25 research outputs found
Nonlinear waves in counter-current gas-liquid film flow
We investigate the dynamics of a thin laminar liquid film flowing under gravity
down the lower wall of an inclined channel when turbulent gas flows above the
film. The solution of the full system of equations describing the gas–liquid flow faces
serious technical difficulties. However, a number of assumptions allow isolating the
gas problem and solving it independently by treating the interface as a solid wall.
This permits finding the perturbations to pressure and tangential stresses at the
interface imposed by the turbulent gas in closed form. We then analyse the liquid
film flow under the influence of these perturbations and derive a hierarchy of model
equations describing the dynamics of the interface, i.e. boundary-layer equations, a
long-wave model and a weakly nonlinear model, which turns out to be the Kuramoto–
Sivashinsky equation with an additional term due to the presence of the turbulent
gas. This additional term is dispersive and destabilising (for the counter-current case;
stabilizing in the co-current case). We also combine the long-wave approximation with
a weighted-residual technique to obtain an integral-boundary-layer approximation
that is valid for moderately large values of the Reynolds number. This model is
then used for a systematic investigation of the flooding phenomenon observed in
various experiments: as the gas flow rate is increased, the initially downward-falling
film starts to travel upwards while just before the wave reversal the amplitude of the
waves grows rapidly. We confirm the existence of large-amplitude stationary waves by
computing periodic travelling waves for the integral-boundary-layer approximation
and we corroborate our travelling-wave results by time-dependent computations
Kinetic Monte Carlo and hydrodynamic modelling of droplet dynamics on surfaces, including evaporation and condensation
We present a lattice-gas (generalised Ising) model for liquid droplets on
solid surfaces. The time evolution in the model involves two processes: (i)
Single-particle moves which are determined by a kinetic Monte Carlo algorithm.
These incorporate into the model particle diffusion over the surface and within
the droplets and also evaporation and condensation, i.e. the exchange of
particles between droplets and the surrounding vapour. (ii) Larger-scale
collective moves, modelling advective hydrodynamic fluid motion, determined by
considering the dynamics predicted by a thin-film equation. The model enables
us to relate how macroscopic quantities such as the contact angle and the
surface tension depend on the microscopic interaction parameters between the
particles and with the solid surface. We present results for droplets joining,
spreading, sliding under gravity, dewetting, the effects of evaporation, the
interplay of diffusive and advective dynamics, and how all this behaviour
depends on the temperature and other parameters
Absolute and convective instabilities in non-local active-dissipative equations arising in the modelling of thin liquid films
Absolute and convective instabilities in a non-local model that arises in the analysis of thin-film flows over flat or corrugated walls in the presence of an applied electric field are discussed. Electrified liquid films arise, for example, in coating processes where liquid films are deposited onto a target surfaces with a view to producing an evenly coating layer. In practice, the target surface, or substrate, may be irregular in shape and feature corrugations or indentations. This may lead to non-uniformities in the thickness of the coating layer. Attempts to mitigate film-surface irregularities can be made using, for example, electric fields. We analyse the stability of such thin-film flows and show that if the amplitude of the wall corrugations and/or the strength of the applied electric field is increased the convectively unstable flow undergoes a transition to an absolutely unstable flo
Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder
We discuss the behavior of partially wetting liquids on a rotating cylinder using a model
that takes into account the effects of gravity, viscosity, rotation, surface tension and wettability. Such a system can be considered as a prototype for many other systems where the interplay of spatial heterogeneity and a lateral driving force in the proximity of a first- or second-order phase transition results in intricate behavior. So does a partially wetting drop
on a rotating cylinder undergo a depinning transition as the rotation speed is increased, whereas for ideally wetting liquids the behavior only changes quantitatively. We analyze the bifurcations that occur when the rotation speed is increased for several values of the
equilibrium contact angle of the partially wetting liquids. This allows us to discuss how the entire bifurcation structure and the flow behavior it encodes changes with changing wettability. We employ various numerical continuation techniques that allow us to track stable/unstable steady and time-periodic film and drop thickness profiles. We support our findings by time-dependent numerical simulations and asymptotic analyses of steady and time-periodic profiles for large rotation numbers
