Viscous sintering of unimodal and bimodal cylindrical packings with shrinking pores

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Exact solutions for rotating vortex arrays with finite-area cores

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Compressible bubbles in Stokes flow

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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

Stuart vortices on a sphere

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Steady nonlinear capillary waves on curved sheets

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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

A two-dimensional model of low-Reynolds number swimming beneath a free surface

Biological organisms swimming at low Reynolds number are often influenced by the presence of rigid boundaries and soft interfaces. In this paper we present an analysis of locomotion near a free surface with surface tension. Using a simplified two-dimensional singularity model, and combining a complex variable approach with conformal mapping techniques, we demonstrate that the deformation of a free surface can be harnessed to produce steady locomotion parallel to the interface. The crucial physical ingredient lies in the nonlinear hydrodynamic coupling between the disturbance flow created by the swimmer and the free boundary problem at the fluid surface

Laplacian Growth and Whitham Equations of Soliton Theory

The Laplacian growth (the Hele-Shaw problem) of multi-connected domains in the case of zero surface tension is proven to be equivalent to an integrable systems of Whitham equations known in soliton theory. The Whitham equations describe slowly modulated periodic solutions of integrable hierarchies of nonlinear differential equations. Through this connection the Laplacian growth is understood as a flow in the moduli space of Riemann surfaces.Comment: 33 pages, 7 figures, typos corrected, new references adde