A linear stability analysis is presented for the contact instability of a soft thin elastic film which is rigidly bonded to a physically patterned substrate, and is in adhesive contact with a smooth rigid contactor. Increasing roughness by enhancing the substrate-amplitude produces increasingly smaller instability length-scales. The smallest wavelengths obtainable are 0.3 Ã h, an order of magnitude smaller than that observed with films on flat substrates (3 Ã h). Instability length-scales are found to be largely independent of substrate length-scales. For van der Waals interaction, increase in substrate roughness increases the energy penalty and, consequently, requires smaller gap distances (< 1nm for stiff films) to engender instabilities. When an externally controllable long-range electric field is employed instead, instabilities can be initiated at very low critical voltages ($32 V) even in relatively stiff films, making it a more suitable route to produce miniaturized instability patterns.

Microswimmers exposed to microchannel flows exhibit an intriguing coupling between propulsion, shape, hydrodynamics, and flow which gives rise to distinct swimming behaviors. We employ a generic coarse-grained model of prolate spheroidal microswimmers, denoted as squirmers, exposed to channel flow to shed light onto their transport properties. The embedding fluid is implemented by the multiparticle collision dynamics approach (MPC), a particle-based mesoscale simulation method, which includes thermal fluctuations. Specifically, the influence of swimmer shape-spherical vs spheroidal-, active stress-pusher, ciliate, puller-, and thermal fluctuations on their rheotactic behavior is analyzed. The microswimmers accumulate at the confining walls at very low flow rates. With increasing flow strength, squirmers are depleted from the walls, and at high flow rates are also depleted from the channel center. The squirmers show pronounced cross-channel swimming between the confining walls with mixed oscillating and rotational motions due to thermal fluctuations. This strongly affects their rheotactic behavior. In particular, spherical pullers and ciliates swim upstream, whereas spherical pushers essentially swim downstream. The anisotropic shape of spheroidal squirmers enhances wall and center depletion and the alignment of the propulsion direction parallel to the flow, which leads to preferred downstream swimming for all active stresses. This emphasizes the importance of swimmer shape and hydrodynamic wall interactions on the transport properties of a microswimmer such as Volvox and Opalina, for example.

Length scales of instabilities exhibited by soft, thin elastic films cast on smooth and sharp corrugated surfaces and in adhesive contact with an external contactor are investigated by means of linear stability analysis (LSA) and non-linear finite element analysis. The instability length scales are found to decrease with either an increase in the amplitude β or a decrease in the wavelength λp of the substrate pattern. For same substrate parameters, a step-patterned surface with higher RMS roughness is generally found to engender smaller length scales. The linear stability analysis with sinusoidally patterned substrates shows a reduced scaling of critical wavelength with substrate amplitude: λc = 2.96(1 − β)h, where h is the mean film thickness. The largest substrate amplitudes explored with finite element analysis are limited to β = 0.7, which is found to beget instability length scales of 0.89h, that are much smaller than the 3h length scale that is obtained with flat substrates. This suggests that an increase in substrate roughness via patterning can prove to be an attractive route for the production of miniaturized patterns.

A linear stability analysis is presented to understand the instabilities that arise in an elastic bilayer, consisting of a very thin bottom layer (thickness < 100 nm) that acts as a wetting film and a top layer that acts as an adhesive film, when placed in contact proximity with an external rigid contactor. Depending on whichever layer is more compliant, "squeezing modes" of instability with a variety of length scales ranging from <<3h to <<3h (h: bilayer thickness) are found to be possible. The least length scales obtained are 0.1h. The squeezing instabilities are, however, accompanied by delamination of the film-film interface. The instability length scales, the strength of interactions required, and the delamination decrease as the compliance of the top film increases. Surface tension effects are found to have a stabilizing influence which increases the instability length scales and decreases the degree of delamination at the cost of high interaction penalty.

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