Biomedical subjects

Michael Bestehorn

Publications and source records attributed to Michael Bestehorn.

8 recordsLinked to original sources

PubMed2006

Regular surface patterns on Rayleigh-Taylor unstable evaporating films heated from below.

We study a thin liquid film with a free surface on the underside of a cooled horizontal substrate. We show that if the fluid is initially in equilibrium with its own vapor in the gas phase below, regular surface patterns in the form of long-wave hexagons having a well-defined lateral length scale are observed. This is in sharp contrast to the case without evaporation where rupture or coarsening to larger and larger patterns is seen in the long time limit. In this way, evaporation could be used for regular structuring of the film surface. Finally, we estimate the finite wave length for the simplified case of an extended Cahn-Hilliard equation.

Chemistry, Physical↗

PubMed2005

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.

Journal Article↗

PubMed2004

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.

Journal Article↗

PubMed2003

Phase-field model for Marangoni convection in liquid-gas systems with a deformable interface.

We developed a phase-field model for Marangoni convection in a liquid-gas system with a deformable interface, heated from below. In order to describe both Marangoni instabilities (with short and long wavelengths), an additional force component must be considered in the Navier-Stokes equation. This term describes the coupling of the temperature to the velocity field via the phase-field function. It results by minimizing the free-energy functional of the system. For a bidimensional problem in linear approximation we performed a numerical code that successfully computes both Marangoni instabilities. In the limit of sharp and rigid interfaces, our results are compared with the literature.

Journal Article↗

PubMed2003

Activity dynamics in nonlocal interacting neural fields.

We study the activity of a synaptically coupled neuronal network consisting of an excitatory and an inhibitory layer with isotropic connections and nonlinear interactions. Using the mathematical model of Wilson and Cowan in two spatial dimensions, we first discuss a spatial hysteresis phenomenon. Then we analyze special traveling wave solutions with stationary shape. We establish existence conditions, derive analytic expressions of the particular solutions and their velocity, and finally present numerical simulations.

Animals↗

PubMed2003

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.

Action Potentials↗

PubMed1994

Motion of defects in rotating fluids.

We study defect motion in a rotating convection cell. We present numerical results of a generalized Swift-Hohenberg equation, which provides a model description of the vertically averaged three-dimensional (3-D) hydrodynamic equations. Our model includes non-Boussinesq effects. It also accounts for the effects of the Coriolis force induced by a rotation of the fluid layer around its vertical symmetry axis. We show that even a slow rotation well below the Kuppers-Lortz instability causes defect motion perpendicular to the convective rolls. We derive an analytic estimation of that motion.

Journal Article↗

PubMed1994

Stability of fronts separating domains with different symmetries in hydrodynamical instabilities.

A generalization of the Swift-Hohenberg (SH) equation is used to study several stationary patterns that appear in hydrodynamical instabilities. The corresponding amplitude equations allow one to find the stability of planforms with different symmetries. These results are compared with numerical simulations of a generalized SH equation (GSHE). The transition between different symmetries, the hysteretic effects, and the characteristics of the defects observed in experiments are well reproduced in these simulations. The existence of steady fronts between domains with different symmetries is also analyzed. Steady domain boundaries between hexagons and rolls, and between hexagons and squares are possible solutions in the amplitude equation framework and are obtained in numerical simulations for a full range of coefficients in the GSHE.

Journal Article↗