M.C.T. Wilson

Gravity-driven flow of continuous thin liquid films on non-porous substrates with topography

A range of two- and three-dimensional problems is explored featuring the gravity-driven flow of a continuous thin liquid film over a non-porous inclined flat surface containing well-defined topography. These are analysed principally within the framework of the lubrication approximation, where accurate numerical solution of the governing nonlinear equations is achieved using an efficient multigrid solver. Results for flow over one-dimensional steep-sided topographies are shown to be in very good agreement with previously reported data. The accuracy of the lubrication approximation in the context of such topographies is assessed and quantified by comparison with finite element solutions of the full Navier–Stokes equations, and results support the consensus that lubrication theory provides an accurate description of these flows even when its inherent assumptions are not strictly satisfied. The Navier–Stokes solutions also illustrate the effect of inertia on the capillary ridge/trough and the two-dimensional flow structures caused by steep topography. Solutions obtained for flow over localized topography are shown to be in excellent agreement with the recent experimental results of Decre & Baret (2003) for the motion of thin water films over finite trenches. The spread of the ‘bow wave’, as measured by the positions of spanwise local extrema in free-surface height, is shown to be well-represented both upstream and downstream of the topography by an inverse hyperbolic cosine function. An explanation, in terms of local flow rate, is given for the presence of the ‘downstream surge’ following square trenches, and its evolution as trench aspect ratio is increased is discussed. Unlike the upstream capillary ridge, this feature cannot be completely suppressed by increasing the normal component of gravity. The linearity of free-surface response to topographies is explored by superposition of the free surfaces corresponding to two ‘equal-but-opposite’ topographies. Results confirm the findings of Decre & Baret (2003) that, under the conditions considered, the responses behave in a near-linear fashion.

Competing geometric and inertial effects on local flow structure in thick gravity-driven fluid films

The formation and presence of eddies within thick gravity-driven free-surface film flow over a corrugated substrate are considered, with the governing equations solved semianalytically using a complex variable method for Stokes flow and numerically via a full finite element formulation for the more general problem when inertia is significant. The effect of varying geometry (involving changes in the film thickness or the amplitude and wavelength of the substrate) and inertia is explored separately. For Stokes-like flow and varying geometry, excellent agreement is found between prediction and existing flow visualizations and measured eddy center locations associated with the switch from attached to locally detached flow. It is argued that an appropriate measure of the influence of inertia at the substrate is in terms of a local Reynolds number based on the characteristic corrugation length scale. Since, for small local Reynolds numbers, the local flow structure there becomes effectively decoupled from the i...

Displacement of liquid droplets on a surface by a shearing air flow.

The motion of droplets on surfaces is crucial to the performance of a wide range of processes; this study examines the initiation of droplet motion through a shearing mechanism generated here by a controlled air flow. Systematic experiments are carried out for a range of fluids and well defined surfaces. A model is postulated that balances surface tension forces at the contact line and the drag force due to the air motion. Experiments reveal that the critical velocity at which droplet motion is initiated depends on the contact angle and the droplet size. Visualizations highlight three modes of motion: (I) the droplet retains a footprint similar to that at the point of motion; (II) a tail exists at the rear of the droplet; (III) a trail remains behind the droplet (that can shed smaller droplets). The predictions of droplet initiation velocity are good for type I motion, in accordance with the assumptions inherent within the model. This model confirms the dominant physics associated with the initiation of droplet motion and provides a useful predictive expression.

Dynamics of contact line motion during the wetting of rough surfaces and correlation with topographical surface parameters.

Dynamics of contact line motion and wettability is essential in many industrial applications such as liquid coating, lubrication, printing, painting, condensation, etc. However, the wettability of surfaces depends not only on liquid-solid chemical properties but also can be strongly affected by surface roughness. As a practical application of controlled wettability, we can mention the self-cleaning surfaces, protective clothing, microfluidics devices, electro wetting, etc. In this article, we experimentally investigate the spreading of droplets deposited onto rough surfaces. Anisotropic surfaces were prepared by abrasive polishing on the following materials: aluminium alloy AA7064, titanium alloy Ti-6Al-4V, steel AISI 8630, copper alloy UNS C17000, machinable glass ceramic, and poly-methylmethacrylate. Topographical 2D parameters were calculated according to the following standards, defining Geometrical Product Specifications (GPS): ISO 4287, ISO 12085, ISO 13565, ISO 12780, and ISO 12181. The influence of topographical parameters on wettability and spreading phenomenon has been evaluated by statistical covariance analysis. The following parameters have strong influence on fluid spreading on rough surfaces: R(mr) is the relative material ratio of the roughness profile, T(rc) is the microgeometric material ratio, P(mr) is the relative material ratio of the raw profile, K(r) is the mean slope of the roughness motifs, RON(t) is the peak to valley roundness deviation, and P(sk) is the Skewness of the raw profile. The physical meaning of selected parameters is discussed, and K(r) (the mean slope of the roughness motifs) is selected as the most important and physically meaningful parameter. It has been found that for all tested materials, fluid spreading shows increasing tendency when mean slope of the roughness motifs (K(r) ) increases.

