Capillary flow in an interior corner

Abstract

The design of fluids management processes in the low-gravity environment of space requires an accurate description of capillarity-controlled flow in containers. Here we consider the spontaneous redistribution of fluid along an interior corner of a container due to capillary forces. The analytical portion of the work presents an asymptotic formulation in the limit of a slender fluid column, slight surface curvature along the flow direction z, small inertia, and low gravity. The scaling introduced explicitly accounts for much of the variation of flow resistance due to geometry and so the effects of corner geometry can be distinguished from those of surface curvature. For the special cases of a constant height boundary condition and a constant flow condition, the similarity solutions yield that the length of the fluid column increases as t1/2 and t3/5, respectively. In the experimental portion of the work, measurements from a 2.2 s drop tower are reported. An extensive data set, collected over a previously unexplored range of flow parameters, includes estimates of repeatability and accuracy, the role of inertia and column slenderness, and the effects of corner angle, container geometry, and fluid properties. At short times, the fluid is governed by inertia (t[lsim ]tLc). Afterwards, an intermediate regime (tLc[lsim ]t[lsim ] tH) can be shown to be modelled by a constant-flow-like similarity solution. For t[ges ]tH it is found that there exists a location zH at which the interface height remains constant at a value h(zH, t)=H which can be shown to be well predicted. Comprehensive comparison is made between the analysis and measurements using the constant height boundary condition. As time increases, it is found that the constant height similarity solution describes the flow over a lengthening interval which extends from the origin to the invariant tip solution. For t[Gt ]tH, the constant height solution describes the entire flow domain. A formulation applicable throughout the container (not just in corners) is presented in the limit of long times.

Multiscale dynamic wetting of a droplet on a lyophilic pillar-arrayed surface

“…Once the MCL reached the pillars ( t = 0.52 s, figure 3b), the excess driving force forced the MCL to accelerate, making the liquid propagate much faster at the interior corner between the pillar and the substrate, known as the Concus-Finn effect (Concus & Finn 1969). In an interior corner with opening angle 2α, the equilibrium velocity could be calculated as U = fU CA = f γ LV /µ (Weislogel & Lichter 1998), where f = sin α(cos θ 0 − sin α)/S is the topological coefficient for capillary flow at the interior corner. θ 0 is the equilibrium contact angle.…”

Study of Capillary Driven Flow in an Interior Corner of Rounded Wall Under Microgravity

“…Weislogel (1996) found that the capillary flow in V-type interior corner has a constant meniscus height by drop tower experiments, namely initial meniscus height. The capillary flow in an interior corner of rounded wall is numerically simulated using FLOW-3D; the results show that like capillary flow in an interior corner of V-type, the rounded wall also has the initial meniscus height, which is …”

“…When the radius of rounded wall R 2 → ∞, the rounded wall transforms to the straight wall, the interior corner transforms to the sharp interior corner, where A is positive and proportional to h 2 (Weislogel 1996). Figure 5 χ,% …”

“…According to Weislogel (1996), the boundary condition of capillary flow in interior corner can be described as follows:…”

“…Concus-Finn condition under non-gravity, and classified capillary flow in interior corners as steady and unsteady solutions. Weislogel (1996) simplified the three dimensional Navier-Stokes equations to one dimensional case, and got the solution by introducing the lubrication approximation. For special cases of constant height boundary condition, the length of the fluid column increases in the interior corner (L ∝ t 1/2 ).…”