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Register a new userElastic deformations driven by non-uniform lubrication flows
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The ability to create dynamic deformations of micron-sized structures is relevant to a wide variety of applications such as adaptable optics, soft robotics, and reconfigurable microfluidic devices. In this work we examine non-uniform lubrication flow as a mechanism to create complex deformation fields in an elastic plate. We consider a Kirchoff-Love elasticity model for the plate and Hele-Shaw flow in a narrow gap between the plate and a parallel rigid surface. Based on linearization of the Reynolds equation, we obtain a governing equation which relates elastic deformations to gradients in non-homogenous physical properties of the fluid (e.g. body forces, viscosity, and slip velocity). We then focus on a specific case of non-uniform Helmholtz-Smoluchowski electroosmotic slip velocity, and provide a method for determining the zeta-potential distribution necessary to generate arbitrary static and quasi-static deformations of the elastic plate. Extending the problem to time-dependent solutions, we analyze transient effects on asymptotically static solutions, and finally provide a closed form solution for a Greens function for time periodic actuations.
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We present a detailed comparison of the rheological behaviour of sheared sediment beds in a pressure-driven, straight channel configuration based on data that was generated by means of fully coupled, grain-resolved direct numerical simulations and experimental measurements reviously published by Aussillous {it et al.} (J. Fluid Mech., vol. 736, 2013, pp. 594-615). The highly-resolved simulation data allows to compute the stress balance of the suspension in the streamwise and vertical directions and the stress exchange between the fluid and particle phase, which is information needed to infer the rheology, but has so far been unreachable in experiments. Applying this knowledge to the experimental and numerical data, we obtain the statistically-stationary, depth-resolved profiles of the relevant rheological quantities. The scaling behavior of rheological quantities such as the shear and normal viscosities and the effective friction coefficient are examined and compared to data coming from rheometry experiments and from widely-used rheological correlations. We show that rheological properties that have previously been inferred for annular Couette-type shear flows with neutrally buoyant particles still hold for our setup of sediment transport in a Poiseuille flow and in the dense regime we found good agreement with empirical relationships derived therefrom. Subdividing the total stress into parts from particle contact and hydrodynamics suggests a critical particle volume fraction of 0.3 to separate the dense from the dilute regime. In the dilute regime, i.e., the sediment transport layer, long-range hydrodynamic interactions are screened by the porous media and the effective viscosity obeys the Einstein relation.
A string of tracers, interacting elastically, in a turbulent flow is shown to have a dramatically different behaviour when compared to the non-interacting case. In particular, such an elastic chain shows strong preferential sampling of the turbulent flow unlike the usual tracer limit: an elastic chain is trapped in the vortical regions and not the straining ones. The degree of preferential sampling and its dependence on the elasticity of the chain is quantified via the Okubo-Weiss parameter. The effect of modifying the deformability of the chain, via the number of links that form it, is also examined.
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