Hele-Shaw flow

About: Hele-Shaw flow is a research topic. Over the lifetime, 5451 publications have been published within this topic receiving 151320 citations.

Plane Poiseuille flow of miscible layers with different viscosities: instabilities in the Stokes flow regime

Abstract: We investigate the linear stability of miscible, viscosity-layered Poiseuille flow. In the Stokes flow regime, diffusion is observed to have a destabilizing effect very similar to that of inertia in finite-Reynolds-number flows. For two-layer flows, four types of instability can dominate, depending on the interface location. Two interfacial modes exhibit large growth rates, while two additional bulk modes grow more slowly. Three-layer Stokes flows give rise to diffusive modes for each interface. These two diffusive interface modes can be in resonance, thereby enhancing the growth rate. Furthermore, modes without inertia and diffusion are also observed, consistent with a previous long-wave analysis for sharp interfaces. In contrast to that earlier investigation, the present analysis demonstrates that instability can also occur when the more viscous layer is in the centre, at larger wavenumbers.

Optical Stokes Flow Estimation: An Imaging-Based Control Approach

Abstract: We present an approach to particle image velocimetry based on optical flow estimation subject to physical constraints. Admissible flow fields are restricted to vector fields satifying the Stokes equation. The latter equation includes control variables that allow to control the optical flow so as to fit to the apparent velocities of particles in a given image pair. We show that when the real unknown flow observed through image measurements conforms to the physical assumption underlying the Stokes equation, the control variables allow for a physical interpretation in terms of pressure distribution and forces acting on the fluid. Although this physical interpretation is lost if the assumptions do not hold, our approach still allows for reliably estimating more general and highly non-rigid flows from image pairs and is able to outperform cross-correlation based techniques. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

On the amplification of small disturbances in a channel flow with a normal magnetic field

Abstract: Optimal perturbations are investigated in a magnetohydrodynamic flow bounded by perfectly insulating or conducting walls. The parallel channel flow submitted to uniform, normal magnetic field is taken as an example. The stability equations (linearized Navier–Stokes and Maxwell equations) are solved simultaneously, because of the natural existence of a coupling between them. Exponential instability is studied first to set ideas and to fix some reference magnetic Prandtl and magnetic Reynolds numbers. Then, optimal perturbations are searched for by employing the approach first proposed by Butler and Farrell [Phys. Fluids A 4, 1637 (1992)]. The shape of the optimally perturbed velocity is poorly affected by the magnetic field; however, the magnetic field is found to stabilize both exponential instability and algebraically growing perturbations. The critical Reynolds numbers in the presence of magnetic fields can be very large and it is thus possible to find very significant transient growth in subcritical co...

Two-dimensional laminar flow of a power-law fluid across a confined square cylinder

Abstract: Two-dimensional laminar flow of power-law fluids past a long square cylinder confined in a planar channel is investigated numerically for the range of conditions as 60 ≤ R e ≤ 160 , 0.5 ≤ n ≤ 1.8 and β = 1 / 6 , 1 / 4 , and 1/2. A semi-explicit finite volume method is used on a non-uniform collocated grid arrangement. The third order QUICK scheme and the second-order central difference scheme are used to discretize the convective and diffusive terms respectively. Depending upon the value of blockage ratio, power-law index and Reynolds number, the nature of flow in the above range of conditions is either steady or unsteady (periodic in time). An increase in the blockage ratio delays the onset of vortex shedding to higher Reynolds number in both shear-thinning and shear-thickening fluids whereas it advances the occurrence of the quasi-periodicity in flow to lower Reynolds numbers in shear-thinning fluids. Extensive numerical results are presented to elucidate the effects of blockage, power-law index and Reynolds number on the drag coefficient, stream function, vorticity, Strouhal number and amplitudes of drag and lift coefficients in the unsteady flow regime.

Modulation of large-scale structures by neutrally buoyant and inertial finite-size particles in turbulent Couette flow

Abstract: Particle-resolved numerical simulations based on the Force Coupling Method are carried out to study the effect of finite-size particles on turbulent plane Couette flow. The Reynolds number is close to the laminar-turbulent transition, such that large scale rotational structures are well developed and self-sustained. The study particularly considers the effect of concentration, particle size and particle-to-fluid density ratio on the mixture flow features. Time averaged profiles, in the wall-normal direction, of the mean flow and Reynolds stress components reveal that there is no significant difference between single phase and two-phase flows at equivalent effective Reynolds number, except that the wall shear stress is higher for the two-phase flow. However temporal and modal analysis of flow fluctuations, suggest that besides injecting small scale perturbation due to their rigidity, particles have an effect on the regeneration cycle of turbulence. Indeed, the shape of the streaks and the intermittent character of the flow (amplitude and period of oscillation of the modal fluctuation energy) are all altered by the particle presence, and especially by the inertial ones