Liquid film coating a fiber as a model system for the formation of bound states in active dispersive-dissipative nonlinear media
We analyze the coherent-structure interaction and the formation of bound states in active dispersivedissipative
nonlinear media using a viscous film coating a vertical fiber as a prototype. The coherent
structures in this case are droplike pulses that dominate the evolution of the film.We study experimentally
the interaction dynamics and show evidence for formation of bound states. A theoretical explanation is
provided through a coherent-structures theory of a simple model for the flow
Self-similar finite-time singularity formation in degenerate parabolic equations arising in thin-film flows
A thin liquid film coating a planar horizontal substrate may be unstable to perturbations in the film thickness due to unfavourable intermolecular interactions between the liquid and the substrate, which may lead to finitetime rupture. The self-similar nature of the rupture has been studied before
by utilising the standard lubrication approximation along with the Derjaguin (or disjoining) pressure formalism used to account for the intermolecular interactions, and a particular form of the disjoining pressure with exponent n = 3 has been used, namely, Π(h) ∝ −1/h3, where h is the film thickness. In
the present study, we use a numerical continuation method to compute discrete solutions to self-similar rupture for a general disjoining pressure exponent n (not necessarily equal to 3), which has not been previously performed. We focus on axisymmetric point-rupture solutions and show for the first time that pairs of solution branches merge as n decreases, starting at nc ≈ 1.485. We verify that this observation also holds true for plane-symmetric line-rupture solutions for which the critical value turns out to be slightly larger than for the axisymmetric case, nplane c ≈ 1.499. Computation of the full time-dependent problem also demonstrates the loss of stable similarity solutions and the subsequent onset of cascading, increasingly small structures
Noise-induced state transitions, intermittency, and universality in the noisy Kuramoto-Sivashinksy [sic] equation
[We] consider the effect of pure additive noise on the long-time dynamics of the noisy Kuramoto-
Sivashinsky (KS) equation close to the instability onset. When the noise acts only on the first stable
mode (highly degenerate), the KS solution undergoes several state transitions, including critical on-off
intermittency and stabilized states, as the noise strength increases. Similar results are obtained with the
Burgers equation. Such noise-induced transitions are completely characterized through critical exponents,
obtaining the same universality class for both equations, and rigorously explained using multiscale
techniques
Axisymmetric self-similar rupture of thin films with general disjoining pressure
A thin film coating a dewetting substrate may be unstable to perturbations in the thickness, which leads to finite time rupture. The self-similar nature of the rupture has been studied by numerous authors for a particular form of the disjoining pressure, with exponent
n = 3. In the present study we use a numerical continuation method to compute discrete solutions to self-similar rupture for a general disjoining pressure exponent n. Pairs of solution branches merge when n is close to unity, indicating that a more detailed examination of the dynamics of a thin film in this regime is warranted. We also numerically evaluate the power law behaviour of characteristic quantities of
solutions in the limit of large branch number
Healing capillary films
We investigate, by means of theoretical arguments, numerical simulation and numerics, the closing of a circular cavity (healing) in a thin liquid film. We assume that the process is dominated by capillary forces. The final stages of the evolution can be described by means of self-similar solutions to the problem. A comparison with experimental data is also presented
Healing capillary films
Consider the dynamics of a healing film driven by surface tension, that is, the inward spreading process of a liquid film to fill a hole. The film is modelled using the lubrication (or thin-film) approximation, which results in a fourth-order nonlinear partial differential equation. We obtain a self-similar solution describing the early-time relaxation of an initial step-function condition and a family of self-similar solutions governing the finite-time
healing. The similarity exponent of this family of solutions is not determined purely from scaling arguments; instead, the scaling exponent is a function of the finite thickness of the prewetting film, which we determine numerically. Thus, the solutions that govern the finite-time healing are self-similar solutions of the second kind. Laboratory experiments and time-dependent computations of the partial differential equation are also performed. We compare the self-similar profiles and exponents with both measurements in experiments and time-dependent computations near the healing time, and we observe good agreement in each case