Michael Bestehorn

Morphology changes in the evolution of liquid two-layer films

We consider a thin film consisting of two layers of immiscible liquids on a solid horizontal (heated) substrate. Both the free liquid-liquid and the liquid-gas interface of such a bilayer liquid film may be unstable due to effective molecular interactions relevant for ultrathin layers below 100-nm thickness, or due to temperature-gradient-caused Marangoni flows in the heated case. Using a long-wave approximation, we derive coupled evolution equations for the interface profiles for the general nonisothermal situation allowing for slip at the substrate. Linear and nonlinear analyses of the short- and long-time film evolution are performed for isothermal ultrathin layers, taking into account destabilizing long-range and stabilizing short-range molecular interactions. It is shown that the initial instability can be of a varicose, zigzag, or mixed type. However, in the nonlinear stage of the evolution the mode type, and therefore the pattern morphology, can change via switching between two different branches of stationary solutions or via coarsening along a single branch.

Pattern formation in intracortical neuronal fields

This paper introduces a neuronal field model for both excitatory and inhibitory connections. A single integro-differential equation with delay is derived and studied at a critical point by stability analysis, which yields conditions for static periodic patterns and wave instabilities. It turns out that waves only occur below a certain threshold of the activity propagation velocity. An additional brief study exhibits increasing phase velocities of waves with decreasing slope subject to increasing activity propagation velocities, which are in accordance with experimental results. Numerical studies near and far from instability onset supplement the work.

Alternative pathways of dewetting for a thin liquid two-layer film

We consider two stacked ultrathin layers of different liquids on a solid substrate. Using long-wave theory, we derive coupled evolution equations for the free liquid-liquid and liquid-gas interfaces. Depending on the long-range van der Waals forces and the ratio of the layer thicknesses, the system follows different pathways of dewetting. The instability may be driven by varicose or zigzag modes and leads to film rupture either at the liquid-gas interface or at the substrate. We predict that the faster layer drives the evolution and may accelerate the rupture of the slower layer by orders of magnitude, thereby promoting the rupture of rather thick films.

Long-wave theory of bounded two-layer films with a free liquid-liquid interface: Short- and long-time evolution

We consider two layers of immiscible liquids confined between an upper and a lower rigid plate. The dynamics of the free liquid–liquid interface is described for arbitrary amplitudes by an evolution equation derived from the basic hydrodynamic equations using long-wave approximation. After giving the evolution equation in a general way, we focus on interface instabilities driven by gravity, thermocapillary and electrostatic fields. First, we study the linear stability discussing especially the conditions for destabilizing the system by heating from above or below. Second, we use a variational formulation of the evolution equation based on an energy functional to predict metastable states and the long-time pattern morphology (holes, drops or maze structures). Finally, fully nonlinear three-dimensional numerical integrations are performed to study the short- and long-time evolution of the evolving patterns. Different coarsening modes are discussed and long-time scaling exponents are extracted.

Bénard–Marangoni convection in a strongly evaporating fluid

We consider a volatile fluid with a free surface. If the evaporation rate is large enough, the temperature gradient caused by latent heat may destabilize the conducting, motionless state and convection sets in. The conditions for instability are computed by means of a linear stability analysis of the full two-layer system. A 3D numerical integration of the one-layer system with a very large effective Biot number shows the evolution of squares as a secondary bifurcation rather close above onset. Time dependent, chaotic states are obtained for larger temperature gradients. The influence of a large Biot number on wave length selection and pattern morphology is studied.

Sliding drops on an inclined plane

Abstract An evolution equation for the film thickness was derived recently combining diffuse interface theory and long-wave approximation (Phys. Rev. E 62 (2000) 2480). Based on results for the structure formation in a thin liquid film on a horizontal plane, we study one-dimensional periodic drop profiles sliding down an inclined plane. The analysis of the dependence of their amplitude, velocity, advancing and receding dynamic contact angles on period and the interaction parameters reveals an universal regime of flat drops. The main properties of the flat drops do not depend on their volume. Both types of drops—the universal flat drops and the non-universal drops—are analyzed in detail, especially the dependence of their properties on inclination angle. Finally, an outlook is given on two-dimensional drops and front instabilities.

Interfacial turbulence in evaporating liquids: Theory and preliminary results of the ITEL-master 9 sounding rocket experiment

Abstract Evaporation of a pure liquid into a inert gas is studied theoretically and experimentally. In contrast with the case where the gas phase is made of pure vapor, the thermocapillary (Marangoni) effect strongly destabilizes the system, and results in intensive and often chaotic forms of interfacial convection. Theoretically, a generalized one-sided model is proposed, which allows the solution of the thermo-hydrodynamic equations in the liquid phase only, still taking into account relevant effects in the gas phase. The equivalent heat transfer coefficient (Biot number) to be incorporated in this one-sided model appears to be high, which results in an acceleration of transitions to polygonal chaotic patterns. Chaotic interfacial patterns driven by the Marangoni effect have indeed been observed during the ITEL-Maser 9 sounding rocket experiment flown in March 2002, in preparation of the CIMEX (Convection and Interfacial Mass Exchange) experiment foreseen for the International Space Station.

Associative memory of a dynamical system: the example of the convection instability

It is shown that a fluid heated from below can reconstruct an incomplete initial pattern in the sense of an associative memory. This property of the fluid is based on the formal similarity between the order parameter equations of the fluid close to its instability point and those used in pattern recognition by means of synergetic computers. Under certain external conditions the system may additionally show multistable behaviour and discriminate between two offered initial patterns with different symmetries, such as a square and a rectangle.

Effect of fluctuations on the onset of density-driven convection in porous media

We study the dissolution of CO2 in saline aquifers. The long diffusion times can be accelerated by orders of magnitude from mass transfer that origins from convection. Convection occurs at a critical time via a phase transition from the horizontally homogeneous diffusion state. To start the instability, perturbations that break the horizontal translation symmetry are necessary. We start with the basic equations and the boundary conditions, examine the linearized equations around the diffusive time and z-dependent base state and compare different definitions of the critical time found in the literature. Taking a simple model we show the role of fluctuations for delayed instabilities if the control parameter is slowly swept through the bifurcation point. Apart from the critical time we use a “visible” time where convection is manifested in the vertical CO2 transport. We specify the perturbations with respect to their strength and length scale, and compute the critical times for various cases by numerical in...

Transient patterns of the convection instability: a model-calculation

Using a recently derived non-linear partial differential equation describing the temperature field we have performed computer calculations on the evolving convection patterns in different geometries. In this way we calculate the generation of various patterns e.g. of rolls or hexagons.