Modeling the shielding effect on the evaporation of ordered and scattered drop arrays on hydrophobic and hydrophilic substrates

A new analytical model to predict the evaporation of arrays of identical sessile drops was developed and tested. This model extends the use of analytical solutions for single drops to drop arrays of virtually any structure. A comparison with the results obtained by accurate numerical solutions of the same problem showed the reliability of the method. The accuracy of the model was tested through validation with the results obtained from four different experimental investigations on arrays of evaporating sessile drops. More than 1000 different drop arrays with numerosity between four to 49 drops on seven different hydrophilic and hydrophobic substrates (contact angles ranging from 30 degrees to 150 degrees) with different compactness (drop average interdistances) were analyzed to develop relatively simple correlations to predict the minimum, maximum, and average screening coefficient of the drops in the array. It was shown that the structure of the array must be taken into account to obtain reliable results, and a method based on the use of the cross-correlation matrix of the drop coordinates was proposed and tested.