THE INFLUENCE OF THE MARANGONI EFFECT ON THE ONSET OF GRAVITACTIC BIOCONVECTION

Abstract

Self-movement of such microorganisms as Tetrahymena against gravity leads to the accumulation of cells at the free surface and, as a consequence, to an unstable density distribution. The study considers the onset of gravitactic bioconvection in a horizontal layer of a nonisothermal liquid with a free nondeformable boundary, taking into account the dependence of surface tension on the concentration of microorganisms. The dependence of the critical concentration Rayleigh number characterizing the onset of instability on the Marangoni number is analytically obtained in the long-wave approximation. It is shown that the long-wave concentration Rayleigh number does not depend on the thermal Rayleigh number, as well as on the Schmidt and Lewis numbers. The parameter ranges (the Marangoni and thermal Rayleigh numbers) in which the long-wave instability exists are found. Critical wave numbers and critical concentration Rayleigh numbers are determined from the numerical solution of the linear stability problem.