240 research outputs found
On the anomalous dynamics of capillary rise in porous media
The anomalous dynamics of capillary rise in a porous medium discovered
experimentally more than a decade ago (Delker et al., Phys. Rev. Lett. 76
(1996) 2902) is described. The developed theory is based on considering the
principal modes of motion of the menisci that collectively form the wetting
front on the Darcy scale. These modes, which include (i) dynamic wetting mode,
(ii) threshold mode and (iii) interface de-pinning process, are incorporated
into the boundary conditions for the bulk equations formulated in the regular
framework of continuum mechanics of porous media, thus allowing one to consider
a general case of three-dimensional flows. The developed theory makes it
possible to describe all regimes observed in the experiment, with the time
spanning more than four orders of magnitude, and highlights the dominant
physical mechanisms at different stages of the process
Finite Element Simulation of Dynamic Wetting Flows as an\ud Interface Formation Process
A mathematically challenging model of dynamic wetting as a process of interface formation has been, for the first time, fully incorporated into a numerical code based on the finite element method and applied, as a test case, to the problem of capillary rise. The motivation for this work comes from the fact that, as discovered experimentally more than a decade ago, the key variable in dynamic wetting flows — the dynamic contact angle — depends not just on the velocity of the three-phase contact line but on the entire flow field/geometry. Hence, to describe this effect, it becomes necessary to use the mathematical model that has this dependence as its integral part. A new physical effect, termed the ‘hydrodynamic resist to dynamic wetting’, is discovered where the influence of the capillary’s radius on the dynamic contact angle, and hence on the global flow, is computed. The capabilities of the numerical framework are then demonstrated by comparing the results to experiments on the unsteady capillary rise, where excellent agreement is obtained. Practical recommendations on the spatial resolution required by the numerical scheme for a given set of non-dimensional similarity parameters are provided, and a comparison to asymptotic results available in limiting cases confirms that the code is converging to the correct solution. The appendix gives a userfriendly step-by-step guide specifying the entire implementation and allowing the reader to easily reproduce all presented results, including the benchmark calculations
The Dynamics of Liquid Drops Coalescing in the Inertial Regime
We examine the dynamics of two coalescing liquid drops in the `inertial
regime', where the effects of viscosity are negligible and the propagation of
the bridge front connecting the drops can be considered as `local'. The
solution fully computed in the framework of classical fluid-mechanics allows
this regime to be identified and the accuracy of the approximating scaling laws
proposed to describe the propagation of the bridge to be established. It is
shown that the scaling law known for this regime has a very limited region of
accuracy and, as a result, in describing experimental data it has frequently
been applied outside its limits of applicability. The origin of the scaling
law's shortcoming appears to be the fact that it accounts for the capillary
pressure due only to the longitudinal curvature of the free surface as the
driving force for the process. To address this deficiency, the scaling law is
extended to account for both the longitudinal and azimuthal curvatures at the
bridge front which, fortuitously, still results in an explicit analytic
expression for the front's propagation speed. This new expression is then shown
to offer an excellent approximation for both the fully-computed solution and
for experimental data from a range of flow configurations for a remarkably
large proportion of the coalescence process. The derived formula allows one to
predict the speed at which drops coalesce for the duration of the inertial
regime which should be useful for the analysis of experimental data.Comment: Accepted for publication in Physical Review
Wetting Front Dynamics in Isotropic Porous Media
A new approach to the modelling of wetting fronts in porous media on the
Darcy scale is developed, based on considering the types (modes) of motion the
menisci go through on the pore scale. This approach is illustrated using a
simple model case of imbibition of a viscous incompressible liquid into an
isotropic porous matrix with two modes of motion for the menisci, the wetting
mode and the threshold mode. The latter makes it necessary to introduce an
essentially new technique of conjugate problems that allows one to link
threshold phenomena on the pore scale with the motion on the Darcy scale. The
developed approach (a) makes room for incorporating the actual physics of
wetting on the pore scale, (b) brings in the physics associated with pore-scale
thresholds, which determine when sections of the wetting front will be brought
to a halt (pinned), and, importantly, (c) provides a regular framework for
constructing models of increasing complexity
Viscous flows in corner regions: Singularities and hidden eigensolutions
Numerical issues arising in computations of viscous flows in corners formed
by a liquid-fluid free surface and a solid boundary are considered. It is shown
that on the solid a Dirichlet boundary condition, which removes multivaluedness
of velocity in the `moving contact-line problem' and gives rise to a
logarithmic singularity of pressure, requires a certain modification of the
standard finite-element method. This modification appears to be insufficient
above a certain critical value of the corner angle where the numerical solution
becomes mesh-dependent. As shown, this is due to an eigensolution, which exists
for all angles and becomes dominant for the supercritical ones. A method of
incorporating the eigensolution into the numerical method is described that
makes numerical results mesh-independent again. Some implications of the
unavoidable finiteness of the mesh size in practical applications of the finite
element method in the context of the present problem are discussed.Comment: Submitted to the International Journal for Numerical Methods in
Fluid
