Nganguia Herve, Pak On Shun, Young Y-N
Department of Mathematical and Computer Sciences, Indiana University of Pennsylvania, Indiana, Pennsylvania 15705, USA.
Department of Mechanical Engineering, Santa Clara University, Santa Clara, California 95053, USA.
Phys Rev E. 2019 Jun;99(6-1):063104. doi: 10.1103/PhysRevE.99.063104.
In this work we quantify the effects of surfactant transport on the deformation of a viscous drop under a DC electric field. We study how convective and diffusive transport of surfactants at drop surfaces influence the equilibrium and dynamic deformation of a leaky dielectric drop and a conducting drop. Focusing on the prolate drop shape (elongates along the electric field), we show the differences in equilibrium deformation and flow circulation between a leaky dielectric drop and a conducting drop. We quantify the drop electrodeformation via its dependence on the interior flow circulation and the dominant surfactant transport regime (characterized by the surface Péclet number Pe_{s}). For a leaky dielectric drop with dominant surfactant diffusion (Pe_{s}≪1), equator-to-pole (pole-to-equator) circulation yields smaller (larger) equilibrium deformation with increasing surfactant coverage, compared to a clean drop. However, when convection dominates (Pe_{s}≫1), the equilibrium drop deformation increases (decreases) with larger surfactant coverage for equator-to-pole (pole-to-equator) circulation. Larger equilibrium drop deformation is found for a leaky dielectric drop than a conducting drop when the interior flow is from equator to pole. For an interior flow from pole to equator, we identify cases where larger deformation is found for a conducting interior fluid. Finally, we study the effect of the surfactant transport on the dynamic evolution of drop shape. We found the drop undergoes an overshoot in the early deformation phase, before settling to its equilibrium shape-similar to the overshoot observed for unsteady Stokes flow.
在这项工作中，我们量化了表面活性剂输运对直流电场作用下粘性液滴变形的影响。我们研究了液滴表面表面活性剂的对流和扩散输运如何影响漏电介质液滴和导电液滴的平衡变形和动态变形。聚焦于长椭球形液滴形状（沿电场方向伸长），我们展示了漏电介质液滴和导电液滴在平衡变形和流动环流方面的差异。我们通过其对内部流动环流和主导表面活性剂输运模式（以表面佩克莱数(Pe_{s})表征）的依赖性来量化液滴的电致变形。对于以表面活性剂扩散为主导的漏电介质液滴（(Pe_{s}\ll1)），与清洁液滴相比，随着表面活性剂覆盖率的增加，赤道到极点（极点到赤道）的环流产生较小（较大）的平衡变形。然而，当对流占主导时（(Pe_{s}\gg1)），对于赤道到极点（极点到赤道）的环流，平衡液滴变形随着表面活性剂覆盖率的增加而增大（减小）。当内部流动从赤道到极点时，漏电介质液滴的平衡液滴变形比导电液滴大。对于从极点到赤道的内部流动，我们确定了导电内部流体变形更大的情况。最后，我们研究了表面活性剂输运对液滴形状动态演变的影响。我们发现液滴在早期变形阶段会出现超调，然后才稳定到其平衡形状——这与非定常斯托克斯流中观察到的超调现象类似。
