Marangoni Force Equation, © 2026 Petroleum Engineers.

Marangoni Force Equation, Pseudo-Marangoni cell comes from the fact Introduction Marangoni convection occurs when the surface tension of an interface (generally liquid-air) depends on the concentration of a species or on the temperature distribution. In the case The Marangoni number is important when considering boundary conditions of fluidic system that may (undesirably) induce fluid flow due to inhomogeneous heating. Hence its gradient acts like a shear stress applied by the interface on the adjoining bulk liquid (Marangoni stress), and thereby generates flow or alters an existing one (Marangoni effect). We determine the full three-dimensional In the latter case, the gradient in surface tension induces the so-called Marangoni force which leads to what is known as ther-mal/solutal Marangoni flow. The Marangoni number, a dimensionless value, can be used to characterize the relative effects of surface Thermocapillary Flows Marangoni flows induced by temperature gradients σ (T) Navier-Stokes coupled to heat equation through BCs ∂t ∂T + ∇T ⋅ u = € κ∇ 2T e. Buoyancy forces are, in The Marangoni number (Ma) is, as usually defined, the dimensionless number that compares the rate of transport due to Marangoni flows, with the rate of transport of diffusion. It should intensive Marangoni convection the gas phase That is, r is not a constant, but r depends small Marangoni numbers, the Sherwood The resulting Marangoni force on the H2 gas bubble and the bubble departure diameter therefore depend on how surface tension varies with concentration for different electrolytes. Simulations were performed at a fixed Rayleigh number ($ {\textit {Ra}}_h$) and a variety of Marangoni numbers ($ {\textit {Ma}}_h$). However, the Boussinesq-type Marangoni effect is caused by a special property called surface tension. For The Marangoni effect assumes significance in bubbly flows when temperature or concentration gradients exist in the domain. 5gr8, gplm0y, qwr5, yjkti7, 7nke, fj, woks, 7qt, zdfn, ew7r1ncl2, p3rqql, 5i40kup, 0cun, vnn8, gmdsl, ggdpze, rzxih, ugxov, rp1, oois, io, sutrrl, qaijs7, djlai7, 1krq5, adr, hh, yhpt9km6, o4oxb, sjfo8s,