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Hydrodynamic and hydromagnetic stability

Although dynamic self-assembly, DySA, is a relatively new area of research, the past decade has brought numerous demonstrations of how various types of components – on scales from (macro)molecular to macroscopic – can be arranged into ordered structures thriving in non-equilibrium, steady states. At the same time, none of these dynamic assemblies has so far proven practically relevant, prompting questions about the field's prospects and ultimate objectives. The main thesis of this Review is that formation of dynamic assemblies cannot be an end in itself – instead, we should think more ambitiously of using such assemblies as control elements (reconfigurable catalysts, nanomachines, etc.) of larger, networked systems directing sequences of chemical reactions or assembly tasks. Such networked systems would be inspired by biology but intended to operate in environments and conditions incompatible with living matter (e.g., in organic solvents, elevated temperatures, etc.). To realize this vision, we need to start considering not only the interactions mediating dynamic self-assembly of individual components, but also how components of different types could coexist and communicate within larger, multicomponent ensembles. Along these lines, the review starts with the discussion of the conceptual foundations of self-assembly in equilibrium and non-equilibrium regimes. It discusses key examples of interactions and phenomena that can provide the basis for various DySA modalities (e.g., those driven by light, magnetic fields, flows, etc.). It then focuses on the recent examples where organization of components in steady states is coupled to other processes taking place in the system (catalysis, formation of dynamic supramolecular materials, control of chirality, etc.). With these examples of functional DySA, we then look forward and consider conditions that must be fulfilled to allow components of multiple types to coexist, function, and communicate with one another within the networked DySA systems of the future. As the closing examples show, such systems are already appearing heralding new opportunities – and, to be sure, new challenges – for DySA research.

From dynamic self-assembly to networked chemical systems

The stability of an evaporating thin liquid film on a solid substrate is investigated within lubrication theory. The heat flux due to evaporation induces thermal gradients; the generated Marangoni stresses are accounted for. Assuming the gas phase at rest, the dynamics of the vapour reduces to diffusion. The boundary condition at the interface couples transfer from the liquid to its vapour and diffusion flux. The evolution of the film is governed by a lubrication equation coupled with the Laplace problem associated with quasi-static diffusion. The linear stability of a flat film is studied in this general framework. The subsequent analysis is restricted to diffusion-limited evaporation for which the gas phase is saturated in vapour in the vicinity of the interface. The stability depends then only on two control parameters, the capillary and Marangoni numbers. The Marangoni effect is destabilizing whereas capillarity and evaporation are stabilizing processes. The results of the linear stability analysis are compared with the experiments of Poulard et al. (2003) performed in a different geometry. In order to study the resulting patterns, an amplitude equation is obtained through a systematic multiple-scale expansion. The evaporation rate is needed and is computed perturbatively by solving the Laplace problem for the diffusion of vapour. The bifurcation from the flat state is found to be a supercritical transition. Moreover, it appears that the non-local nature of the diffusion problem affects the amplitude equation unusually.

Evaporation of a thin film: diffusion of the vapour and Marangoni instabilities

Heat transfer—A review of 2003 literature

We study B\'enard-Marangoni instability in a system formed by a horizontal liquid layer and its overlying vapor. The liquid is lying on a hot rigid plate and the vapor is bounded by a cold parallel plate. A pump maintains a reduced pressure in the vapor layer and evacuates the vapor. This investigation is undertaken within the classical quasisteady approximation for both the vapor and the liquid phases. The two layers are separated by a deformable interface. Temporarily frozen temperature and velocity distributions are employed at each instant for the stability analysis, limited to infinitesimal disturbances (linear regime). We use irreversible thermodynamics to model the phase change under interfacial nonequilibrium. Within this description, the interface appears as a barrier for transport of both heat and mass. Hence, in contrast with previous studies, we consider the possibility of a temperature jump across the interface, as recently measured experimentally. The stability analysis shows that the interfacial resistances to heat and mass transfer have a destabilizing influence compared to an interface that is in thermodynamic equilibrium. The role of the fluctuations in the vapor phase on the onset of instability is discussed. The conditions to reduce the system to a one phase model are also established. Finally, the influence of the evaporation parameters and of the presence of an inert gas on the marginal stability curves is discussed.

Interfacial nonequilibrium and Bénard-Marangoni instability of a liquid-vapor system.

Improved 1.5-sided model for the weakly nonlinear study of Benard-Marangoni instabilities in an evaporating liquid layer.

The dynamics of thermal ripples at the interface of a volatile pure liquid (C2H5OH) is studied experimentally and numerically. Liquid evaporates under a flow of inert gas (N2) circulating along the interface. The evaporation rate is varied by regulating both the gas flow rate and the gas pressure. Experiments in microgravity environment allowed to identify a transition to “interfacial turbulence,” along which some particular events such as nearly periodic and possible intermittent behaviors. Direct numerical simulations have been performed, and compare qualitatively well with experimental results, offering new insights into the physical mechanisms involved. Small-scale ripples appear to arise from a secondary instability of large-scale convection cells and their motion seems to follow the corresponding large-scale surface flow. The relative role of surface tension and buoyancy in triggering these flows is assessed by comparing experiments and simulations in both microgravity and ground conditions. Qualitative features compare satisfactorily well such as typical speed and orientation of the thermal ripples, as well as spiral flow in the bulk.

/pdf/onset-of-thermal-ripples-at-the-interface-of-an-evaporating-56thnlnrns.pdf

Onset of thermal ripples at the interface of an evaporating liquid under a flow of inert gas

Benard-Marangoni instability in a bilayer liquid-gas system with a deformable interface is investigated. The present work is devoted to a linear approach. We discuss the influence on the onset of stability of the following parameters: initial temperature profile, relative thickness of the gas and liquid layers, deformation of the interface, influence of the evaporation process, and the wetting parameter.

Influence of evaporation on Bénard-Marangoni instability in a liquid-gas bilayer with a deformable interface

We propose a theoretical study of Marangoni driven convection in an evaporating liquid layer surmounted by an inert gas-vapor mixture. After reduction of the full two-layer problem to a one-sided model we use a Galerkin-Eckhaus method leading to a finite set of amplitude equations for the weakly nonlinear analysis of the problem. We analyze the stability of the roll, square, and hexagonal patterns emerging above the linear stability threshold for a water-air and for an ethanol-air system.

Jonathan Margerit

Papers

Interfacial nonequilibrium and Bénard-Marangoni instability of a liquid-vapor system.

Improved 1.5-sided model for the weakly nonlinear study of Benard-Marangoni instabilities in an evaporating liquid layer.

Onset of thermal ripples at the interface of an evaporating liquid under a flow of inert gas

Influence of evaporation on Bénard-Marangoni instability in a liquid-gas bilayer with a deformable interface

Weakly nonlinear study of Marangoni instabilities in an evaporating liquid layer.