20 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
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
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
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
The Formation of a Bubble from a Submerged Orifice
The formation of a single bubble from an orifice in a solid surface,
submerged in an in- compressible, viscous Newtonian liquid, is simulated. The
finite element method is used to capture the multiscale physics associated with
the problem and to track the evolution of the free surface explicitly. The
results are compared to a recent experimental analysis and then used to obtain
the global characteristics of the process, the formation time and volume of the
bubble, for a range of orifice radii; Ohnesorge numbers, which combine the
material parameters of the liquid; and volumetric gas flow rates. These
benchmark calculations, for the parameter space of interest, are then utilised
to validate a selection of scaling laws found in the literature for two regimes
of bubble formation, the regimes of low and high gas flow rates.Comment: Accepted for publication in the European Journal of Mechanics
B/Fluid