Retention analysis of droplets over compliant substrates

Abstract

Droplet dynamics over substrates hold numerous applications including fuel cell technologies, anti-icing, and cleaning technologies. However, a fundamental understanding of droplet retention over compliant substrates has not received much attention. This paper presents a detailed investigation of the effect of substrate compliance over contact angles and maximum retentive/adhesive force applied over the droplet by a substrate (of varying degrees of compliance). We have defined a non-dimensional number called "Substrate Compliance (Cs)" as Cs=γPt+ρVgtF, which can act as the parameter representing the degree of compliance of the substrate. An analytical model is developed to determine the maximum retention force applied over the droplet, which could predict the retention force offered by the substrates (with 0≤Cs≤12000) satisfactorily with a maximum deviation of 11.52 % from experimental results. Further, the effect of substrate compliance over contact angle hysteresis (CAH), the shape of the droplet, and the retention force has been investigated. CAH of droplets over a compliant substrate is found to be higher (≥200 % at inclination angle of 30o) with more elongation and higher aspect ratios as compared to a non-compliant substrate. Also, a free-hanging thin Polydimethylsiloxane (PDMS) membrane (a compliant substrate) could retain ∼146−276% higher droplet volumes compared to a PDMS-coated glass substrate. In the end, we have developed and employed an Artificial Neural Network (ANN) model to predict the composition of PDMS membranes using experimental data, which is successful with an overall R=0.90.