Trapping mechanism of a compound droplet on a heterogeneous substrate undergoing the Marangoni effect

Abstract

We numerically study the trapping mechanism of a compound droplet attached to a heterogeneous substrate undergoing the Marangoni effect. The substrate consists of a main part and a wettability-contrasted part. The investigated parameters included Ma (ranging from 0.4 to 0.8), μ_am (varying from 0.8 to 2.4), R_io (varying from 0.3 to 0.7), and Δθ_e (ranging from 3° to 7°). The droplet becomes trapped at a low value of Ma, μ_am, and a high value of Δθ_e as it moves toward the hot side. When the droplet moves toward the cold side, it becomes trapped at a low value of Ma, but a high value of μ_am and Δθ_e. The inner droplet, in terms of the radius ratio R_io, has a significant impact on the trapping behavior of the outer droplet. Interestingly, the compound droplet with R_io≤ 0.3 crosses the wettability-contrasted part more easily the one with R_io = 0.4. In addition, when migrating toward the hot side, the compound droplet with a large contact angle allowing a larger inner droplet (0.5 ≤ R_io ≤ 0.7) is pulled across the wettability-contrasted part by the inner droplet as Ma ≥ 0.5. The trapping behavior rarely occurs in this case. Phase diagrams showing the transition between the trapping and passing behaviors are also proposed.