Jonathan Summers

Modelling and analysis of meniscus roll coating

Three mathematical models are developed for meniscus roll coating in which there is steady flow of a Newtonian fluid in the narrow gap, or nip, between two contra-rotating rolls in the absence of body forces. The zero flux model predicts a constant pressure gradient within the central core and two eddies, each with an inner structure, in qualitative agreement with observation. The small flux model takes account of a small inlet flux and employs the lubrication approximation to represent fluid velocity as a combination of Couette and Poiseuille flows. Results show that the meniscus coating regime is characterized by small flow rates (λ<<1) and a sub-ambient pressure field generated by capillary action at the upstream meniscus. Such flows are found to exist for small modified capillary number, Ca(R/H 0 ) 1/2 ≤ 0.15, where Ca and R/H 0 represent capillary number and the radius to semi-gap ratio, respectively. A third model incorporates the full effects of curved menisci and nonlinear free surface boundary conditions. The presence of a dynamic contact line, adjacent to the web on the upper roll, requires the imposition of an apparent contact angle and slip length.

New Experimental Results of a Single Ridge Passing Through an EHL Conjunction

The micro-elastohydrodynamic lubrication of a single transverse ridge is revisited using an experimental technique, which combines an optical interferometry technique and a high-speed color video camera. The purpose of this study is to augment prior experimental analyses, by providing a complete and detailed history of the ridge associated with changes in film thickness as it passes through a high-pressure conjunction. An enhanced experimental procedure has been developed to enable an automatic analysis of the interferograms. In particular, the methodology allows abrupt changes in film thickness and rapid variations of interference orders to be taken into account. The observations presented in this paper exhibit interesting and fascinating features that have not been previously reported. In particular, it is observed that under rolling/sliding conditions the ridge undergoes further deformations as it proceeds to the exit to the contact. In addition, there appears to be an important contribution of pressure flow to the transport of lubricant and, contrary to current understanding, entrapped lubricant is seen to accompany the ridge as it passes through the contact, therefore appearing not to move at the entraining velocity.

Finite Element Simulation of Three-Dimensional Free-Surface Flow Problems

An adaptive finite element algorithm is described for the stable solution of three-dimensional free-surface-flow problems based primarily on the use of node movement. The algorithm also includes a discrete remeshing procedure which enhances its accuracy and robustness. The spatial discretisation allows an isoparametric piecewise-quadratic approximation of the domain geometry for accurate resolution of the curved free surface. The technique is illustrated through an implementation for surface-tension-dominated viscous flows modelled in terms of the Stokes equations with suitable boundary conditions on the deforming free surface. Two three-dimensional test problems are used to demonstrate the performance of the method: a liquid bridge problem and the formation of a fluid droplet.

Optimized implementation of the Lattice Boltzmann Method on a graphics processing unit towards real-time fluid simulation

Real-time fluid simulation is an active field of research in computer graphics, but they usually focus on visual impact rather than physical accuracy. However, by combining a lattice Boltzmann model with the parallel computing power of a graphics processing unit, both real-time compute capability and satisfactory physical accuracy are now achievable. The implementation of an optimized 3D real-time thermal and turbulent fluid flow solver with a performance of half a billion lattice node updates per second is described in detail. The effects of the hardware error checking code and the competition between appropriate boundary conditions and performance capabilities are discussed.

Creeping flow analyses of free surface cavity flows

Two industrially important free surface flows arising in polymer processing and thin film coating applications are modelled as lid-driven cavity problems to which a creeping flow analysis is applied. Each is formulated as a biharmonic boundary-value problem and solved both analytically and numerically. The analytical solutions take the form of a truncated biharmonic series of eigenfunctions for the streamfunction, while numerical results are obtained using a linear, finite-element formulation of the governing equations written in terms of both the streamfunction and vorticity. A key feature of the latter is that problems associated with singularities are alleviated by expanding the solution there in a series of separated eigenfunctions. Both sets of results are found to be in extremely good agreement and reveal distinctive flow transformations that occur as the operating parameters are varied. They also compare well with other published work and experimental observation.

