Criterion for Reversal of Thermal Marangoni Flow in Drying Drops

Abstract

The thermal Marangoni flow induced by nonuniform surface temperature has been widely invoked to interpret the deposition pattern from drying drops. The surface temperature distribution of a drying droplet, although being crucial to the Marangoni flow, is still controversial. In this paper, the surface temperature in the drop central region is analyzed theoretically based on an asymptotic analysis on the heat transfer in such region, and a quantitative criterion is established for the direction of the surface temperature gradient and the direction of the induced Marangoni flow of drying drops. The asymptotic analysis indicates that these two directions will reverse at a critical contact angle, which depends not only on the relative thermal conductivities of the substrate and liquid, but also on the ratio of the substrate thickness to the contact-line radius of the droplet. The theory is corroborated experimentally and numerically, and may provide a potential means to control deposition patterns from drying droplets.

Microdroplet evaporation on superheated surfaces

“…There is a relatively vast literature on these topics, and we refer the reader to Refs. [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] and the citations therein.…”

Thermal effects of substrate on Marangoni flow in droplet evaporation: Response surface and sensitivity analysis

“…Here, R N ¼ h s k l =R 0 k s is a non-dimensional parameter: the product of relative substrate thickness h s =R 0 and relative thermal conductivity of liquid and substrate k l =k s . The analysis of Xu et al [13] for a non-heated substrate indicates that for the values of R N above the curve, i.e. R N > aðhÞ, the resultant Marangoni flow is directed radially outward along the liquid-gas interface.…”

“…We compare our numerical results with an asymptotic analysis reported in the literature [13], where a quantitative criterion to determine the direction of the induced Marangoni flow is described. The curve of the critical function R N ¼ aðhÞ is plotted in Fig.…”

“…Marangoni flow) and resultant bulk flow have been extensively studied, the influence of thermal effects of the substrate on Marangoni flow patterns is less well-understood. Further theoretical analysis has pointed out that the direction of Marangoni flow is determined by both the relative thermal conductivity [12] and the relative substrate thickness [13], ultimately alters the deposition patterns. However, these investigations were limited to the case of nonheated substrate; the impact of substrate temperature was not taken into account.…”

Onset of Marangoni convection for evaporating sessile droplets

“…Many researchers have investigated the Marangoni flow patterns in evaporating sessile droplets [1,[9][10][11][12]2,13,14]. It has been argued that the direction and magnitude of the circulating flow within evaporating sessile droplets depends sensitively on the ratio of thermal conductivities of the liquid and substrate [2,13,14].…”