Related papers: Interface dynamics in Hele-Shaw flows with centrif…
The interface shape of a fluid in rigid body rotation about its axis and partially filling the container is often the subject of a homework problem in the first graduate fluids class. In that problem, surface tension is neglected, the…
The aim of this work is to study the dynamics and stability of soft shape-morphing configurations and specifically the modes of interaction between the front and rear airfoil segments. Initially we present several steady-state solutions,…
We study convection in a volumetrically heated fluid which is cooled from both plates and is under rotation through the use of direct numerical simulations. The onset of convection matches similar systems and predictions from asymptotic…
Using air to displace a viscous fluid contained in Hele-Shaw cell can create a fingering pattern at the interface between the fluids, if the capillary number exceeds a critical value. This Saffman-Taylor instability is revisited for the…
The exact analytic solution is built for the plane flow of incompressible fluid through the wheel with profiles of blades approximating logarithmic spirals.
Within a class of exact time-dependent non-singular N-logarithmic solutions (Mineev-Weinstein and Dawson, Phys. Rev. E 50, R24 (1994); Dawson and Mineev-Weinstein, Phys. Rev. E 57, 3063 (1998)), we have found solutions which describe the…
The formation of singularities on a free surface of a conducting ideal fluid in a strong electric field is considered. It is found that the nonlinear equations of two-dimensional fluid motion can be solved in the small-angle approximation.…
Droplet migration in a Hele--Shaw cell is a fundamental multiphase flow problem which is crucial for many microfluidics applications. We focus on the regime at low capillary number and three-dimensional direct numerical simulations are…
The linear stability of miscible displacement for radial source flow at infinite P\'eclet number in a Hele-Shaw cell is calculated theoretically. The axisymmetric self-similar flow is shown to be unstable to viscous fingering if the…
The linear instability of Faraday waves in Hele-Shaw cells is investigated with consideration of the viscosity of fluids after gap-averaging the governing equations due to the damping from two lateral walls and the dynamic behavior of…
We study the combined effects of natural convection and rotation on the dissolution of a solute in a solvent-filled circular cylinder. The density of the fluid increases with the increasing concentration of the dissolved solute, and we…
We demonstrate experimentally the existence of a purely elastic fingering instability which arises when air penetrates into an elastomer confined in a Hele-Shaw cell. Fingers appear sequentially and propagate within the bulk of the material…
Direct numerical simulations of spanwise-rotating turbulent channel flow with a parabolic bump on the bottom wall are employed to investigate the effects of rotation on flow separation. Four rotation rates of $Ro_b := 2\Omega H/U_b = \pm…
Using a specially designed experimental set up, we have studied the so-called continuous to intermittent flow transition in sand piles confined in a Hele-Shaw cell where the deposition height of the sand can be controlled. Through…
The Saffman-Taylor viscous fingering instability occurs when a less viscous fluid displaces a more viscous one between narrowly spaced parallel plates in a Hele-Shaw cell. Experiments in radial flow geometry form fan-like patterns, in which…
Hele-Shaw flows with time-dependent gaps create fingering patterns, and magnetic fluids in Hele-Shaw cells create intriguing patterns.We propose a simple numerical method for Hele-Shaw type problems by the method of fundamental…
We present a theoretical study on pattern formation occurring in miscible fluids reacting by a second-order reaction $A + B \to S$ in a vertical Hele-Shaw cell under constant gravity. We have recently reported that concentration-dependent…
We are concerned with a model describing the motion of two compressible, immiscible fluids with density-dependent viscosity in the whole $\mathbb R^3$. The phases of the flow may have different pressure and viscosity laws and are separated…
The conditions in which meridional recirculations appear in swirling flows above a fixed wall are analysed. In the classical Bodew\"adt problem, where the swirl tends towards an aysmptotic value away from the wall, the well-known "tea-cup…
We report direct experimental observations of self-organized rotating flames of premixed CH4 and air in an open circular Hele-Shaw burner equipped with an annulus cavity flame holder. These flames formed spontaneously at sufficiently low…