Simulations demonstrate droplets climbing

Microfluidics and droplet manipulation have inspired important biomedical and chemical applications. One surprising phenomenon that may provide new possibilities in microscopic vessels is the observation of droplets climbing upward against gravity on a vibrating plate. Using a proper orthogonal decomposition method, Jiao-Jiao Guo, Xiao-Peng Chen and Langquan Shui studied this counterintuitive behavior.

The authors found the first two modes of the decomposition conceptually correspond to previously proposed swaying and spreading, collectively leading to rocking. Together, they adequately modelled many of the droplet’s dynamics, including upward climbing.

Additionally, the rocking can be separated into two stages, an uphill stage and a downhill stage. During the uphill stage, a capillary wave on the droplet’s boundary travels in the inertial direction, leading to mass transfer. The wave sways back during the downhill stage before disappearing. The resulting wetting differs for the uphill and downhill stages, consistent with previous results.

The group simulated the droplet motion under the action of a periodic volumetric force to mimic vibration. The proper orthogonal decomposition was further applied on the results to simplify the problem by reducing its dimensionality.

By expanding on their simulations, additional unexpected effects may become apparent.

“A wider parameter space is going to be scanned by tuning the viscosity, contact angle and substrate vibrating parameters,” said Chen. “Of course, if we search in a wider parameter space, nonlinear effects will become more prominent, and other modes might grow.”

Source: “Surface wave mechanism for directional motion of droplet on an obliquely vibrated surface,” by Jiao-Jiao Guo, Xiao-Peng Chen, and Langquan Shui, Physics of Fluids (2020). The article can be accessed at https://doi.org/10.1063/1.5143874 .