Collective propulsion of viscous drop pairs based on Quincke rotation in a uniform electric field

Abstract

Droplet collective propulsion is a crucial technology for microscale engineering applications. Despite great progress, current approaches to droplet manipulation still face many challenges. Here, a novel strategy for the collective propulsion of droplet pairs is proposed, which is based on two fundamental dynamics phenomena: i) the Quincke rotation; ii) the dynamics of vortex pairs. In this work, a two-dimensional (2D) numerical computation is performed to study the effect of viscosity ratio (λ = μi/μo ≤ 60, “i” and “o” indicate the drop and bulk phase) and electric field strength (E0*≤ 6.78) on the collectively propelling performance and reveal the propelled mechanisms of the droplet pair with fixed conductivity ratio Q (=σi/σo) = 0.01 and permittivity ratio S (=εi/εo) = 0.5. The novel approach to spontaneous propulsion proposed in this work achieves the remote manipulation of droplets without limiting the translation distance. The translation velocity can reach 2.0 mm/s for the examined cased in this work. In addition, the findings indicate that two factors determine the collective propulsion of droplet pairs: the strength of the Quincke vortex (Γ*) and the front vortex pair, which appears at the front end of the droplet pair and essentially counteracts the propulsion. For 5.0 < λ < 10, a weaker front vortex pair is generated. The increase in λ augments the strength of the Quincke vortex and in turn accelerates the collective propulsion. As 10 < λ < 28, the increasing λ results in a stronger front vortex pair and thus weakens the performance. As λ > 28, the direction of translation is reversed and the front vortex pair becomes weaker until it disappears completely at λ = 50. Thus, the increase in λ improves the collectively propelled performance in λ > 28. In addition, the effect of E0* on the collective propulsion is examined with varied λ (=8, 15, 50) and the fixed Q = 0.01, S = 0.5. The stronger E0* can lead to a faster translation. However, when the drop pair with the higher viscosity (λ = 50) is exposed to a stronger electric field (E0* = 5.08), two drops undergo irregular electrorotation (the direction of rotation changes alternately). The alternating up/down translation cannot produce the directional translation.