Browsing by Author "Thiele, Uwe"

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Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder
(2016-08)
Lin, Te-Sheng
;
Rogers, Steven
;
Tseluiko, Dmitri
;
Thiele, Uwe
;
應用數學系
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 change 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. Published by AIP Publishing.
Instabilities of Layers of Deposited Molecules on Chemically Stripe Patterned Substrates: Ridges versus Drops
(2015-09-29)
Honisch, Christoph
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Lin, Te-Sheng
;
Heuer, Andreas
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Thiele, Uwe
;
Gurevich, Svetlana V.
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.