We propose a passive technique for a drop to climb along the staircase textured surface using chemical wettability gradients. The stair structure, droplet configuration, and contact angle gradient are modeled using Lagrangian smoothed particle hydrodynamics. The stair climb efficiency of the droplet is found to be a function of wettability gradient strength. Using analytical balance of actuation and resistive forces across droplets, physical reasons behind stair climbing are established and influencing parameters are identified. Evolution of the droplet shape along with the advancing and the receding contact angles is presented from where instantaneous actuation and hysteresis forces are calculated. Using history of Lagrangian particles, circulation at the foot of stairs and progressing development of the advancing drop front are monitored. Higher efficiency in stair climbing in the case of a bigger sized drop than smaller one is obtained from simulation results and realized from force balance. Difficulty in climbing steeper stairs is also demonstrated to delineate the effect of gravitational pull against the actuation force due to the wettability gradient.
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