This paper presents a finite-element simulation of the interfacial flow during propulsion of water walkers such as fishing spiders and water striders. The unsteady stroke of the driving leg is represented by a two-dimensional cylinder moving on a specified trajectory. The interface and the moving contact lines are handled by a diffuse-interface model. We explore the mechanism of thrust generation in terms of the interfacial morphology and flow structures. Results show that the most important component of the thrust is the curvature force related to the deformation of the menisci and the asymmetry of the dimple. For water walkers with thick legs, the pressure force due to the inertia of the water being displaced by the leg is also important. The viscous force is negligible. An extensive parametric study is performed on the effect of leg velocity, stroke depth, leg diameter and surface wettability. The propulsive force is insensitive to the contact angle on the leg. However, the hydrophobicity of the leg helps it detach from the surface during the recovery stroke and thus decreases the resistance. It is also important for averting or delaying penetration of the interface at large rowing velocity and depth. In two dimensions, surface waves are more efficient than vortices in transferring the momentum imparted by the leg to the water.
The effect of insoluble surface and interfacial surfactants on the inertialess instability of a two-fluid film flow down an inclined plane is investigated based on a normal mode analysis. The results reveal that the inertialess instability of relatively long waves can be predominantly weakened by a surface surfactant and enhanced by an interfacial surfactant. For sufficiently large viscosity ratio of the upper layer to the lower one, a destabilizing influence of the surface surfactant is also detected; this is thus a rare example demonstrating the possible destabilizing effect of the surfactant on the flow with a free surface. When the upper layer is less viscous and hence the instability due to the viscosity stratification disappears, a new instability can be triggered by the presence of an interfacial surfactant. Both the surfactants on the surface and the interface can stabilize or destabilize the short-wave instabilities, which occur for negligible surface and interfacial tensions.
We report numerical simulations of wicking through micropores of two types of geometries, axisymmetric tubes with contractions and expansions of the cross section, and two-dimensional planar channels with a Y-shaped bifurcation. The aim is to gain a detailed understanding of the interfacial dynamics in these geometries, with an emphasis on the motion of the three-phase contact line. We adopt a diffuse-interface formalism and use Cahn-Hilliard diffusion to model the moving contact line. The Stokes and Cahn-Hilliard equations are solved by finite elements with adaptive meshing. The results show that the liquid meniscus undergoes complex deformation during its passage through contraction and expansion. Pinning of the interface at protruding corners limits the angle of expansion into which wicking is allowed. For sufficiently strong contractions, the interface negotiates the concave corners, thanks to its diffusive nature. Capillary competition between branches downstream of a Y-shaped bifurcation may result in arrest of wicking in the wider branch. Spatial variation of wettability in one branch may lead to flow reversal in the other.
Effects of insoluble surfactants on the stability of film flow driven by an oscillatory plate are investigated in the limit of long-wavelength perturbations. Two particular Floquet modes are identified and the corresponding growth rates are obtained by solving a quadratic equation. Results show that the oscillatory film flow can be stabilized by surface surfactant in the sense of raising the critical Froude number and narrowing the bandwidths of the unstable frequencies.
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