The Rayleigh–Benard problem in extremely confined geometries with and without the Soret effect

We examine the linear stability of a liquid layer heated from below (the classical Rayleigh–Benard problem) but laterally confined between four vertical rigid and adiabatic boundaries. The main feature of the present study is that the height of the layer is much greater than the two other horizontal dimensions. The Soret effect is also taken into account. The ultimate objective of the study is a better knowledge of the operation of thermogravitational columns, and the search for a possible new way to measure positive Soret coefficients based on the variation of the critical Rayleigh number.