A Parametric Study of the Coalescence of Liquid Drops in a Viscous Gas
The coalescence of two liquid drops surrounded by a viscous gas is considered
in the framework of the conventional model. The problem is solved numerically
with particular attention to resolving the very initial stage of the process
which only recently has become accessible both experimentally and
computationally. A systematic study of the parameter space of practical
interest allows the influence of the governing parameters in the system to be
identified and the role of viscous gas to be determined. In particular, it is
shown that the viscosity of the gas suppresses the formation of toroidal bubble
predicted in some cases by early computations where the gas' dynamics was
neglected. Focussing computations on the very initial stages of coalescence and
considering the large parameter space allows us to examine the accuracy and
limits of applicability of various `scaling laws' proposed for different
`regimes' and, in doing so, reveal certain inconsistencies in recent works. A
comparison to experimental data shows that the conventional model is able to
reproduce many qualitative features of the initial stages of coalescence, such
as a collapse of calculations onto a `master curve' but, quantitatively,
overpredicts the observed speed of coalescence and there are no free parameters
to improve the fit. Finally, a phase diagram of parameter space, differing from
previously published ones, is used to illustrate the key findings.Comment: Accepted for publication in the Journal of Fluid Mechanic
Coalescence of Liquid Drops: Different Models Versus\ud Experiment
The process of coalescence of two identical liquid drops is simulated numerically in the framework of two essentially different mathematical models, and the results are compared with experimental data on the very early stages of the coalescence process reported recently. The first model tested is the ‘conventional’ one, where it is assumed that coalescence as the formation of a single body of fluid occurs by an instant appearance of a liquid bridge smoothly connecting the two drops, and the subsequent process is the evolution of this single body of fluid driven by capillary forces. The second model under investigation considers coalescence as a process where a section of the free surface becomes trapped between the bulk phases as the drops are pressed against each other, and it is the gradual disappearance of this ‘internal interface’ that leads to the formation of a single body of fluid and the conventional model taking over. Using the full numerical solution of the problem in the framework of each of the two models, we show that the recently reported electrical measurements probing the very early stages of the process are better described by the interface formation/disappearance model. New theory-guided experiments are suggested that would help to further elucidate the details of the coalescence phenomenon. As a by-product of our research, the range of validity of different ‘scaling laws’ advanced as approximate solutions to the problem formulated using the conventional model is\ud
established
A continuum model for the flow of thin liquid films over intermittently chemically patterned surfaces
It is known from both experiments and molecular dynamics simulations that
chemically patterning a solid surface has an effect on the flow of an adjacent
liquid. This fact is in stark contrast with predictions of classical fluid
mechanics where the no-slip boundary condition is insensitive to the chemistry
of the solid substrate. It has been shown that the influence on the flow caused
by a steep change in the wettability of the solid substrate can be described in
the framework of continuum mechanics using the interface formation theory. The
present work extends this study to the case of intermittent patterning. Results
show that variations in wettability of the substrate can significantly affect
the flow, especially of thin films, which may have applications to the design
of microfluidic devices
Viscous Flow in Domains with Corners: Numerical Artifacts, their Origin and Removal
We show that an attempt to compute numerically a viscous flow in a domain
with a piece-wise smooth boundary by straightforwardly applying well-tested
numerical algorithms (and numerical codes based on their use, such as COMSOL
Multiphysics) can lead to spurious multivaluedness and nonintegrable
singularities in the distribution of the fluid's pressure. The origin of this
difficulty is that, near a corner formed by smooth parts of the piece-wise
smooth boundary, in addition to the solution of the inhomogeneous problem,
there is also an eigensolution. For obtuse corner angles this eigensolution (a)
becomes dominant and (b) has a singular radial derivative of velocity at the
corner. A method is developed that uses the knowledge about the eigensolution
to remove multivaluedness and nonintegrability of the pressure. The method is
first explained in the simple case of a Stokes flow in a corner region and then
generalised for the full-scale unsteady Navier-Stokes flow in a domain with a
free surface.Comment: Under consideration for publication in the Journal of Fluid
Mechanics. Figure bouding box problems resolve
The effect of substrate roughness on air entrainment in dip coating
YesDynamic wetting failure was observed in the simple dip coating flow with a series of substrates, which had a rough side and a comparatively smoother side. When we compared the air entrainment speeds on both sides, we found a switch in behaviour at a critical viscosity. At viscosity lower than a critical value, the rough side entrained air at lower speeds than the smooth side. Above the critical viscosity the reverse was observed, the smooth side entraining air at lower speed than the rough side. Only substrates with significant roughness showed this behaviour. Below a critical roughness, the rough side always entrained air at lower speeds than the smooth side. These results have both fundamental and practical merits. They support the hydrodynamic theory of dynamic wetting failure and imply that one can coat viscous fluids at higher speeds than normal by roughening substrates. A mechanism and a model are presented to explain dynamic wetting failure on rough surfaces
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