Coupled self-organization: Thermal interaction between two liquid films undergoing long-wavelength instabilities

The effects of thermal coupling between two thin liquid layers, separated by a gas layer, are discussed. The liquid layers undergo long-wavelength instabilities driven by gravitational and thermocapillary stresses. To study the dynamics, both a linear stability analysis and a full numerical solution of the thin-film equations are performed. The results demonstrate that the stability properties of the combined system differ substantially from the case where both layers evolve independently from each other. Most prominently, oscillatory instabilities, not present in single-liquid layer configurations, may occur.Comment: 12 pages, 9 figure

Electroosmotic flow in small-scale channels induced by surface-acoustic waves

Numerical simulations of the Navier-Stokes, Nernst-Planck, and the Poisson equations are employed to describe the transport processes in an aqueous electrolyte in a parallel-plate nanochannel, where surface-acoustic waves (SAWs) are standing or traveling along (piezo-active) channel walls. It is found that -- in addition to the conventional acoustic streaming flow -- a time-averaged electroosmotic flow is induced. Employing the stream function-vorticity formulation, it is shown that the Maxwell stress term causes an electroosmotic propulsion that is qualitatively identical to the one discussed in the context of alternating current (AC) electroosmosis (EOF). Differences arise mainly due to the high actuation frequencies of SAWs, which are in the MHz range rather than in the kHz regime typical for ACEOF. Moreover, the instantaneous spatial periodicity of the EOF in the travel direction of the SAW is intrinsically linked to the dispersion relation of the latter rather than a free geometric parameter. This leads to a specific frequency band where an EOF of sizable magnitude can be found. On the low frequency end, the ratio between the electric double layer (EDL) thickness and the SAW wavelength becomes extremely small so that the net force leading to a non-vanishing time-averaged flow becomes equally small. On the high frequency end, the RC time of the EDL is much larger than the inverse of the SAW frequency leading to a vanishing effective charge density of the EDL. For a parallel-plate channel, the EOF can be maximized by using two SAWs on both channel walls that have the same frequency but are phase-shifted by $180^\circ$. It appears that the SAW-EOF is the dominant pumping mechanism for such a scenario. The proposed actuation might be a viable alternative for driving liquid electrolytes through narrow ducts and channels, without the need for electric interconnects and electrodes.Comment: 16 pages, 6 figure

Mechanism for Spontaneous Growth of Nanopillar Arrays in Ultrathin Films Subject to a Thermal Gradient

Several groups have reported spontaneous formation of periodic pillar-like arrays in molten polymer nanofilms confined within closely spaced substrates maintained at different temperatures. These formations have been attributed to a radiation pressure instability caused by acoustic phonons. In this work, we demonstrate how variations in the thermocapillary stress along the nanofilm interface can produce significant periodic protrusions in any viscous film no matter how small the initial transverse thermal gradient. The linear stability analysis of the interface evolution equation explores an extreme limit of B\'{e}nard-Marangoni flow peculiar to films of nanoscale dimensions in which hydrostatic forces are altogether absent and deformation amplitudes are small in comparison to the pillar spacing. Finite element simulations of the full nonlinear equation are also used to examine the array pitch and growth rates beyond the linear regime. Inspection of the Lyapunov free energy as a function of time confirms that in contrast to typical cellular instabilities in macroscopically thick films, pillar-like elongations are energetically preferred in nanofilms. Provided there occurs no dewetting during film deformation, it is shown that fluid elongations continue to grow until contact with the cooler substrate is achieved. Identification of the mechanism responsible for this phenomenon may facilitate fabrication of extended arrays for nanoscale optical, photonic and biological applications.Comment: 20 pages, 9 figure

Formation of Nanopillar Arrays in Ultrathin Viscous Films: The Critical Role of Thermocapillary Stresses

Experiments by several groups during the past decade have shown that a molten polymer nanofilm subject to a large transverse thermal gradient undergoes spontaneous formation of periodic nanopillar arrays. The prevailing explanation is that coherent reflections of acoustic phonons within the film cause a periodic modulation of the radiation pressure which enhances pillar growth. By exploring a deformational instability of particular relevance to nanofilms, we demonstrate that thermocapillary forces play a crucial role in the formation process. Analytic and numerical predictions show good agreement with the pillar spacings obtained in experiment. Simulations of the interface equation further determine the rate of pillar growth of importance to technological applications.Comment: 5 pages, 4 figure

Constraints on the preservation of proxy data in carbonate archives – lessons from a marine limestone to marble transect, Latemar, Italy

This work evaluates an exceptionally complex natural laboratory, the Middle Triassic Latemar isolated platform in the northern Italian Dolomite Mountains and explores spatial and temporal gradients in processes and products related to contact metamorphism, dolomitization and dedolomitization of marine limestones. The relation between petrographic change and re-equilibration of geochemical proxy data is evaluated from the perspective of carbonate-archive research. Hydrothermal dolomitization of the limestone units is triggered by dykes and associated hydrothermal fluids radiating from the nearby Predazzo Intrusion. Detailed petrography, fluid inclusion analysis, δ13C and δ18O data and 87Sr/86Sr isotope ratios shed light on the extreme textural and geochemical complexity. Metamorphic and diagenetic patterns include: (i) peak-metamorphic and retrograde-metamorphic phases including three dolomite marbles, two dedolomite marbles, brucite, magnesium silicates and late-stage meteoric/vadose cement at the contact aureole; (ii) four spatially defined episodes of dolomitization, authigenic quartz, low magnesium calcite and late-stage meteoric cement at the Latemar isolated platform; and (iii) kilometre-scale gradients in δ13C values from the contact aureole towards the platform interior. Results shown here are relevant for two reasons: first, the spatial analysis of alteration products ranging from high-grade metamorphic overprint of marbles at temperatures of 700˚C in the contact aureole to moderately altered limestones in the platform interior at temperatures 20 km. Second, under rock-buffered conditions, and irrespective of metamorphic to diagenetic fluid-rock interactions, both marbles, and low-temperature hydrothermal dolomites have conservative marine δ13C and δ18O values. The fact that metamorphism and hydrothermal dolomitization of precursor limestones and early diagenetic dolostones did not per se reset environmental proxy data is of interest for those concerned with carbonate archive research in Earth’s deep time