Thermal Modeling of Mixed Hydrophilic and Hydrophobic Surfaces

Abstract Dropwise condensation on super hydrophobic surfaces have the potential of obtaining an order of magnitude higher heat transfer than film formation and could be used for water harvesting. It can also help in desalinization and reducing cooling tower drift. Dropwise condensation could decrease the temperature difference required and thus reduce the size of condensers. A model of condensation on highly hydrophobic surfaces is presented to gain better understanding of key parameters impacting droplet growth, allow direct calculation of mass collection and heat transfer of individual droplets, and evaluation of bulk surface performance. The thermal analysis includes rapid micro droplet growth, thermal resistance due to diffusion, and impact on individual droplet by neighboring droplets and nucleation of new droplets based on time-dependent nucleation rate. It enhances the traditional thermal model by including an equivalent thermal resistance for diffusion. The model evaluates diffusion boundary layer thickness for laminar flow, temperature difference to saturation, surface orientation angle, drop contact angle and material properties. The simulation shows strong agreement with reported values for collected mass. The model confirms that the mass on surface and drainage ratio fall within the experimentally reported tolerances. Once the validity of the model has been established for highly hydrophobic surface, the model is then modified for mixed hydrophilic and hydrophobic surfaces. The hydrophilic surface significantly reduces the energy barrier for nucleation allowing nucleation to the hydrophilic nodules to be treated as instantaneous while the hydrophilic surface constrains the base size of the droplets and aids in removal of the droplets from the surface. This allows for prediction of surface performance based on the environmental conditions and surface configuration. The model includes evaluation of the diffusion boundary layer thickness for natural convection, laminar and turbulent flow regimes. The model is benchmarked against published data for validation of the model. Experimental results indicate a condensation rate of 0.406 g over 2 hours and the model predicts a condensation rate of 0.39 g over the same duration with a deviation of only 4%. The model is used to optimize mass transfer by evaluating performance based on nodule size ranging from 0.1 to 0.5 mm with 10°C subcooling below saturation. The surfaces are modeled under various boundary layer thickness in the laminar and turbulent flow conditions. The model shows that the primary source of thermal resistance is the conduction through the droplet and the equivalent thermal resistance due to diffusion. Under turbulent flow conditions, a nodule size of 0.2 mm provides the maximum condensation rate. Laminar flow conditions require a nodule size greater than 0.5 mm due to the large equivalent thermal resistance of diffusion. Laminar flow regimes have higher thermal resistance from conduction through the drop due to the large equivalent thermal resistance of diffusion. Nodule sizes ranging from 1.1 mm up to 3.7 mm are evaluated. Laminar flow is trimodal for maximum mass transfer rates with nodule sizes of 1.5 mm, 2.3 mm and 3.1 mm. At low laminar flow rates, the nodule size of 3.1 mm produces the maximum mass transfer rate with nodule sizes of 1.5 mm and 2.3 mm performing well. As flow rates increase, approaching turbulent flow transitions the maximum mass transfer rate to a nodule size of 1.5 mm with a nodule size of 2.3 mm performing well. The nodule size of 3.1 mm experiences a significant drop off in mass transfer rate at the turbulent flow regimes. The key finds are as follows: • Nucleation barrier severely limits mass collection of hydrophobic surfaces under turbulent flow conditions. • Primary source of thermal resistance is diffusion. • Under optimized turbulent flow conditions thermal resistance of droplet and diffusion are approximately equal • Thermal resistance due to surface coating is minimal • Optimum nodule sizes for turbulent flow is 0.2 mm. • Optimum nodule size for laminar flow is 1.5 mm, 2.3 mm and 3.1 mm. • Increased flow rates favor smaller nodule sizes for mass collection.