A plane‐strain hydraulic fracture driven by a shear‐thinning Carreau fluid
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The propagation of fluid driven fractures is used in a number of industrial applications (well stimulation of unconventional reservoirs, development of deep geothermal systems) but also occurs naturally (magmatic dyke intrusion). While the mechanics of hyd ...
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In impermeable media, a hydraulic fracture can continue to expand even without additional fluid injection if its volume exceeds the limiting volume of a hydrostatically loaded radial fracture. This limit depends on the mechanical properties of the surround ...
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In viscous fluids, motile microentities such as bacteria or artificial swimmers often display different transport modes than macroscopic ones. A current challenge in the field aims at using friction asymmetry to steer the motion of microscopic particles. H ...
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We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers, in the salient di ...
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Hydraulic fracturing is a widespread technology used to enhance reservoir production but also to measure the in-situ stress field. It consists of growing a tensile (mode I) fracture via the injection of a viscous fluid (usually at a constant rate) from a w ...
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Buoyant hydraulic fractures occur in nature as magmatic dikes and sills. In industrial applications like well stimulation, the emergence of buoyant fractures is undesirable and often limited by the injected volume and/or variation of in-situ stress. This c ...