Eddy genesis and transformation of Stokes flow in a double-lid driven cavity

Abstract Stokes flow is considered in a rectangular driven cavity of depth 2H and width 2L, with two stationary side walls and two lids moving in opposite directions with speeds U1 and U2. The flow is governed by two control parameters: the cavity aspect ratio, A = H/L, and the speed ratio, S = U1/U2. The solution for the streamfuntion is expressed as an infinite series of Papkovich-Faddle eigenfunctions, which is then expanded about any stagnation point to reveal changes in the local flow structure as A and S are varied. An (S, A) control space diagram is constructed, which exhibits an intricate structure due to the intersection and confluence of several critical curves representing flow bifurcations at degenerate critical points. There are eight points where two critical curves intersect and the flow bifurcations are described and interpreted with reference to the theoretical work of Bakker (Bifurcations in Flow Patterns, Kluwer Academic, 1991) and Brøns and Hartnack (Phys. Fluids, 1999, 11, 314). For a speed ratio in the range -1 ≤ S < O the various flow trnsformations are tracked as A increases in the range O < A < 3.2, and hence the means is identified by which new eddies appear and become fully developed. It is shown that for S ≠ O, the number of eddies increases from 1 to 3 via several key flow transformations, which become more complicated as |S| is reduced.

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.

A Semi-deterministic Wear Model Considering the Effect of Zinc Dialkyl Dithiophosphate Tribofilm

AbstractTribochemistry plays a very important role in the behaviour of systems in tribologically loaded contacts under boundary lubrication conditions. Previous works have mainly reported contact mechanics simulations for capturing the boundary lubrication regime, but the real mechanism in which tribofilms reduce wear is still unclear. In this paper, the wear prediction capabilities of a recently published mechanochemical simulation approach (Ghanbarzadeh et al. in Tribol Int, 2014) are tested. The wear model, which involves a time- and spatially dependent coefficient of wear, was tested for two additive concentrations and three temperatures at different times, and the predictions are validated against experimental results. The experiments were conducted using a mini-traction machine in a sliding/rolling condition, and the spacer layer interferometry method was used to measure the tribofilm thickness. Wear measurements have been taken using a white-light interferometry. Good agreement is seen between simulation and experiment in terms of tribofilm thickness and wear depth predictions.

Eddy genesis and manipulation in plane laminar shear flow

Eddy formation and presence in a plane laminar shear flow configuration consisting of two infinitely long plates orientated parallel to each other is investigated theoretically. The upper plate, which is planar, drives the flow; the lower one has a sinusoidal profile and is fixed. The governing equations are solved via a full finite element formulation for the general case and semianalytically at the Stokes flow limit. The effects of varying geometry (involving changes in the mean plate separation or the amplitude and wavelength of the lower plate) and inertia are explored separately. For Stokes flow and varying geometry, excellent agreement between the two methods of solution is found. Of particular interest with regard to the flow structure is the importance of the clearance that exists between the upper plate and the tops of the corrugations forming the lower one. When the clearance is large, an eddy is only present at sufficiently large amplitudes or small wavelengths. However, as the plate clearance ...

Nested separatrices in simple shear flows: The effect of localized disturbances on stagnation lines

The effects of localized two-dimensional disturbances on the structure of shear flows featuring a stagnation line are investigated. A simple superposition of a planar Couette flow and Moffatt’s [J. Fluid Mech. 18, 1–18 (1964)] streamfunction for the decay of a disturbance between infinite stationary parallel plates shows that in general the stagnation line is replaced by a chain of alternating elliptic and hyperbolic stagnation points with a separation equal to 2.78 times the half-gap between the plates. The flow structure associated with each saddle point consists of a homoclinic separatrix and two other separatrices which locally diverge but become parallel far from the disturbance. This basic structure repeats to give a sequence of nested separatrices permitting the streamfunction to approach that of simple shear flow far from the disturbance. Using the finite-element method, the specific disturbance caused by a stationary cylinder placed on the stagnation line is considered, and results confirm the ex...

Moving Contact-Line Models and the Effect of Hydrodynamic Assist of Dynamic Wetting

The variations with flow rate of ‘apparent’ contact angles calculated from a 2-D finite element simulation of curtain coating are compared with experiments to illustrate the inadequacy of standard models. An improved wetting model featuring a variable dynamic contact angle is also tested and shown to give better agreement with experiments.