We present a mathematical model for dropwise condensation (DWC) heat transfer on a surface with wettability gradient. We adapt well-established population balance model for DWC on inclined surfaces to model DWC on a surface with wettability gradient. In particular, our model takes into account the effect of wettability gradient and energy released during drop coalescence to determine the drop departure size. We validate our model with published experimental data of DWC heat flux and drop size distribution. Based on various experimental studies on drop motion, we also propose a mechanism that explains how the energy released during drop coalescence on a surface with wettability gradient and in a condensation environment aids drop motion. The mechanism correctly explains the shift of center of mass of two coalescing drops on a surface with wettability gradient toward the drop on high wetting region. Using the model, we analyze the effect of wettability gradient on the DWC heat flux. Our model predictions show that the optimal choice of wettability gradient is governed by differential variations in population density and heat transfer through a drop with change in wettability of the surface. We also demonstrate that contact angle at which there is maximum heat transfer through a drop varies with thickness of coating layer leading to change in optimal wettability gradient.

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