Recent work on liquid-surface-protected plasma facing components has resulted in the establishment of operating windows for candidate liquids, as well as limits on the maximum allowable liquid surface temperature in order to limit plasma impurities from liquid evaporation. In this study, an additional constraint on the maximum allowable surface temperature gradient (i.e., heat flux gradient) has been quantified. Spatial variations in the wall and liquid surface temperatures are expected due to variations in the incident radiation and particle fluxes. Thermocapillary forces created by such temperature gradients can lead to film rupture and dry spot formation in regions of elevated local temperatures. Here, attention has been focused on "non-flowing" thin liquid films similar to those formed on the surface of porous wettedwall components. Future analyses will include the effects of macroscopic fluid motion, and MHD forces.
A numerical model using the level contour reconstruction method was used to follow the evolution of the liquid free surface above a non-isothermal solid surface. The model was used to develop generalized charts for the maximum allowable spatial temperature gradients (i.e., the critical Marangoni number) as a function of the governing non-dimensional variables, viz. the Weber, Froude, and Prandtl numbers, and aspect ratio. Attention was focused on the asymptotic limit for thin liquid films (i.e., low aspect ratio) which provides a lower bound for the maximum allowable temperature gradients. Specific examples for lithium, Flibe, lithium-lead, tin, and gallium are presented. The generalized charts developed in this investigation will allow reactor designers to identify design windows for successful operation of liquid-protected plasma facing components for various coolants, film thicknesses, and operating conditions.