TY - JOUR
T1 - Effects of surfactant transport on electrodeformation of a viscous drop
AU - Nganguia, Herve
AU - Pak, On Shun
AU - Young, Y. N.
N1 - Funding Information:
H.N. thanks K. Pietrzyk for helpful discussions about the analytical derivations and C. Sorgentone for providing boundary integral simulation results for comparison. Y.-N.Y. was partially supported by NSF under Grants No. DMS-1412789 and No. DMS-1614863 and by the Flatiron Institute, a division of the Simons Foundation. O.S.P. was partially supported by NSF under Grant No. EFMA-1830958.
Funding Information:
H.N. thanks K. Pietrzyk for helpful discussions about the analytical derivations and C. Sorgentone for providing boundary integral simulation results for comparison. Y.-N.Y. was partially supported by NSF under Grants No. DMS-1412789 and No. DMS-1614863 and by the Flatiron Institute, a division of the Simons Foundation. O.S.P. was partially supported by NSF under Grant No. EFMA-1830958.
Publisher Copyright:
© 2019 American Physical Society.
PY - 2019/6/10
Y1 - 2019/6/10
N2 - 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 Pes). For a leaky dielectric drop with dominant surfactant diffusion (Pes1), 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 (Pes≫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.
AB - 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 Pes). For a leaky dielectric drop with dominant surfactant diffusion (Pes1), 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 (Pes≫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.
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U2 - 10.1103/PhysRevE.99.063104
DO - 10.1103/PhysRevE.99.063104
M3 - Article
C2 - 31330602
AN - SCOPUS:85067346638
SN - 1063-651X
VL - 99
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 6
M1 - 063104
ER -