Rayleigh–Bénard–Marangoni convection in a weakly non-Boussinesq fluid layer with a deformable surface

2018 ◽  
Vol 30 (2) ◽  
pp. 024103 ◽  
Author(s):  
D. V. Lyubimov ◽  
T. P. Lyubimova ◽  
N. I. Lobov ◽  
J. I. D. Alexander
Keyword(s):  
Marangoni Convection ◽  
Fluid Layer ◽  
Deformable Surface ◽  
Boussinesq Fluid ◽  
Rayleigh Benard

Oscillatory instability in a weakly non-Boussinesq fluid layer with a deformable surface

2018 ◽  
Vol 30 (7) ◽  
pp. 074102
Author(s):  
D. V. Lyubimov ◽  
T. P. Lyubimova ◽  
N. I. Lobov ◽  
A. E. Samoilova
Keyword(s):  
Fluid Layer ◽  
Oscillatory Instability ◽  
Deformable Surface ◽  
Boussinesq Fluid

Stabilization of the no-motion state in the Rayleigh–Bénard problem

1994 ◽  
Vol 447 (1931) ◽  
pp. 587-607 ◽  
Keyword(s):  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Control Flow ◽  
Feedback Controller ◽  
Linear Stability Theory ◽  
Motion State ◽  
Conduction State ◽  
Bénard Problem ◽  
Benard Problem ◽  
Rayleigh Benard

Using linear stability theory and numerical simulations, we demonstrate that the critical Rayleigh number for bifurcation from the no-motion (conduction) state to the motion state in the Rayleigh–Bénard problem of an infinite fluid layer heated from below and cooled from above can be significantly increased through the use of a feedback controller effectuating small perturbations in the boundary data. The controller consists of sensors which detect deviations in the fluid’s temperature from the motionless, conductive values and then direct actuators to respond to these deviations in such a way as to suppress the naturally occurring flow instabilities. Actuators which modify the boundary’s temperature or velocity are considered. The feedback controller can also be used to control flow patterns and generate complex dynamic behaviour at relatively low Rayleigh numbers.

Marangoni convection of a viscous fluid over a vibrating plate

2019 ◽  
Vol 475 (2227) ◽  
pp. 20190214
Author(s):  
M. Celli ◽  
A. V. Kuznetsov
Keyword(s):  
Viscous Dissipation ◽  
Marangoni Convection ◽  
Fluid Layer ◽  
Plane Waves ◽  
Internal Heat ◽  
Runge Kutta Method ◽  
Insight Into ◽  
Unstable Temperature ◽  
Upper Boundary ◽  
Vibrating Plate

This research presents a new insight into Marangoni convection through investigating, both numerically and analytically, the surface tension driven instability activated by a coupled effect of a vibrating plate and viscous dissipation. A horizontal, thin fluid layer is bounded from below by an impermeable, adiabatic plate that vibrates in the horizontal direction. The upper boundary is modelled by a free surface subject to a thermal boundary condition of the third kind (Robin). The internal heat generation due to viscous dissipation yields a vertical, potentially unstable temperature gradient. The linear stability analysis of the stationary terms of the basic state is performed. The perturbed flow, in the form of plane waves, is superimposed onto the basic state. The obtained system of ordinary differential equations is solved numerically by means of the Runge–Kutta method coupled with the shooting method. For the two limiting cases, the isothermal upper boundary and adiabatic upper boundary, the analytical solutions of the eigenvalue problem are obtained. The values of the critical parameter, which identifies the threshold for the onset of Marangoni convection, are presented.

Dissipative Structures in Demixing Binary Liquid Systems

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1309-1316 ◽  
Author(s):  
Roland Zander ◽  
Michael Dittmann ◽  
Gerhard M. Schneider
Keyword(s):  
Fluid Layer ◽  
Synergetic Effect ◽  
Sample Volume ◽  
Dissipative Structures ◽  
Vertical Temperature ◽  
Convective Structures ◽  
Liquid Systems ◽  
Convective Pattern ◽  
Rayleigh Benard ◽  
Horizontal Fluid Layer

AbstractThe demixing of a horizontal fluid layer of far-critical composition in the presence of a vertical temperature gradient can cause the formation of dissipative structures and thereby lead to a regular distribution of the precipitate. The occurrence of these convective structures is explained with the model of a Rayleigh-Benard instability (RBI) which is driven by parallel gradients of temperature and concentration. The distribution of the precipitate is a synergetic effect of the macroscopic convective pattern and the local action of the Marangoni flow at the surfaces of the drops. If boundary conditions prohibit an RBI, the distribution of the precipitate also becomes inhomogeneous in course of time; however, in this case no regular pattern is observable and the inhomogeneities develop mainly due to the Marangoni convection near the surfaces of the larger drops that have settled at the boundary of the sample volume

Sign in / Sign up

Export Citation Format

Share Document