numerical and experimental data on using coupled integral equation approach to model a cooling droplet

The physics and modelling of cooling and freezing of droplets in contact with a colder substrate are of interest in various engineering applications. This work provides experimental results of this process employing infrared thermography for temperature measurements at the droplet´s surface. From the experimental observation of a solidification front parallel to the substrate plane, a mixed lumped-differential model of the heat transfer process based on the Coupled Integral Equations Approach (CEIA) is proposed, reformulating the two-dimensional partial differential formulation in cylindrical coordinates into a one-dimensional transient energy equation for the droplet external surface temperature. Direct comparisons of the experimental and theoretical results for the supercooling period show excellent agreement for the droplet surface temperatures at different heights and for different values of the substrate-droplet contact angle.The reduced models, using the H_1,1∣H_0,0and H_0,0∣H_0,0 approximations, were symbolically derived and numerically solved with the NDSolve function in the Wolfram Mathematica® v.13.3 platform and compared with the experimental data collected in this study during the supercooling stage of the sessile droplets.The naming convention is used as follows. SHB, HYB, HYL refer to superhydrophobic hydrophobic and hydrophillic substrates, respectively. (a,b,c) refer to three different locations along the droplet's axis. Comparisons are made between existing and proposed models as well as with experiments while the droplet is cooling. For more details on conditions, see article.<br>