Marangoni instability at a spherical interface. Breakdown of fluid drops at low surface tension and cytokinetic phenomena in the living cell

Abstract

The possibility of unstable normal modes (l= 1, 2, 3…) of deformation of a fluid drop immersed in an infinite amount of another liquid is considered. The instability is produced by Marangoni effects (gradients in interfacial tension) caused by mass transfer of surfactants or surface chemical reactions.

For mass transfer of a single surfactant in the presence of a high surface tension, instabilities can be provoked by diffusion from outside into the drop if the outside diffusion coefficient is lower than the inside diffusion coefficient. For lower inside diffusion coefficients, modes below a certain l-value may be unstable for diffusion from outside into the drop, whereas modes above this l-value can only be unstable for the reverse direction of diffusion. For low surface tensions, instability can be provoked only by diffusion from outside into the drop; the critical threshold goes to zero when the surface tension goes to zero. The latter feature makes the model useful for conceptualisation of the distruption of fat droplets by detergents during cleansing processes, or of oil ganglia in porous rocks during tertiary oil recovery.

Cytokinetic processes in the living cell can be roughly described by the present model by the introduction of an “effective surface tension” stemming from contractile elements in the ectoplasmic layer adjacent to the cell membrane. Hydrodynamic motion is coupled together with damped oscillations of enzyme concentrations in a simple enzyme cycle by means of enzymes producing contractile elements. The model gives interesting relations between phenomena such as chemotaxis (l= 1) and cell division (l= 2) and makes possible a simple mechanism for the mitotic clock. Some forms of cancer could be understood as anomalous narrowing of the thresholds found between the oscillatory marginal states (“clock states”) and the non-oscillatory marginal states (cell division) for the l= 2 mode.