For the Saffman–Taylor instability, the inertia of the fluid may become important for high finger speeds. We investigate the effects of inertia on the width of the viscous fingers experimentally. We find that, due to inertia, the finger width can increase with increasing speed, contrary to what happens at small Reynolds number Re. We find that inertial effects need to be considered above a critical Weber number We. In this case it can be shown that the finger width is governed by a balance between viscous forces and inertia. This allows us to define a modified control parameter $1/B'$, which takes the corrections due to inertia into account; on rescaling the experimental data with $1/B'$, they all collapse onto the universal curve for the classical Saffman–Taylor instability. Subsequently, we try to rationalize our observations. Numerical simulations, taking into account a modification of Darcy's law to include inertia, are found to only qualitatively reproduce the experimental findings, pointing to the importance of three-dimensional effects.

Understanding the factors that control the transport of soil particles detached by water is essential in predicting the contingency of internal and surface erosion of embankments during storms and floods. It is particularly useful to be able to evaluate the sensitivity of the available soils to erosion at an early stage of a project and the risk assessment of an existing earthwork. The presented study is based on laboratory tests with a hole erosion test apparatus and tries to characterize the internal erosion of soils. The test consists of eroding a drilled soil specimen by water flow with a constant pressure drop at the boundaries of the specimen while recording the flow rate and studying the hole enlargement. A new version of the apparatus with improved instruments and an interpretation method is proposed, estimating the erosion rate based on the turbidity of the outflow and independent of hydraulic charge. Several remolded kaolinite-sand mixtures are tested as reference soil textures, and the ...

We compare quantitatively two experimental situations concerning injection of a miscible fluid into an initially jammed granular medium saturated with the same fluid, confined in a Hele-Shaw cell. The two experiments are identical, apart from the interstitial and injected fluid, which is in one case air injected into a dry granular packing, and in the other case silicone oil injected into a dense suspension. In spite of the strong differences regarding the nature of the two fluids, strikingly similar dynamical and geometrical features are identified as functions of the control parameters: cell thickness and applied fluid injection pressure. In both cases an initial hydrodynamically driven decompaction process controls the unjamming and prepares the final displacement process characterized by fingerlike patterns empty of grains. The pattern shapes are comparable. In addition, the mobilities of the coupled fluid-grain flow, rescaled by the interstitial fluid viscosity and grain diameter squared, are of the same range and behave comparably. The mobility proves to depend on the initial solid fraction of the medium. Subtle differences are observed in geometrical aspects like the finger width with respect to the control parameters.