Enhancement of Meniscus Pump by Multiple Particles

We numerically investigate the behavior of a droplet spreading on a smooth substrate with multiple obstacles. As experimental works have indicated, the macroscopic contact line or the three-phase boundary line of a droplet exhibits significant deformation resulting in a local acceleration by successive interactions with an array of tiny obstacles settled on the substrate (Mu et al., Langmuir 2019, 35). We focus on the menisci formation and the resultant pressure and velocity fields inside a liquid film in a two-spherical-particle system to realize an optimal design for the effective liquid-transport phenomenon. Special attention is paid to the meniscus formation around the second particle, which influences the liquid supply related to the pressure difference around the first particle as a function of the distance between the two particles. We find that the meniscus around the first particle plays an additional role as the reservoir of the liquid supplied toward the second particle, which is found to enhance the total pumping effect.