Analytical solution of Stokes flow inside an evaporating sessile drop: Spherical and cylindrical cap shapes

Exact analytical solutions are derived for the Stokes flows within evaporating sessile drops of spherical and cylindrical cap shapes. The results are valid for arbitrary contact angle. Solutions are obtained for arbitrary evaporative flux distributions along the free surface as long as the flux is bounded at the contact line. The field equations, E^4(Psi)=0 and Del^4(Phi)=0, are solved for the spherical and cylindrical cap cases, respectively. Specific results and computations are presented for evaporation corresponding to uniform flux and to purely diffusive gas phase transport into an infinite ambient. Wetting and non-wetting contact angles are considered with the flow patterns in each case being illustrated. For the spherical cap with evaporation controlled by vapor phase diffusion, when the contact angle lies in the range 0<theta_c<pi, the mass flux of vapor becomes singular at the contact line. This condition required modification when solving for the liquid phase transport. Droplets in all of the above categories are considered for the following two cases: the contact lines are either pinned or free to move during evaporation. The present viscous flow behavior is compared to the inviscid flow behavior previously reported. It is seen that the streamlines for viscous flow lie farther from the substrate than the corresponding inviscid ones.Comment: Revised version; in review in Physics of Fluid

Which canonical algebras are derived equivalent to incidence algebras of posets?

We give a full description of all the canonical algebras over an algebraically closed field that are derived equivalent to incidence algebras of finite posets. These are the canonical algebras whose number of weights is either 2 or 3.Comment: 8 pages; slight revision; to appear in Comm. Algebr

No many-scallop theorem: Collective locomotion of reciprocal swimmers

To achieve propulsion at low Reynolds number, a swimmer must deform in a way that is not invariant under time-reversal symmetry; this result is known as the scallop theorem. We show here that there is no many-scallop theorem. We demonstrate that two active particles undergoing reciprocal deformations can swim collectively; moreover, polar particles also experience effective long-range interactions. These results are derived for a minimal dimers model, and generalized to more complex geometries on the basis of symmetry and scaling arguments. We explain how such cooperative locomotion can be realized experimentally by shaking a collection of soft particles with a homogeneous external field

Non-equilibrium hydrodynamics of a rotating filament

The nonlinear dynamics of an elastic filament that is forced to rotate at its base is studied by hydrodynamic simulation techniques; coupling between stretch, bend, twist elasticity and thermal fluctuations is included. The twirling-overwhirling transition is located and found to be strongly discontinuous. For finite bend and twist persistence length, thermal fluctuations lower the threshold rotational frequency, for infinite persistence length the threshold agrees with previous analytical predictions

Symmetric three-particle motion in Stokes flow: equilibrium for heavy spheres in contrast to "end-of-world" for point forces

A stationary stable solution of the Stokes equations for three identical heavy solid spheres falling in a vertical plane is found. It has no analog in the point-particle approximation. Three spheres aligned horizontally at equal distances evolve towards the equilibrium relative configuration while the point particles collapse onto a single point in a finite time.Comment: 4 pages, 7 figure

Brownian Dynamics of a Sphere Between Parallel Walls

We describe direct imaging measurements of a colloidal sphere's diffusion between two parallel surfaces. The dynamics of this deceptively simple hydrodynamically coupled system have proved difficult to analyze. Comparison with approximate formulations of a confined sphere's hydrodynamic mobility reveals good agreement with both a leading-order superposition approximation as well as a more general all-images stokeslet analysis.Comment: 4 pages, 3 figures, REVTeX with PostScript figure

Microscale swimming: The molecular dynamics approach

The self-propelled motion of microscopic bodies immersed in a fluid medium is studied using molecular dynamics simulation. The advantage of the atomistic approach is that the detailed level of description allows complete freedom in specifying the swimmer design and its coupling with the surrounding fluid. A series of two-dimensional swimming bodies employing a variety of propulsion mechanisms -- motivated by biological and microrobotic designs -- is investigated, including the use of moving limbs, changing body shapes and fluid jets. The swimming efficiency and the nature of the induced, time-dependent flow fields are found to differ widely among body designs and propulsion mechanisms.Comment: 5 pages, 3 figures (minor changes to text

Influence of flow confinement on the drag force on a static cylinder

The influence of confinement on the drag force $F$ on a static cylinder in a viscous flow inside a rectangular slit of aperture $h_0$ has been investigated from experimental measurements and numerical simulations. At low enough Reynolds numbers, $F$ varies linearly with the mean velocity and the viscosity, allowing for the precise determination of drag coefficients $\lambda_{||}$ and $\lambda_{\bot}$ corresponding respectively to a mean flow parallel and perpendicular to the cylinder length $L$. In the parallel configuration, the variation of $\lambda_{||}$ with the normalized diameter $\beta = d/h_0$ of the cylinder is close to that for a 2D flow invariant in the direction of the cylinder axis and does not diverge when $\beta = 1$. The variation of $\lambda_{||}$ with the distance from the midplane of the model reflects the parabolic Poiseuille profile between the plates for $\beta \ll 1$ while it remains almost constant for $\beta \sim 1$. In the perpendicular configuration, the value of $\lambda_{\bot}$ is close to that corresponding to a 2D system only if $\beta \ll 1$ and/or if the clearance between the ends of the cylinder and the side walls is very small: in that latter case, $\lambda_{\bot}$ diverges as $\beta \to 1$ due to the blockage of the flow. In other cases, the side flow between the ends of the cylinder and the side walls plays an important part to reduce $\lambda_{\bot}$: a full 3D description of the flow is needed to account for these effects

On Berenstein-Douglas-Seiberg Duality

I review the proposal of Berenstein-Douglas for a completely general definition of Seiberg duality. To give evidence for their conjecture I present the first example of a physical dual pair and explicitly check that it satisfies the requirements. Then I explicitly show that a pair of toric dual quivers is also dual according to their proposal. All these computations go beyond tilting modules, and really work in the derived category. I introduce all necessary mathematics where needed.Comment: 22 pages, LaTe

A dynamic density functional theory for particles in a flowing solvent

We present a dynamic density functional theory (dDFT) which takes into accou nt the advection of the particles by a flowing solvent. For potential flows we can use the same closure as in the absence of solvent flow. The structure of the resulting advected dDFT suggests that it could be used for non-potential flows as well. We apply this dDFT to Brownian particles (e.g., polymer coils) in a solvent flowing around a spherical obstacle (e.g., a colloid) and compare the results with direct simulations of the underlying Brownian dynamics. Although numerical limitations do not allow for an accurate quantitative check of the advected dDFT both show the same qualitative features. In contrast to previous works which neglected the deformation of the flow by the obstacle, we find that the bow-wave in the density distribution of particles in front of the obstacle as well as the wake behind it are reduced dramatically. As a consequence the friction force exerted by the (polymer) particles on the colloid can be reduced drastically.Comment: 7 pages, 5 figures, 2 tables, submitte