3 research outputs found
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
Effect of driving on coarsening dynamics in phase-separating systems
We consider the Cahn-Hilliard (CH) equation with a Burgers-type convective term that is used as a model of coarsening dynamics in laterally driven phase-separating systems. In the absence of driving, it is known that solutions to the standard CH equation are characterized by an initial stage of phase separation into regions of one phase surrounded by the other phase (i.e., clusters or drops/holes or islands are obtained) followed by the coarsening process, where the average size of the structures grows in time and their number decreases. Moreover, two main coarsening modes have been identified in the literature, namely, coarsening due to volume transfer and due to translation. In the opposite limit of strong driving, the well-known Kuramoto-Sivashinsky (KS) equation is recovered, which may produce complicated chaotic spatio-temporal oscillations. The primary aim of the present work is to perform a detailed and systematic investigation of the transitions in the solutions of the convective CH (cCH) equation for a wide range of parameter values, and, in particular, to understand in detail how the coarsening dynamics is affected by an increase of the strength of the lateral driving force. Considering symmetric two-drop states, we find that one of the coarsening modes is stabilized at relatively weak driving, and the type of the remaining mode may change as driving increases. Furthermore, there exist intervals in the driving strength where coarsening is completely stabilized. In the intervals where the symmetric two-drop states are unstable they can evolve, for example, into one-drop states, two-drop states of broken symmetry or even time-periodic two-drop states that consist of two traveling drops that periodically exchange mass. We present detailed stability diagrams for symmetric two-drop states in various parameter planes and corroborate our findings by selected time simulations
Instabilities of Layers of Deposited Molecules on Chemically Stripe Patterned Substrates: Ridges versus Drops
A mesoscopic continuum model is employed
to analyze the transport
mechanisms and structure formation during the redistribution stage
of deposition experiments where organic molecules are deposited on
a solid substrate with periodic stripe-like wettability patterns. Transversally invariant ridges
located on the more wettable stripes are identified as very important
transient states and their linear stability is analyzed accompanied
by direct numerical simulations of the fully nonlinear evolution equation
for two-dimensional substrates. It is found that there exist two different
instability modes that lead to different nonlinear evolutions that
result (i) at large ridge volume in the formation of bulges that spill
from the more wettable stripes onto the less wettable bare substrate
and (ii) at small ridge volume in the formation of small droplets
located on the more wettable stripes. In addition, the influence of
different transport mechanisms during redistribution is investigated
focusing on the cases of convective transport with no-slip at the
substrate, transport via diffusion in the film bulk and via diffusion
at the film surface. In particular, it is shown that the transport
process does neither influence the linear stability thresholds nor
the sequence of morphologies observed in the time simulation, but
only the ratio of the time scales of the different process phases