Related papers: Walking Droplets Through the Lens of Dynamical Sys…
Viscoelastic materials containing bubbles or drops are encountered in numerous application fields, and are presently the object of much interest. The motion of bubbles and drops in these matrices can be significantly different than in…
We consider a thin droplet that spreads over a flat, horizontal and chemically heterogeneous surface. The droplet is subjected to changes in its volume though a prescribed, arbitrary spatiotemporal function, which varies slowly and vanishes…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
The applications and impact of high fidelity simulation of fluid flows are far-reaching. They include settling some long-standing and fundamental questions in turbulence. However, the computational resources required for such efforts are…
Cavitation and bubble dynamics are central concepts in engineering, the natural sciences, and the mathematics of fluid mechanics. Due to the nonlinear nature of their dynamics, the governing equations are not fully solvable. Here, the…
For a system to qualify as a quantum fluid, quantum-statistical effects should operate in addition to quantum-mechanical ones. Here, we address the hitherto unexplored dynamical condition for the quantum-statistical effects to be…
Hypothesis: Droplet coalescence process is important in many applications and has been studied extensively when two droplets are surrounded by gas. However, the coalescence dynamics would be different when the two droplets are surrounded by…
I examine contemporary work in fluids in motion to demonstrate strong connections between art, science and technology. In one burgeoning domain, falling liquid drops impacting solid substrates or pools it is valuable to compare how artists…
Dynamics in glassy systems near the phase transition is characterized by particle jumps. Approaches to describe these dynamics are based on models in which the time and length scales defining the jumps are parameters to be determined. We…
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…
Whirling and swerving, a bacterium is swimming in a test tube, foraging for food. On the surface of a vibrating bath, a droplet starts walking. A certain similarity, but mostly dissimilarity, between the physical memory that emerges in…
Granular simulations are used to probe the particle scale dynamics at short, intermediate, and long time scales for gravity driven, dense granular flows down an inclined plane. On approach to the angle of repose, where motion ceases, the…
Multiphase fluid dynamics, such as falling droplets and rising bubbles, are critical to many industrial applications. However, simulating these phenomena efficiently is challenging due to the complexity of instabilities, wave patterns, and…
The motion of the three-phase contact line between two immiscible fluids and a solid surface arises in a variety of wetting phenomena and technological applications. One challenge in continuum theory is the effective representation of…
We study the pairwise interactions of drops in an applied uniform DC electric field within the framework of the leaky dielectric model. We develop three-dimensional numerical simulations using the boundary integral method and an analytical…
A new class of walking droplets, coined superwalkers, has been observed when a bath of silicone oil is vibrated simultaneously at a given frequency and its subharmonic tone with a relative phase difference between them~[1]. In this paper,…
The interaction of 'walking droplets' and capillary waves in a weakly subcritical Faraday wave experiment has been studied as a hydrodynamic analog to Bohmian quantum mechanics (see "Hydrodynamic Quantum Analogs", J. Bush and A. Oza, Rep.…
We propose a simple model to analyze the traffic of droplets in microfluidic ``dual networks''. Such functional networks which consist of two types of channels, namely those accessible or forbidden to droplets, often display a complex…
We study the motion of a two-dimensional droplet on an inclined surface, under the action of gravity, using a diffuse interface model which allows for arbitrary equilibrium contact angles. The kinematics of motion is analysed by decomposing…
Many disordered systems show a superdiffusive dynamics, intermediate between the diffusive one, typical of a classical stochastic process, and the so called ballistic behaviour, which is generally expected for the spreading in a quantum…