Direct numerical simulation of oscillatory Marangoni convection in cylindrical liquid bridges

A three-dimensional oscillatory Marangoni (thermocapillary) convection with Prandtl number Pr = 16.0849 and Marangoni number Ma = 3.30508×10⁴ in a large aspect ratio (As = H/R) range, As = 0.2-4, in a silicone oil liquid bridge with a non-deformable cylindrical surface is investigated by the finite volume method. The azimuthal wave numbers 1, 2, 3, 4, 5, 6, 10 and 16 are obtained for different aspect ratios, As. The dimensionless main frequency f*_p = fMa^-1/2H²/κ of periodic or quasi-periodic temperature oscillations strongly depends on aspect ratio, As. f*_p increases with the increment of As with approximately a bi-linear relation, and its gradient for As = 0.2-1 is less than that for As>1. The periodic and quasi-periodic oscillations are found to depend on aspect ratio, As, for fixed Pr and Ma.