Analytical formulas for longitudinal slip lengths over unidirectional superhydrophobic surfaces with curved menisci

This paper reports new analytical formulas for the longitudinal slip lengths for simple shear over a superhydrophobic surface, or bubble mattress, comprising a periodic array of unidirectional circular menisci, or bubbles, protruding into, or out of, the fluid. The accuracy of the formulas is tested against results from full numerical simulations; they are found to give small relative errors even at large no-shear fractions. In the dilute limit the formulas reduce to an earlier result by the author [Phys. Fluids, 22, 121703, (2011)]. They also extend analytical results of Sbragaglia & Prosperetti [Phys Fluids, 19, 043603, (2007)] beyond a small protrusion angle limit

Compressible bubbles in Stokes flow

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Exact solutions for rotating vortex arrays with finite-area cores

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Stuart vortices on a sphere

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Stress fields around two pores in an elastic body: exact quadrature domain solutions

Analytical solutions are given for the stress fields, in both compression and far-field shear, in a two-dimensional elastic body containing two interacting non-circular pores. The two complex potentials governing the solutions are found by using a conformal mapping from a pre-image annulus with those potentials expressed in terms of the Schottky–Klein prime function for the annulus. Solutions for a three-parameter family of elastic bodies with two equal symmetric pores are presented and the compressibility of a special family of pore pairs is studied in detail. The methodology extends to two unequal pores. The importance for boundary value problems of plane elasticity of a special class of planar domains known as quadrature domains is also elucidated. This observation provides the route to generalization of the mathematical approach here to finding analytical solutions for the stress fields in bodies containing any finite number of pores

Surface-tension-driven Stokes flow: a numerical method based on conformal geometry

AbstractA novel numerical scheme is presented for solving the problem of two dimensional Stokes flows with free boundaries whose evolution is driven by surface tension. The formulation is based on a complex variable formulation of Stokes flow and use of conformal mapping to track the free boundaries. The method is motivated by applications to modelling the fabrication process for microstructured optical fibres (MOFs), also known as “holey fibres”, and is therefore tailored for the computation of multiple interacting free boundaries. We give evidence of the efficacy of the method and discuss its performance