i) single-phase flow; (ii) wetted surfaces and (iii) low levels of shear rates. Under such conditions, careful experiments have shown that fluid comes to rest within a few molecular diameters from the surface [9,10,11,12]. Conditions (i-iii) are not exhaustive, though. For instance, partial slips of simple (Newtonian) flows, such as alkanes and water, is predicted by an increasing number of experiments [13,14,15,16] and simulations [4,5,6,7,8] (see [17] for a review on experiments and numerics). Under this state of affairs, there appears to be a great need to provide a convincing, and possibly general, theoretical picture for the onset of slip motion. Among others, an increasingly popular explanation is that the flowing fluid would develop a lighter (less dense) phase and dynamically segregate it in the form of a thin film sticking to the wall [18,19]. This thin film would then provide a "gliding" surface for the bulk fluid which would slip on it without ever coming in contact with the solid wall. This gives rise to the so-called apparent slip phenomenon, that is, the extrapolated bulk flow speed would vanish far-out away from the wall, even though the actual flow s...

Implications of hydrophobic interactions and consequent apparent slip phenomenon on the entrance region transport of liquids through microchannels

“…Their results clearly suggest that the apparent fluid slip experimentally observed in microchannels with hydrophobic surfaces may arise from either the presence of nanobubbles or a layer of low density fluid at the surface. [8][9][10][11] Motivated by the intriguing influences of the consequent apparent slip phenomenon, researchers have been in a continuous endeavor to understand the detailed mechanism of nanobubble formation in micro-nanofluidic conduits. It is often argued that the interfacial shear mechanisms may induce nucleation of vapor bubbles.…”

Flow past superhydrophobic surfaces with cosine variation in local slip length

“…Slip over hydrophobic surfaces is commonly modeled by the introduction of a phenomenological repulsive force [40][41][42][43][44]. The magnitude of interactions between different fluid components and surfaces, as determined by simulation parameters, allows us to specify arbitrary contact angles [40,[45][46][47].…”

Mobility tensor of a sphere moving on a superhydrophobic wall: application to particle separation

“…To address the problem, one may exploit system (10)(11)(12) by noticing that the equations for x(t) and h(t) are y-independent. Hence the system can be first solved for the unknowns x(t) and h(t) for a constant force F 1 = 1, F 3 = 0, as in § 5.1.…”

“…1). All the typical length scales (particle radius, wall pattern length, and particle-wall gap) considered here are on the order of micrometers, sufficiently large to describe the fluid as a continuum obeying the Navier-Stokes equations [8,9,10,11,12] with no slippage at the solid wall [13,14,15,16,17,18,19]. Our model corresponds to the real case of sufficiently deep grooves where it can be safely assumed perfect-slip at the liquid-gas interface, see e.g.…”