The effect of Marangoni convection on heat transfer during dropwise condensation on hydrophobic and omniphobic surfaces

A multi-fold enhancement in the rate of heat transfer can be achieved by promoting the dropwise condensation mode (DWC) over the filmwise condensation mode. Recent material developments are increasing the chances that DWC will transition into industrial applications. Consequently, the ability to quantitatively model heat transfer rate during DWC of water and low surface tension liquids will become increasingly important in design of condensers. DWC heat transfer models developed so far consider only conduction inside the condensate droplets. However, scaling analysis shows that, in contrast to buoyancy driven flow, thermocapillary flow could be present in a wide range of droplet sizes in industrially relevant conditions. In the present work, we theoretically quantify the effect of Marangoni convection on heat transfer across individual condensing droplets as well as its impact on the overall DWC heat transfer. Specifically, we use Finite Element simulations to estimate the change in heat transfer that thermocapillary flow induces in condensing drops with spherical cap geometry. Besides water, we also study heat transfer across drops of organic liquids including toluene, ethanol, and pentane. Our results indicate that heat transfer rates across droplets are higher in the conjugate heat transfer case than the conduction only case (up to 6-fold increase for large water droplets on hydrophobic and superhydrophobic surfaces under extreme subcooling of 50 K). However, irrelevant of fluid and contact angle, for smaller droplets with radius below 100 µm at most a twofold thermocapillary heat transfer enhancement was obtained. When integrated with the dropsize distribution, these multi-fold increases in heat transfer across individual drops translate in most cases to a minor 10% or lower increase in the overall dropwise condensation heat transfer coefficient. Thus, with exception of a few special cases, the Marangoni flow contribution to DWC heat transfer coefficient is on the order of typical experimental uncertainties and can be neglected.