Mathematical Model for Dropwise Condensation on a Surface With Wettability Gradient

Abstract

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.

About the Role of Falling Droplets’ Sweeping in Surface Renewal during Dropwise Condensation

“…Assuming a regular array of these nucleation sites on the substrate leads to in the case of a hydrophilic substrate and in the case of a hydrophobic substrate, where N s is the nucleation site density and θ is the advancing contact angle. For the size distribution N ( r ) of large drops, the authors ,,− , generally used the semiempirical law introduced by Le Fevre and Rose . A useful expression of this law was derived by Rose and Glicksman where r max is the maximum curvature radius of the drops, that is, the radius of the drop when it starts moving on the surface.…”

“…To solve eq without knowing τ, two boundary conditions are required. Usually, these boundary conditions are chosen at r = r e , assuming continuity of both the distribution function and its derivative ,,− , …”

“…Assuming a regular array of these nucleation sites on the substrate leads to = in the case of a hydrophobic substrate, where N s is the nucleation site density 18 and θ is the advancing contact angle. For the size distribution N(r) of large drops, the authors 3,4,[14][15][16][17]19 generally used the semiempirical law introduced by Le Fevre and Rose. 2 A useful expression of this law was derived by Rose and Glicksman 18 i k j j j j j y…”

“…The second approach, widely used, ,− considers a hybrid model combining the semiempirical law for the biggest droplets (BDs) and statistical considerations for the smallest ones. As the analysis of such a model is part of the objectives of the present work, its outlines are reported in the following section.…”

Advances in vapor dropwise condensation heat transfer

“…值得注意的是, (3) 工程应用场景下的综合考虑. 在优化基本模型 的同时, 学界也对凝结传热模型在各种工程应用背景 下的发展进行了研究, 考虑了包括水平管 [43] 和倾斜 管 [44,45] 、湿空气 [46] 、特殊功能表面 [47,48] 等因素对传热 系数的影响. 相关代表性工作小结如下.…”