On a dynamic wetting model for the finite-density multiphase lattice Boltzmann method

The contact line problem, where a liquid/fluid interface moves relative to a solid boundary (either slipping or spreading), is an important feature of many engineering and naturally occurring free-surface flows. This paper discusses the current state-of-the-art in applying wetting line models to computational fluid dynamics simulations and contrasts and compares it with a new wetting model (based on one physical parameter, notably the solid boundary surface affinity) for the finite-density multiphase lattice Boltzmann method (LBM). Results of two-dimensional filament (natural and forced) spreading flows over different types of surfaces are presented to illustrate the capability and drawbacks of the new dynamic wetting model for the finite-density multiphase LBM.

Stokes flow in closed, rectangular domains

Abstract Three practically relevant, Stokes flows in closed, rectangular cavities are considered. The first involves a solid-walled cavity where flow is driven by the motion of either one or both of its horizontal bounding walls; the other two have an upper free surface and are driven either by the motion of vertical side walls or by a horizontally-moving lower wall. Each problem is formulated as a biharmonic boundary value problem (bvp) for the streamfunction. The relative merits of two different coefficient determination methods for the corresponding analytical solutions are assessed and, in addition, each solution is compared with its numerical counterpart obtained using a finite element formulation of the governing equations. It is shown that, provided the number N of terms in each solution is sufficiently large, they are in extremely good agreement and, similarly, they compare well with work from other published theoretical and experimental studies. Streamlines are presented, over a wide range of operating parameters, for the geometries containing an upper free surface. For the flow generated by two moving vertical side walls two flow transformation mechanisms are identified. For cavities with small and decreasing width to depth (aspect) ratios, there is a sequence of critical aspect ratios at which flow bifurcations arise with a centre becoming a saddle point and vice versa, whereas for large aspect ratios increasing the ratio further leads to eddy growth from the lower wall, resulting in a regular sequence of separatrices along the cavity width. In the case of flow generated by a horizontally-moving lower wall the streamlines are simpler and exhibit the regular array of separatrices reported previously for flow in a solid-walled cavity with a single moving wall.

Modelling of electrokinetically driven mixing flow in microchannels with patterned blocks

Mixing in microchannels is an important process since certain microfluidic applications require the rapid mixing of species. This paper investigates the mixing in microchannels via the simulation of two-dimensional electrokinetically driven flow where the microchannel is populated with patterned blocks. The effects of the number, the size and the displacement of blocks are analysed to determine the efficiency of the mixing. The fluid flow is simulated via the single relaxation time lattice Boltzmann method (LBM) with a forcing term from the electric field. The concentration of species within the channel is governed by an advection-diffusion equation with Peclet number of the order 1000.

Fourier analysis of a single transverse ridge passing through an elastohydrodynamically lubricated rolling contact: A comparison with experiment

Abstract An image analysis technique is employed to measure lubricant film thickness fluctuations introduced by a single flat-top transverse ridge passing under pure rolling conditions through an elastohydrodynamically lubricated contact. The experimental observations are compared with the film thickness profiles predicted by the discrete Fourier transform method for real surface roughness given by Morales-Espejel et al. in 2000. The results show that the theoretical approach adequately predicts the overall film thickness, thus giving credence to its potential practical application. On a local scale, however, important differences are seen regarding the deformed shape of the feature.

Enclosed liquid natural convection as a means of transferring heat from microelectronics to cold plates

Liquid immersion of datacom electronics can be configured as a cooling mechanism when components are in direct contact with a high dielectric strength liquid. This paper analyses the heat transfer capabilities of datacom electronics when they are enclosed in a cassette with a dielectric liquid and sandwiched against a cold plate positioned in parallel with the printed circuit board. A proxy server motherboard with controllable heat cells and temperature sensors is used to conduct a series of heat transfer experiments. The results of which demonstrate that the thermal conductance processes via the naturally convecting dielectric liquid improves as the power demand of the electronics increases.