The modified Kachanov method. Evaporation of multiple droplets

Abstract Evaporation of multiple sessile droplets deposited on an impermeable flat substrate is considered in the diffusion-limited isothermal regime, with particular emphasis on determining the total quasi-stationary vapor fluxes from the droplet surfaces. The proposed approximate solution is based on Kachanov’s approximation for the vapor concentration field in the semi-infinite air domain, expressed as a linear combination of solutions to single-droplet problems, with the coefficients determined by imposing appropriate Bubnov–Galerkin orthogonality relations to enforce the boundary conditions on the droplet surfaces. A comparison of the proposed modified Kachanov method with other approximate approaches is presented. The case of multiple thin circular sessile droplets is examined in detail.