Frontiers in Heat and Mass Transfer (FHMT), 14, 1 (2020) DOI: 10.5098/hmt.14.1 Global Digital Central ISSN: 2151-8629 1 DIRECT SIMULATIONS OF BIPHILIC-SURFACE CONDENSATION: OPTIMIZED SIZE EFFECTS Zijie Chen a , Sanat Modak a , Massoud Kaviany a,* , Richard Bonner b a Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, 48109, the United States b Advanced Cooling Technologies, Lancaster, PA, 17601, the United States ABSTRACT In dropwise condensation on vertical surface, droplets grow at nucleation sites, coalesce and reach the departing diameter. In biphilic surfaces, when the hydrophobic domain is small, the maximum droplet diameter is controlled by the shortest dimension where the droplets merge at the boundary. Through direct numerical simulations this size-effect heat transfer coefficient enhancement is calculated. Then the 1-D biphilic surface is optimized considering the size-dependent hydrophilic domain partial flooding (directly simulated as a liquid rivulet and using the capillary limit), the subcooling (heat flux) and condenser length effects. The predicted performance is in good agreement with the available experiments. Keywords: Dropwise condensation, biphilic (hydrophobic-hydrophilic) surface, size effect, partial flooding, heat transfer coefficient enhancement 1. INTRODUCTION The heat transfer coefficient for dropwise condensation (DWC) on vertical surfaces is an order of magnitude larger than that for filmwise condensation (FWC) (Glicksman and Hunt, 1972), however, the DWC is challenging to maintain and easily transits to FWC (Ghosh et al., 2014). DWC consists of droplet nucleation, growth, coalescence, and departure followed by re-nucleation, with droplets ranging in size from the smallest nucleating droplets to departing droplets or even larger (Kim et al., 2015). After the droplet reaches the departure size, sweeping occurs and this could accelerate the process of dropwise condensation since the falling droplet will coalesce with and sweep the droplets in its path (Dietza et al., 2010). Under ideal dropwise condensation, the equilibrium size distribution for the droplets generally follows a power law distribution as incorporated in the so-called Rose model (Rose and Glicksman, 1972). In practice, various interfacial, constriction and other resistances can shift the droplet distribution, causing a reduction in the DWC heat transfer coefficient. To promote the DWC, micro/nano surface structures (Shang et al., 2018 and Zarei et al., 2018), as well as inorganic (gold) coatings Wilkins et al., 1973, hydrophobic porous membranes (Hu and N. Chung, 2018) and hydrophobic organic (polymers (Lu et al., 2015), self-assembled monolayers (Modak et al., 2019)), wick structure in pipe (Yunus and S. Alsoufi, 2019) have been used. To further enhance the heat transfer coefficient, bilphilic (patterned hydrophobic and hydrophilic) surfaces have been created with one- dimensional (1-D) (Peng et al., 2015) and two-dimensional (2-D) (Van Dyke et al., 2015) patterns. Due to the advantages of the DWC, its studies have a rather long history, including analytical studies of the dropwise condensation mechanism e.g., growth rate, drop size distribution, nucleation density. The direct simulations of the DWC also investigate the nucleation density, the effect of saturation temperature (Glicksman and Hunt, 1972), the drop size distribution (Leach et al., 2016), the vapor pressure effect (Wu et al., 2001), self-propelling mechanism for poly-sized droplets (Chen et al., 2019). The DWC experiments generally are for surfaces larger than several hundred microns, the experimental evaluation of the * Corresponding author. Email: kaviany@umich.edu very small droplets is challenging (due to the rapid growth, large number of droplets, small scale, etc.). So far no study has addressed the surface size effect on enhancing the heat transfer coefficient of the DWC (and its direct simulations). Therefore, the surface size effect around and below hundred microns is addressed here with direct simulations using random droplet generation followed by the dropwise condensation processes. Then we consider periodic 1-D biphilic surface pattern, with the hydrophilic strips draining the condensate that formed in the hydrophobic strips by the DWC. We evaluate the surface-averaged heat transfer coefficient and compare with the available experimental results. The goal is to show the interplay of enhancement of the heat transfer by the surface size-effect of the hydrophobic domain, while avoiding flooding of the hydrophilic domain. 2. SIZE EFFECT OF DWC When the domain size is below a threshold, as in biphilic patterned surfaces or partially-exposed surfaces, the droplets disappear at the boundaries. This intervening droplet removal process limits the maximum droplet size which in turn increases the heat transfer coefficient. Here we directly (numerically) simulate the DWC and evaluate the domain size effect and define the size-effect and no-size- effect regimes. 2.1 Direct simulation of DWC Heat transfer through a droplet Direct simulations of conduction through a droplet is made using the Star CCM+ code. The geometry is a spherical cap, as shown in Fig. 1(a). Progressively smaller mesh size was used until heat transfer results varied by less than 1%. The spherical cap can also be presented alternatively by a liquid film of uniform thickness δ l (Modak et al., 2019), through δ l = k l ∆T sc q , (1) Frontiers in Heat and Mass Transfer Available at www.ThermalFluidsCentral.org