Rotational control of droplet impact behavior on a soft substrate

Understanding droplet dynamics is essential for advancing biotechnology and material science. However, studies investigating droplet behavior on rotating soft substrates remain limited. This work addresses this gap by exploring the underlying physical mechanism of deionized water droplet dynamics and transport on rotating soft substrates, providing both experimental insights and theoretical scaling formulations. Unlike research on hard substrates, we introduce a modified maximum spreading factor ${\beta }_s\sim {\left(\text{We}-k\right)}^{1/4}$for droplets impacting stationary soft substrates by incorporating substrate flexibility, which aligns precisely with our experimental data. For rotating soft substrates, the interplay between flexibility and air viscosity results in highly asymmetric wetting behaviors. Through theoretical and experimental analyses, we establish a scaling law for the contact area ${\left({\beta }_{\max -T}{\beta }_{\max -R}\right)}^{1/2}\sim C{a}^{1/6}{\left(\text{We}-k\right)}^{1/4}$and an inverse scaling law ${\tau }_s\sim C{a}^{-1/6}{\left(\text{We}-k\right)}^{-1/4}$ for the spreading time. The use of rotating substrates can reduce spreading time by as much as 24 %, showing its potential for enhanced droplet control. Furthermore, we identify a critical rotational speed Bo_r,c that triggers two distinct droplet impact behaviors, independent of impact velocity. These findings provide insights for control and directional transport in droplet screening and sorting applications.