相关论文: Exact solutions for a periodic assembly of bubbles…

Analytical solutions are constructed for an assembly of any finite number of bubbles in steady motion in a Hele-Shaw channel. The solutions are given in the form of a conformal mapping from a bounded multiply connected circular domain to…

Exact solutions are presented for a doubly-periodic array of steadily moving bubbles in a Hele-Shaw cell when surface tension is neglected. It is assumed that the bubbles either are symmetrical with respect to the channel centreline or have…

Exact solutions are reported for a stream of asymmetric bubbles steadily moving in a Hele-Shaw channel. From the periodicity along the streamwise direction, the flow region is reduced to a rectangular unit cell containing one bubble, which…

Analytical solutions for both a finite assembly and a periodic array of bubbles steadily moving in a Hele-Shaw channel are presented. The particular case of multiple fingers penetrating into the channel and moving jointly with an assembly…

We present a unified numerical method to determine the shapes of multiple Hele-Shaw bubbles in steady motion, and in the absence of surface tension, in three planar domains: free space, the upper half-plane, and an infinite channel. Our…

Deformable bubbles propagated by the flow of a viscous liquid in a planar Hele-Shaw channel of uniform depth tend to travel steadily along the channel's streamwise axis and pairs of neighbouring bubbles will either separate or coalesce…

New numerical solutions to the so-called selection problem for one and two steadily translating bubbles in an unbounded Hele-Shaw cell are presented. Our approach relies on conformal mapping which, for the two-bubble problem, involves the…

Consider the motion of a thin layer of electrically conducting fluid, between two closely spaced parallel plates, in a classical Hele-Shaw geometry. Furthermore, let the system be immersed in a uniform external magnetic field (normal to the…

A new general class of exact solutions is presented for the time evolution of a bubble of arbitrary initial shape in a Hele-Shaw cell when surface tension effects are neglected. These solutions are obtained by conformal mapping the viscous…

Motivated by the desire to understand complex transient behaviour in fluid flows, we study the dynamics of an air bubble driven by the steady motion of a suspending viscous fluid within a Hele-Shaw channel with a centred depth perturbation.…

We study the dynamics of two air bubbles driven by the motion of a suspending viscous fluid in a Hele-Shaw channel with a small elevation along its centreline via physical experiment and numerical simulation of a depth-averaged model. For a…

Using a vortex sheet method we prove global existence of a near circular initial bubble in a Hele-Shaw cell with surface tension and generally finite nonzero viscosity ratio between fluids inside and outside the bubble. The circular shape…

We hypothesize that dynamical systems concepts used to study the transition to turbulence in shear flows are applicable to other transition phenomena in fluid mechanics. In this paper, we consider a finite air bubble that propagates within…

We construct steady non-spherical bubbles and drops, which are traveling wave solutions to the axisymmetric two-phase Euler equations with surface tension, whose inner phase is a bounded connected domain. The solutions have a uniform…

Bubbles of inviscid fluid surrounded by a viscous fluid in a Hele-Shaw cell can merge and break-off. During the process of break-off, a thinning neck pinches off to a universal self-similar singularity. We describe this process and reveal…

We present a new way to construct analytical solutions for flow in complex microfluidic channel networks, as well as planar disordered media. Using a combination of Schwarz-Christoffel maps and segmentation techniques inspired by integrated…

We study the propagation of finite bubbles in a Hele-Shaw channel, where a centred occlusion (termed a rail) is introduced to provide a small axially-uniform depth constriction. For bubbles wide enough to span the channel, the system's…

In this paper we deal with the numerical solution of a Hele--Shaw-like system via a cell model with active motion. Convergence of approximations is established for well-posed initial data. These data are chosen in such a way the time…

We study the dynamics of two-component Bose-Einstein condensates in periodic potentials in one dimension. Elliptic potentials which have the sinusoidal optical potential as a special case are considered. We construct exact nonstationary…

We develop a systematic method to derive all orders of mode couplings in a weakly nonlinear approach to the dynamics of the interface between two immiscible viscous fluids in a Hele-Shaw cell. The method is completely general. It includes…