539 research outputs found
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
Viscous sintering of unimodal and bimodal cylindrical packings with shrinking pores
Published versio
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
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
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
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