Capillary effects and short-scale interaction in a weakly viscous supercritical overfall

We consider a thin liquid film past a semi-infinite horizontal plate under the action of gravity acting vertically, surface tension, and relatively low viscosity. This scenario comprises a manifold of effects at play, given the two disparate length scales involved: distance from jet impingement generating the layer to the trailing edge of the plate, height of the film. The yet not fully understood behaviour of a developed viscous film near the edge and previous studies on bores and hydraulic jumps in weakly viscous horizontal layers stimulate the present investigation. In sharp contrast to these, here the flow remains supercritical, and isolated regimes of strong viscous–inviscid interaction are dictated by the short length scale rather than the common shallow-water approximation. Specifically, we show how viscosity produces standing waves upstream of localised interaction and how weak capillarity modifies drastically the potential-flow singularity close to the edge, which in turn affects crucially its viscous regularisation

Correction of coarse-graining errors by a two-level method: Application to the Asakura-Oosawa model.

We present a method that exploits self-consistent simulation of coarse-grained and fine-grained models in order to analyze properties of physical systems. The method uses the coarse-grained model to obtain a first estimate of the quantity of interest, before computing a correction by analyzing properties of the fine system. We illustrate the method by applying it to the Asakura-Oosawa model of colloid-polymer mixtures. We show that the liquid-vapor critical point in that system is affected by three-body interactions which are neglected in the corresponding coarse-grained model. We analyze the size of this effect and the nature of the three-body interactions. We also analyze the accuracy of the method as a function of the associated computational effort.Leverhulme Trus

Heterogeneous Multiscale Methods for modelling surface topography in Elastohydrodynamic Lubrication line contacts

A multiscale method for the Elastohydrodynamic Lubrication (EHL) of line contacts is derived based on the Heterogeneous Multiscale Methods. Periodicity applies to the topographical features and lubricant flow, data is homogenised over a range of variables at a micro-scale and coupled into a macro-scale model. This is achieved using flow factors as calculated from metamodels, which themselves evolve with the solution procedure. Results are given for an idealised topography and illustrate significant deviations from smooth surface assumptions as quantified by the flow factors. Improvements in the accuracy and efficiency with previous work and large fluctuations due to micro-EHL are also presented. Validation of the multiscale method with a deterministic topography is provided demonstrating good accuracy and efficiency

On transcritical states in viscous flow passing the edge of a horizontal plate

This contribution puts forward some recent advances in the rigorous (asymptotic) theory of gravity‐ (and capillarity‐)driven shallow flow of a viscous liquid past a horizontal plate, originating in jet impingement oblique to it. Hence, our concern is twofold: with steady developed flow over the distance from the jet centre to the trailing edge of the plate, referred to as a pronounced hydraulic jump blurred by viscous diffusion; with the predominantly inviscid transcritical limit arising near the edge due to scale reduction given an intrinsic expansive singularity taking place there. In the latter situation envisaged briefly, condensing nonlinear inertial effects, weak time dependence, and (very) weak streamline curvature as the essential ingredients into a distinguished limit demonstrates the generation of a weak (transcritical) hydraulic jump by a plate‐mounted obstacle

Choking and hydraulic jumps in laminar flow

The viscous hydraulic jump still represents research in progress rather than a finalised edifice. The existing rigorous approaches show how this phenomenon is tied in with a bifurcation of the upstream flow adjacent to the guiding rigid plate of finite length, aligned perpendicularly to the direction of gravity. Here, this together with the upstream influence by the detached flow triggers transition from super‐ to subcritical flow (sensing its susceptibility to the upstream propagation of small disturbances). We present recent advances in the self‐consistent theory of single‐layer jumps continued as free shear layers