Asymptotic theory for a moving droplet driven by a wettability gradient

An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and the receding side -- to respective solutions of the problem on the microscale. On the microscale the velocity of movement is used as the small parameter of an asymptotic expansion. Matching gives the droplet shape, velocity of movement as a function of the imposed wettability gradient and droplet volume.Comment: 8 fig

A Method for Geometry Optimization in a Simple Model of Two-Dimensional Heat Transfer

This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations and involving a one-dimensional cooling element represented by a contour on which interface boundary conditions are specified. The problem consists in finding an optimal shape of the cooling element which will ensure that the solution in a given region is close (in the least squares sense) to some prescribed target distribution. We formulate this problem as PDE-constrained optimization and the locally optimal contour shapes are found using a gradient-based descent algorithm in which the Sobolev shape gradients are obtained using methods of the shape-differential calculus. The main novelty of this work is an accurate and efficient approach to the evaluation of the shape gradients based on a boundary-integral formulation which exploits certain analytical properties of the solution and does not require grids adapted to the contour. This approach is thoroughly validated and optimization results obtained in different test problems exhibit nontrivial shapes of the computed optimal contours.Comment: Accepted for publication in "SIAM Journal on Scientific Computing" (31 pages, 9 figures

A mesh adaptivity scheme on the Landau-de Gennes functional minimization case in 3D, and its driving efficiency

This paper presents a 3D mesh adaptivity strategy on unstructured tetrahedral meshes by a posteriori error estimates based on metrics, studied on the case of a nonlinear finite element minimization scheme for the Landau-de Gennes free energy functional of nematic liquid crystals. Newton's iteration for tensor fields is employed with steepest descent method possibly stepping in. Aspects relating the driving of mesh adaptivity within the nonlinear scheme are considered. The algorithmic performance is found to depend on at least two factors: when to trigger each single mesh adaptation, and the precision of the correlated remeshing. Each factor is represented by a parameter, with its values possibly varying for every new mesh adaptation. We empirically show that the time of the overall algorithm convergence can vary considerably when different sequences of parameters are used, thus posing a question about optimality. The extensive testings and debugging done within this work on the simulation of systems of nematic colloids substantially contributed to the upgrade of an open source finite element-oriented programming language to its 3D meshing possibilities, as also to an outer 3D remeshing module

Mechanical behaviour of liquid bridges in microgravity

The mechanical behaviour of liquid bridges is revisited with the emphasis in experimental work under microgravity conditions. A liquid bridge is a liquid mass spanning between two solid supports and held together by surface tension and wetting (i.e. capillary) forces, provided the other mechanical loads (due to gravity, vibration, rotation) are smaller. Apart of its own interest on ground for natural capillary systems, it offers some unique characteristics that makes it interesting for fluid physics research under microgravity. On the one side, the liquid bridge is the simplest mechanical model of the floating zone technique of crystal growth, a key process in material sciences for purification. On the other side, a particular instance of liquid bridges (the cylindrical shape) is one of the simpler free interfaces one can establish in space; the other (simplest) cases, the flat surface and the sphere are much more difficult to handle. Consequently, the liquid bridge configuration has been extensively used to study a number of difficult problems like Marangoni convection among others

Oscillations of a liquid bridge resulting from the coalescence of two droplets

The inertial oscillations of a bridge of liquid maintained between two disks are studied under condition of negligible gravity. Both experimental and theoretical results are reported. In the experiment, the bridge is formed by the coalescence of two droplets so that its static equilibrium shape is either concave or convex depending on its length. After coalescence, the bridge performs weakly damped oscillations until it reaches its equilibrium shape. Four modes of oscillations are extracted from digital processing of images recorded by means of a high-speed camera. Their frequency and damping rate are determined and found to be independent of the initial conditions that fix the amplitudes of each mode. Concurrently, the eigen modes of oscillations of a non-cylindrical bridge have been computed by assuming inviscid flow and small amplitude oscillations. The agreement between theoretical and measured frequencies confirms that the experimental modes correspond to the eigenmodes of the linear inviscid theory. Their characteristics turn out to be significantly different from that of a cylindrical bridge. In particular, the eigenfrequencies scale as root gamma/rho R-m(3), where gamma is the surface tension, rho the liquid density, and R-m the radius at the middle of the bridge, which characterizes the shrunk/swollen character of the mean shape

Bethe-Peierls Approximation for Linear Monodisperse Polymers Re-examined

Bethe-Peierls approximation, as it applies to the thermodynamics of polymer melts, is reviewed. We compare the computed configurational entropy of monodisperse linear polymer melt with Monte Carlo data available in literature. An estimation of the configurational contribution to the total liquid's Cp is presented. We also discuss the relation between Kauzmann paradox and polymer semiflexibility.Comment: 9 pages, 3 figure

Unmasking of Novel Conic Modes in Electrically Stressed Perfectly Conducting Liquids

Liquid metal ion sources (LMIS) are widely used in applications ranging from local ion implantation in semiconductors, to focused ion beam systems for milling and nanolithography, to space micropropulsion devices being developed by NASA. Above a critically large field strength, an electrically stressed liquid metal develops one or more cuspidal protrusions which undergo accelerated conic tip sharpening with runaway field self-enhancement. Zubarev (2001) first predicted from an inviscid model that the electric stresses at the liquid apex undergo self-similar divergent growth in finite time. The inviscid assumption is appropriate to liquid metals since the viscous boundary layer extends only a few tens of nanometers from the moving interface. In this work, we examine in more depth a two-parameter family of far-field self-similar solutions incorporating inertial, electrical and capillary effects, which to leading order describe electric and velocity potential fields corresponding to a rapidly accelerating dynamic Taylor cone. These far field solutions are incorporated self-consistently into boundary integral simulations which reveal the entire liquid shape in the near field. By invoking time reversal symmetry inherent to inviscid flow, we unmask an entire family of novel self-similar conic modes exhibiting features such as inertial recoil, tip bulging from accelerated advance and tip counter-current flow as well as multiple interface stagnation points. These dynamic configurations help explain for the first time the origin of decades old experimental observations that have reported phenomena such as tip oscillation, pulsation and breakup during operation. The various liquid tip shapes accessible to such systems should help correct persistent misconceptions of pre- and post-emission behavior in LMIS systems and related technologies

Fundamental understanding of swirling flow pattern in hydrocyclones

This work is concerned with establishing and validating a physics-based model that describes the swirling flow inside hydrocyclones. The physics is embedded in a Computational Fluid Dynamics (CFD) simulation model whose key features are presented and justified in the paper. Some features are selected in such a way that the model can eventually be used to simulate dense flow inside hydrocyclones. Nevertheless, its underlying physics is here within validated against dilute flow conditions. The model applies a Eulerian multi-fluid modelling approach for fluid–particle turbulent flows, and is computed using the semi-industrial code NEPTUNE_CFD. Simulation results are successfully compared to water split, velocity profiles inside the hydrocyclone and partition function measurements, either produced using our own experimental setup or from the literature. The work finds velocity profiles to be the most discriminating parameter for validation of the physics that describes the swirling flow inside the hydrocyclone. Water split on the other hand shows no relation to the choice of turbulence model and hence cannot be used to validate a mechanistic model of the hydrocyclone. The physics-based model presented here is the first building block towards describing and understanding hydrocyclone flow under dense regime