The Surface Topography of a Magnetic Fluid -- a Quantitative Comparison between Experiment and Numerical Simulation

The normal field instability in magnetic liquids is investigated experimentally by means of a radioscopic technique which allows a precise measurement of the surface topography. The dependence of the topography on the magnetic field is compared to results obtained by numerical simulations via the finite element method. Quantitative agreement has been found for the critical field of the instability, the scaling of the pattern amplitude and the detailed shape of the magnetic spikes. The fundamental Fourier mode approximates the shape to within 10% accuracy for a range of up to 40% of the bifurcation parameter of this subcritical bifurcation. The measured control parameter dependence of the wavenumber differs qualitatively from analytical predictions obtained by minimization of the free energy.Comment: 21 pages, 16 figures; corrected typos, added reference to Kuznetsov and Spector(1976), S.J. Fortune(1995) and Harkins&Jordan (1930). Figures revise

A numerical study of the longitudinal thermoconvective rolls in a mixed convection flow in a horizontal channel with a free surface

This paper presents a numerical study of three-dimensional laminar mixed convection within a liquid flowing on a horizontal channel heated uniformly from below. The upper surface is free and assumed to be flat. The coupled Navier-Stokes and energy equations are solved numerically by the finite volume method taking into account the thermocapillary effects (Marangoni effect). When the strength of the buoyancy, thermocapillary effects and forced convective currents are comparable $(Ri\backsimeq O(1)$ and $Bd=Ra/Ma \backsimeq O(1))$, the results show that the development of instabilities in the form of steady longitudinal convective rolls is similar to those encountered in the Poiseuille-Rayleigh-B\'enard flow. The number and spatial distribution of these rolls along the channel depend on the flow conditions. The objective of this work is to study the influence of parameters, such as the Reynolds, Rayleigh and Biot numbers, on the flow patterns and heat transfer characteristics. The effects of variations in the surface tension with temperature gradients (Marangoni effect) are also considered

Simulation-based analysis of a biologically-inspired micropump with a rotating spiral inside a microchannel

Microorganisms such as bacteria use their rotating helical flagella for propulsion speeds up to tens of tail lengths per second. The mechanism can be utilized for controlled pumping of liquids in microchannels. In this study, we aim to analyze the effects of control parameters such as axial span between helical rounds (wavelength), angular velocity of rotations (frequency), and the radius of the helix (amplitude) on the maximum timeaveraged flow rate, maximum head, rate of energy transfer, and efficiency of the micropump. The analysis is based on simulations obtained from the three-dimensional timedependent numerical model of the flow induced by the rotating spiral inside a rectangular-prism channel. The flow is governed by Navier-Stokes equations subject to continuity in timevarying domain due to moving boundaries of the spiral. Numerical solutions are obtained using a commercial finiteelement package which uses arbitrary Lagrangian-Eulerian method for mesh deformations. Results are compared with asymptotic results obtained from the resistive-force-theory available in the literature

A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics

This paper presents a survey of ocean simulation and rendering methods in computer graphics. To model and animate the ocean's surface, these methods mainly rely on two main approaches: on the one hand, those which approximate ocean dynamics with parametric, spectral or hybrid models and use empirical laws from oceanographic research. We will see that this type of methods essentially allows the simulation of ocean scenes in the deep water domain, without breaking waves. On the other hand, physically-based methods use Navier-Stokes Equations (NSE) to represent breaking waves and more generally ocean surface near the shore. We also describe ocean rendering methods in computer graphics, with a special interest in the simulation of phenomena such as foam and spray, and light's interaction with the ocean surface

Analysis of two-dimensional, unsteady flow in a propellant tank under low gravity by finite difference methods

Two-dimensional unsteady flow in propellant tank under low gravity by finite difference methods - reduction to boundary value proble

Efficient solution of 3D electromagnetic eddy-current problems within the finite volume framework of OpenFOAM

Eddy-current problems occur in a wide range of industrial and metallurgical applications where conducting material is processed inductively. Motivated by realising coupled multi-physics simulations, we present a new method for the solution of such problems in the finite volume framework of foam-extend, an extended version of the very popular OpenFOAM software. The numerical procedure involves a semi-coupled multi-mesh approach to solve Maxwell's equations for non-magnetic materials by means of the Coulomb gauged magnetic vector potential and the electric scalar potential. The concept is further extended on the basis of the impressed and reduced magnetic vector potential and its usage in accordance with Biot-Savart's law to achieve a very efficient overall modelling even for complex three-dimensional geometries. Moreover, we present a special discretisation scheme to account for possible discontinuities in the electrical conductivity. To complement our numerical method, an extensive validation is completing the paper, which provides insight into the behaviour and the potential of our approach.Comment: 47 pages, improved figures, updated references, fixed typos, reverse phase shift, consistent use of inner produc

Topology and shape optimization of induced-charge electro-osmotic micropumps

For a dielectric solid surrounded by an electrolyte and positioned inside an externally biased parallel-plate capacitor, we study numerically how the resulting induced-charge electro-osmotic (ICEO) flow depends on the topology and shape of the dielectric solid. In particular, we extend existing conventional electrokinetic models with an artificial design field to describe the transition from the liquid electrolyte to the solid dielectric. Using this design field, we have succeeded in applying the method of topology optimization to find system geometries with non-trivial topologies that maximize the net induced electro-osmotic flow rate through the electrolytic capacitor in the direction parallel to the capacitor plates. Once found, the performance of the topology optimized geometries has been validated by transferring them to conventional electrokinetic models not relying on the artificial design field. Our results show the importance of the topology and shape of the dielectric solid in ICEO systems and point to new designs of ICEO micropumps with significantly improved performance.Comment: 18 pages, latex IOP-style, 7 eps figure

Controlling liquids using meshes

We present an approach for artist-directed animation of liquids using multiple levels of control over the simulation, ranging from the overall tracking of desired shapes to highly detailed secondary effects such as dripping streams, separating sheets of fluid, surface waves and ripples. The first portion of our technique is a volume preserving morph that allows the animator to produce a plausible fluid-like motion from a sparse set of control meshes. By rasterizing the resulting control meshes onto the simulation grid, the mesh velocities act as boundary conditions during the projection step of the fluid simulation. We can then blend this motion together with uncontrolled fluid velocities to achieve a more relaxed control over the fluid that captures natural inertial effects. Our method can produce highly detailed liquid surfaces with control over sub-grid details by using a mesh-based surface tracker on top of a coarse grid-based fluid simulation. We can create ripples and waves on the fluid surface attracting the surface mesh to the control mesh with spring-like forces and also by running a wave simulation over the surface mesh. Our video results demonstrate how our control scheme can be used to create animated characters and shapes that are made of water