arXiv subjects

Paul H. Steen

Publications and source records attributed to Paul H. Steen.

4 recordsLinked to original sources

arXiv2020

Sweeping by Sessile Drop Coalescence

During coalescence of liquid drops contacting a solid, the liquid sweeps wetted and solid-projected areas. The extent of sweeping dictates the performance of devices such as self-cleaning surfaces, anti-frost coatings, water harvesters, and dropwise condensers. For these applications, weakly- and non-wetting solid substrates are preferred as they enhance drop dynamical behavior. Accordingly, our coalescence studies here are restricted to drops with contact angle 90° $\le θ_{0} \le$ 180°. Binary sessile drop coalescence is the focus, with volume of fluid simulations employed as the primary tool. The simulations, which incorporate a Kistler dynamic contact angle model, are first validated against three different experimental substrate systems and then used to study the influence of solid wettability on sweeping by modifying $θ_{0}$. With increasing $θ_{0}$ up to 150°, wetted and projected swept areas both increase as drop center of mass heightens. For $θ_{0} \ge$ 150°, coalescence-induced drop jumping occurs owing to the decreasing wettability of the substrate and a focusing of liquid momentum due to the symmetry-breaking solid. In this regime, projected swept area continues to increase with $θ_0$ while wetted swept area reaches a maximum and then decreases. The sweeping results are interpreted using the mechanical energy balance from hydrodynamic theory and also compared to free drop coalescence.

physics.flu-dyn↗

arXiv2019

The winner takes all: Volume-scavenging populations of networked droplets

In this work we present and analyze a fluid-mechanical model of competition (scavenging) amongst $N$ liquid droplets (individual competitors). The eventual outcome of this competition depends sensitively on the average resource (volume) per individual $\overline{V}$. For abundant resource, $\overline{V}>1$, there is one winner only and that winner eventually scavenges all or most of the resource. In the socio-economic realm this is is known as the "winner-take-all" outcome: A disproportionately large reward falls to one or a few winners, even though other competitors start out with comparable (or even slightly more) resource and perform only marginally worse. The losing competitors are not rewarded. For less than abundant resource, $\overline{V}<1$, an outcome with resource that is evenly partitioned amongst the $N$ droplets becomes possible. This is the "all-share-evenly" or egalitarian outcome. For sufficiently scarce resource the egalitarian outcome is the only one that can occur. In addition to predicting what kind and how many winners, our analysis shows that once an individual's resource (droplet volume) falls below a fixed threshold, that individual can neither recover nor emerge as winner. This is the "once down-and-out, always down-and-out" outcome. Selected simulations suggest that the winner depends sensitively on population size and the "trading friction" or inefficiency of resource exchange between individuals (liquid rheology). Of all feasible rest states (equilibria), only certain ones are reachable (stable equilibria). Friction turns out to strongly influence the time to reach an end state (stable equilibrium), in surprising ways. Besides the end states, our analysis reveals an array of rest states, ordered in hierarchies of more versus less costly (energetic) outcomes.

physics.flu-dyn↗

arXiv2016

Dynamics of sessile drops. Part 3. Theory of forced oscillations

A partially-wetting sessile drop is driven by a sinusoidal pressure field that produces capillary waves on the liquid/gas interface. The analysis presented in Part 1 of this series (Bostwick & Steen 2014) is extended by computing response diagrams and phase shifts for the viscous droplet, whose three phase contact-line moves with contact-angle that is a smooth function of the contact line speed. Viscous dissipation is incorporated through the viscous potential flow approximation and the critical Ohnesorge number bounding regions beyond which a given mode becomes over-damped is computed. Davis dissipation originating from the contact-line speed condition leads to damped oscillations for drops with finite contact-line mobility, even for inviscid fluids. The critical mobility and associated driving frequency to generate the largest Davis dissipation is computed. Lastly, regions of modal coexistence where two modes can be simultaneously excited by a single forcing frequency are identified. Predictions compare favorably to related experiments on vibrated drops.

physics.flu-dyn↗

arXiv2013

Excited Sessile Drops Dance Harmonically

In our fluid dynamics video, we demonstrate our method of visualizing and identifying various mode shapes of mechanically oscillated sessile drops. By placing metal mesh under an oscillating drop and projecting light from below, the drop's shape is visualized by the visually deformed mesh pattern seen in the top view. The observed modes are subsequently identified by their number of layers and sectors. An alternative identification associates them with spherical harmonics, as demonstrated in the tutorial. Clips of various observed modes are presented, followed by a 10-second quiz of mode identification.

physics.flu-dyn↗