Dropwise condensation in the presence of non-condensable gas: Interaction effects of the droplet array using the distributed point sink method

•Dropwise condensation with the presence of non-condensable gas is studied.•The distributed point sink method is proposed for the interactions between droplets.•The point sink method and the method of images are further considered for comparison.•The interactions between droplets in the full range can be determined by this method. With the presence of NCG, the vapor diffusion from ambient to the vapor/liquid interface must be considered during dropwise condensation. Historically, modeling dropwise condensation often makes the assumption that the droplet is growing in an isolated way. However, the blocking effect of surrounding droplets will tremendously influence the spatial distribution of vapor, which finally determines a different condensation rate comparing with that by the isolated-droplet growth model. Consequently, an accurate prediction for dropwise condensation must include the blocking effect of neighbors (namely the interaction effect). Some classical methods, including the point sink method (PSM) treating the droplet as single point sink, the method of images (MOI) constructing an infinite series of the point sinks in order to satisfy certain boundary conditions, provide a significant improvement comparing the isolated droplet growth model without considering the interaction between droplets. For capturing the strong interaction during dropwise condensation because of a large number of the droplets and the closer inter-droplet spacing, a distributed point sinks method (DPSM) is proposed. Just like in the method of Green’s function with a total mass “sink” responsible for the vapor concentration profile, the condensation droplets are resolved into many mass point “sinks”. For guaranteeing the boundary conditions, for each droplet a series of point sinks are spherically distributed inside the droplet using an average manner. The strengths of the point sinks are solved through a matrix formulation which requires certain boundary conditions and the target points of the droplet surface mapped from the point sinks. Considering some simple droplet arrays and a general droplet array in dropwise condensation, the solutions of DPSM are then compared with those using PSM and MOI. Based on the uniqueness theorem, the exactly satisfied boundary conditions state the ability of DPSM in solving the strong interaction. Finally, the DPSM is used to predict the droplet interactions of a characteristic droplet array from dropwise condensation experiments.