Topological structure evolvement of flow and temperature fields in deformable drop Marangoni migration in microgravity

Using the level-set method and the continuum interface model, the axisymmetric thermocapillary migration of a deformable liquid drop immerged in an immiscible bulk liquid with a temperature gradient is simulated numerically with constant material properties of the two phases. Steady terminal state of the motion can always be reached. The dimensionless terminal migration velocity decreases monotonously with the increase of the Marangoni number. Good agreements with space experimental data and most of previous numerical studies in the literature are evident. The terminal topological structure of flow field, in which a recirculation identical to Hill's vortex exists inside the drop, does not change with the Marangoni number. Only slight movement of the location of vortex center can be observed. On the contrary, bifurcations of the terminal topological structure of temperature field occur twice with increasing Marangoni number. At first, the uniform and straight layer-type structure of temperature field at infinitesimal Reynolds and Marangoni numbers wraps inside of the drop due to convective transport of heat as the Marangoni number increases, resulting in the emergence of an onion-type local cooler zone around the center of the drop beyond a lower critical Marangoni number. Expanding of this zone, particularly in the transverse direction, with the increasing of the Marangoni number leads to a cap- or even shell-type structure. The coldest point within the liquid drop locates on the axis. There is a middle critical Marangoni number, beyond which the coldest point will jump from the rear stagnation into the drop, though the topological structure of the temperature field does not change. The second bifurcation occurs at an upper critical Marangoni number, where the shell-type cooler zone inside drops ruptures from the central point and then a torus-type one emerges. The coldest point departs from the axis, and the so-called "cold-eye" appears in the meridian. It is also found that the inner and outer thermal boundary layers along the interface may exist both inside and outside the drop if Ma > 70. But the thickness decreases with the increasing Marangoni number more slowly than the prediction of potential flow at large Marangoni and Reynolds numbers. A velocity shear layer outside the drop is also introduced formally, of which modality may be affected by the convective transports of heat and/or momentum. (C) 2011 Elsevier Ltd. All rights reserved

Air Entrainment in Dynamic Wetting: Knudsen Effects and the Influence of Ambient Air Pressure

Recent experiments on coating flows and liquid drop impact both demonstrate that wetting failures caused by air entrainment can be suppressed by reducing the ambient gas pressure. Here, it is shown that non-equilibrium effects in the gas can account for this behaviour, with ambient pressure reductions increasing the gas' mean free path and hence the Knudsen number $Kn$. These effects first manifest themselves through Maxwell slip at the gas' boundaries so that for sufficiently small $Kn$ they can be incorporated into a continuum model for dynamic wetting flows. The resulting mathematical model contains flow structures on the nano-, micro- and milli-metre scales and is implemented into a computational platform developed specifically for such multiscale phenomena. The coating flow geometry is used to show that for a fixed gas-liquid-solid system (a) the increased Maxwell slip at reduced pressures can substantially delay air entrainment, i.e. increase the `maximum speed of wetting', (b) unbounded maximum speeds are obtained as the pressure is reduced only when slip at the gas-liquid interface is allowed for and (c) the observed behaviour can be rationalised by studying the dynamics of the gas film in front of the moving contact line. A direct comparison to experimental results obtained in the dip-coating process shows that the model recovers most trends but does not accurately predict some of the high viscosity data at reduced pressures. This discrepancy occurs because the gas flow enters the `transition regime', so that more complex descriptions of its non-equilibrium nature are required. Finally, by collapsing onto a master curve experimental data obtained for drop impact in a reduced pressure gas, it is shown that the same physical mechanisms are also likely to govern splash suppression phenomena.Comment: Accepted for publication in the Journal of Fluid Mechanic

Effects of Marangoni numbers on thermocapillary drop migration: constant for quasi-steady state?

The overall {\it steady}-state energy balance with two phases in a flow domain requires that the change in energy of the domain is equal to the difference between the total energy entering the domain and that leaving the domain. From the condition, the integral thermal flux across the surface is studied for a {\it steady} thermocapillary drop migration in a flow field with uniform temperature gradient at small and large Marangoni (Reynolds) numbers. The drop is assumed to have only a slight axisymmetric deformation from a sphere. It is identified that a conservative/nonconservative integral thermal flux across the surface in the {\it steady} thermocapillary drop migration at small/large Marangoni (Reynolds) numbers. The conservative flux confirms the assumption of {\it quasi-steady} state in the thermocapillary drop migration at small Marangoni (Reynolds) numbers. The nonconservative flux may well result from the invalid assumption of {\it quasi-steady} state, which indicates that the thermocapillary drop migration at large Marangoni (Reynolds) numbers cannot reach {\it steady} state and is thus a {\it unsteady} process.Comment: 21 pages. arXiv admin note: text overlap with arXiv:1112.276

Molecular transport and flow past hard and soft surfaces: Computer simulation of model systems

The properties of polymer liquids on hard and soft substrates are investigated by molecular dynamics simulation of a coarse-grained bead-spring model and dynamic single-chain-in-mean-field (SCMF) simulations of a soft, coarse-grained polymer model. Hard, corrugated substrates are modelled by an FCC Lennard-Jones solid while polymer brushes are investigated as a prototypical example of a soft, deformable surface. From the molecular simulation we extract the coarse-grained parameters that characterise the equilibrium and flow properties of the liquid in contact with the substrate: the surface and interface tensions, and the parameters of the hydrodynamic boundary condition. The so-determined parameters enter a continuum description like the Stokes equation or the lubrication approximation.Comment: 41 pages, 13 figure