Four-stage modeling of Marangoni-enhanced heat transfer in dropwise condensation on micropillars with heat flux decomposition

This study numerically investigates dropwise condensation on structured surfaces by modeling four stages of droplet growth from nucleation through Cassie–Baxter spreading. Using COMSOL Multiphysics, conduction and Marangoni convection are decoupled to demonstrate how Marangoni convection enhances heat transfer at each stage. For a representative case ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>θ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>130</mml:mn> <mml:mo>∘</mml:mo> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mi>u</mml:mi> <mml:mi>b</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>5</mml:mn> <mml:mrow> <mml:mi mathvariant="normal">K</mml:mi> </mml:mrow> </mml:math> ), Marangoni convection increased total heat flux by about 130–140% in stages 1 and 2, rose about 230–250% in stage 3, and by about 210–230% in stage 4, indicating a strong thermocapillary effect even after spreading on pillars. Across angles, the smaller one ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>θ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>100</mml:mn> <mml:mo>∘</mml:mo> </mml:math> ) has the highest absolute heat flux due to greater wall wetting; however, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>θ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>150</mml:mn> <mml:mo>∘</mml:mo> </mml:math> shows higher enhancement with Marangoni convection. Marangoni increases heat transfer by 285–400% in stages 3 and 4, whereas for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>θ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>100</mml:mn> <mml:mo>∘</mml:mo> </mml:math> the enhancement is about 220–240% in stages 1, 2, and 4 and 380% in stage 3. In stage 2, symmetric circulations in the liquid bridge maintain a constant contribution of Marangoni enhancement. In contrast, a nonmonotonic trend of enhancement was observed in stage 3, resulting from the trade-off effects of curvature and interfacial gradients. These stage-specific behaviors provide design-enabling principles for micro/nanostructured condensers to utilize thermocapillary flow, thereby achieving enhanced and uniform heat transfer performance.