Role of Mixed Boundaries on Flow in Open Capillary Channels with Curved Air–Water Interfaces

Abstract

Flow in unsaturated porous media or in engineered microfluidic systems is dominated by capillary and viscous forces. Consequently, flow regimes may differ markedly from conventional flows, reflecting strong interfacial influences on small bodies of flowing liquids. In this work, we visualized liquid transport patterns in open capillary channels with a range of opening sizes from 0.6 to 5.0 mm using laser scanning confocal microscopy combined with fluorescent latex particles (1.0 μm) as tracers at a mean velocity of ∼0.50 mm s(-1). The observed velocity profiles indicate limited mobility at the air-water interface. The application of the Stokes equation with mixed boundary conditions (i.e., no slip on the channel walls and partial slip or shear stress at the air-water interface) clearly illustrates the increasing importance of interfacial shear stress with decreasing channel size. Interfacial shear stress emerges from the velocity gradient from the adjoining no-slip walls to the center where flow is trapped in a region in which capillary forces dominate. In addition, the increased contribution of capillary forces (relative to viscous forces) to flow on the microscale leads to increased interfacial curvature, which, together with interfacial shear stress, affects the velocity distribution and flow pattern (e.g., reverse flow in the contact line region). We found that partial slip, rather than the commonly used stress-free condition, provided a more accurate description of the boundary condition at the confined air-water interface, reflecting the key role that surface/interface effects play in controlling flow behavior on the nanoscale and microscale.

Effect of a surface tension gradient on the slip flow along a superhydrophobic air-water interface

“…It is interesting that, the slip at the side area was also observed to remain opposite to the main flow direction even at the central area, far away from the head wall. Although the reversed slip flow was not observed either by Bolognesi et al [19] or Schaffel et al [41] in the presence of surfactants in a closed microchannel, this phenomenon has been noticed at an air-water interface exposed to the outside at an open channel [22,23]. Nevertheless the details of the reverse flow have not been further investigated up to now.…”

“…It should be noted, however, that the expected drag reduction or slip velocity at the superhydrophobic surfaces was not obtained according to a growing body of work. It was postulated that the air-water interface cannot be treated as shear free in some cases, but that a finite shear stress can exist at the air-water interface especially in the presence of surfactants, particles or other surface-active agents [19][20][21][22][23][24][25][26]. In an open channel, Yang et al [24] found that the no-slip boundary condition at the air-water interface was in better agreement with the experimental data than the shear-free boundary condition.…”

Evidence of slippage breakdown for a superhydrophobic microchannel

“…Lazouskaya et al 24 were the first to report a reduced mobility at the liquidair interface in an open capillary channel, questioning the validity of the no-shear boundary condition at the meniscus interface. More recently, the same research group performed new experiments with a very similar geometry 29 and highlighted the dependence of an effective interfacial shear stress on the channel dimensions. Particularly, for channel width below the water capillary length (i.e., 2.7 mm), the interfacial shear stress increases as the channel size decreases.…”

Modeling Microorganism Transport and Survival in the Subsurface

“…In general, hydrodynamic forces are expected to be more important for microbe retention on the AWI than the SWI due to differences in the boundary conditions. In particular, the SWI is typically considered to be a no-slip boundary condition (the water velocity is zero at the SWI), whereas the AWI is commonly assumed to be a partial-slip (non-zero water velocity at the AWI) or perfect-slip (the water velocity is unaffected by the AWI) boundary condition (Bird et al, 2002;Zheng et al, 2012). Adhesive interactions on the AWI are controlled by hydrophobic, electrostatic, and capillary forces.…”