Steady nonlinear capillary waves on curved sheets

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Viscous sintering of unimodal and bimodal cylindrical packings with shrinking pores

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Boundary Integral Equations for the Laplace-Beltrami Operator

We present a boundary integral method, and an accompanying boundary element discretization, for solving boundary-value problems for the Laplace-Beltrami operator on the surface of the unit sphere $\S$ in $\mathbb{R}^3$. We consider a closed curve ${\cal C}$ on ${\cal S}$ which divides ${\cal S}$ into two parts ${\cal S}_1$ and ${\cal S}_2$. In particular, ${\cal C} = \partial {\cal S}_1$ is the boundary curve of ${\cal S}_1$. We are interested in solving a boundary value problem for the Laplace-Beltrami operator in $\S_2$, with boundary data prescribed on \C

Fluid-structure interaction of two bodies in an inviscid fluid

The interaction of two arbitrary bodies immersed in a two-dimensional inviscid fluid is investigated. Given the linear and angular velocities of the bodies, the solution of the potential flow problem with zero circulation around both bodies is reduced to the determination of a suitable Laurent series in a conformally mapped domain that satisfies the boundary conditions. The potential flow solution is then used to determine the force and moment acting on each body by using generalized Blasius formulas. The current formulation is applied to two examples. First, the case of two rigid circular cylinders interacting in an unbounded domain is investigated. The forces on two cylinders with prescribed motion forced-forced is determined and compared to previous results for validation purposes. We then study the response of a single “free” cylinder due to the prescribed motion of the other cylinder forced-free. This forced-free situation is used to justify the hydrodynamic benefits of drafting in aquatic locomotion. In the case of two neutrally buoyant circular cylinders, the aft cylinder is capable of attaining a substantial propulsive force that is the same order of magnitude of its inertial forces. Additionally, the coupled interaction of two cylinders given an arbitrary initial condition free-free is studied to show the differences of perfect collisions with and without the presence of an inviscid fluid. For a certain range of collision parameters, the fluid acts to deflect the cylinder paths just enough before the collision to drastically affect the long time trajectories of the bodies. In the second example, the flapping of two plates is explored. It is seen that the interactions between each plate can cause a net force and torque at certain instants in time, but for idealized sinusoidal motions in irrotational potential flow, there is no net force and torque acting at the system center

Particle self-diffusiophoresis near solid walls and interfaces

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.The purpose of this paper is to explore, from a theoretical viewpoint, the mechanisms whereby locomotion of low-Reynolds-number organisms and particles is affected by the presence of nearby no-slip surfaces and free capillary surfaces. First, we explore some simple models of the unsteady dynamics of low- Reynolds-number swimmers near a no-slip wall and driven by an arbitrarily imposed tangential surface slip. Next, the self-diffusiophoresis of a class of two-faced Janus particles propelled by the production of gradients in the concentration of a solute diffusing into a surrounding fluid at zero Reynolds and P´eclet numbers is studied, both in free space and near a no-slip wall. The added difficulty now is that the tangential slip is not arbitrarily chosen but is given by the solution of a separate boundary value problem for the solute concentration. Finally, an analysis of a model system is used to identify a mechanism whereby a non-self-propelling swimmer can harness the effects of surface tension and deformability of a nearby free surface to propel itself along it. The challenge here is that it is a free boundary problem requiring determination of the surface shape as part of the solution

Analytical solutions for distributed multipolar vortex equilibria on a sphere

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Growing vortex patches

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Analytical solutions for two-dimensional singly periodic Stokes flow singularity arrays near walls

New analytical representations of the Stokes flows due to periodic arrays of point singularities in a two-dimensional no-slip channel and in the half-plane near a no-slip wall are derived. The analysis makes use of a conformal mapping from a concentric annulus (or a disc) to a rectangle and a complex variable formulation of Stokes flow to derive the solutions. The form of the solutions is amenable to fast and accurate numerical computation without the need for Ewald summation or other fast summation techniques

Phoretic self-propulsion of Janus discs in the fast-reaction limit

Due to the net interfacial consumption of solute, the two-dimensional problem of phoretic swimming is ill posed in the standard description of diffusive transport, where the solute concentration satisfies Laplace's equation. It becomes well posed when solute advection is accounted for. We consider here the case of weak advection, where solute transport is analyzed using matched asymptotic expansions in two separate asymptotic regions, a near-field region in the vicinity of the swimmer and a far-field region where solute advection enters the dominant balance. We carry out the analysis for a standard Janus configuration, where half of the particle boundary is active and the other half is inert. Our main focus lies in the limit of fast reaction, which leads to a mixed boundary-value problem in the near field. That problem is solved using conformal mapping techniques. Our asymptotic scheme furnishes an implicit equation for the particle velocity s in the direction of the active portion of its boundary, 2s(8ln8D|s|a−γ)=bc∞/a, wherein a is the particle radius, D the solute diffusivity, c∞ its far-field concentration, b the diffusio-osmotic slip coefficient, and γ the Euler-Mascheroni constant. The nonlinear dependence of s upon bc∞ is a signature of the nonvanishing effect of solute advection

Superhydrophobicity can enhance convective heat transfer in pressure-driven pipe flow

Theoretical evidence is given that it is possible for superhydrophobicity to enhance steady laminar convective heat transfer in pressure-driven flow along a circular pipe or tube with constant heat flux. Superhydrophobicity here refers to the presence of adiabatic no-shear zones in an otherwise solid no-slip boundary. Adding such adiabatic no-shear zones reduces not only hydrodynamic friction, leading to greater fluid volume fluxes for a given pressure gradient, but also reduces the solid surface area through which heat enters the fluid. This leads to a delicate trade-off between competing mechanisms so that the net effect on convective heat transfer along the pipe, as typically measured by a Nusselt number, is not obvious. Existing evidence in the literature suggests that superhydrophobicity always decreases the Nusselt number, and therefore compromises the net heat transfer. In this theoretical study, we confirm this to be generally true but, significantly, we identify a situation where the opposite occurs and the Nusselt number increases thereby enhancing convective heat transfer along the pipe