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.

Analytical solution of the depth-averaged flow velocity in case of submerged rigid cylindrical vegetation

Abstract: A new model for the depth-averaged velocity for flow in presence of submerged vegetation is developed. The model is based on a two-layer approach, where flow above and through the vegetation layer is described separately. Vegetation is treated as a homogeneous field of identical cylindrical stems, and the flow field is considered stationary and uniform. It is demonstrated that scaling considerations of the bulk flow field can be used to avoid complications associated with smaller scale flow processes and that still the behavior of depth-averaged flow over vegetation is described accurately. The derived scaling expression of the average flow field is simple in form, it follows fundamental laws of fluid flow, and it shows very good agreement with laboratory flume experiments. The new model can be used for quick evaluation of a river’s hydraulic response in cases where vegetated floodplains are inundated.

Creeping flow in two-dimensional networks

Abstract: We discuss creeping incompressible fluid flow in two-dimensional networks consisting of regular lattice arrays of variable-sized channels and junctions. The intended application is to low-Reynolds-number flow in models of porous media. The flow problem is reduced to an analogue linear-network problem and is solved by numerical matrix inversion. It is found that ‘effective-medium theory’ provides an excellent approximation to flow in such networks. Various qualitative features of such flows are discussed, and an elegant general form for the absolute permeability is derived. The latter, and the effective-medium approximation, are equally applicable to three-dimensional networks.

Chaotic flow and efficient mixing in a microchannel with a polymer solution

Abstract: Microscopic flows are almost universally linear, laminar, and stationary because the Reynolds number, Re, is usually very small. That impedes mixing in microfluidic devices, which sometimes limits their performance. Here, we show that truly chaotic flow can be generated in a smooth microchannel of a uniform width at arbitrarily low Re, if a small amount of flexible polymers is added to the working liquid. The chaotic flow regime is characterized by randomly fluctuating three-dimensional velocity field and significant growth of the flow resistance. Although the size of the polymer molecules extended in the flow may become comparable to the microchannel width, the flow behavior is fully compatible with that in a macroscopic channel in the regime of elastic turbulence. The chaotic flow leads to quite efficient mixing, which is almost diffusion independent. For macromolecules, mixing time in this microscopic flow can be three to four orders of magnitude shorter than due to molecular diffusion.

Density-driven unstable flows of miscible fluids in a Hele-Shaw cell

Abstract: Density-driven instabilities between miscible fluids in a vertical Hele-Shaw cell are investigated by means of experimental measurements, as well as two- and three-dimensional numerical simulations. The experiments focus on the early stages of the instability growth, and they provide detailed information regarding the growth rates and most amplified wavenumbers as a function of the governing Rayleigh number Ra. They identify two clearly distinct parameter regimes: a low-Ra, ‘Hele-Shaw’ regime in which the dominant wavelength scales as Ra−1, and a high-Ra ‘gap’ regime in which the length scale of the instability is 5±1 times the gap width. The experiments are compared to a recent linear stability analysis based on the Brinkman equation. The analytical dispersion relationship for a step-like density profile reproduces the experimentally observed trend across the entire Ra range. Nonlinear simulations based on the two- and three-dimensional Stokes equations indicate that the high-Ra regime is characterized by an instability across the gap, wheras in the low-Ra regime a spanwise Hele-Shaw mode dominates.