On the deformation of a shear thinning viscoelastic drop in a steady electric field

TL;DR

This paper investigates how viscoelastic drops deform under electric fields, revealing complex behaviors influenced by fluid properties, with implications for microfluidic and electrohydrodynamic applications.

Contribution

It provides a detailed numerical analysis of viscoelastic drop deformation across different electrical property regimes, highlighting the effects of elasticity and electric parameters on shape dynamics.

Findings

Deformation behavior varies significantly with conductivity and permittivity ratios.

Elasticity opposes deformation, increasing the critical electric capillary number.

Non-monotonic deformation dependence on Deborah number observed.

Abstract

The deformation of viscoelastic drops under electric fields plays a crucial role in applications such as microfluidics, inkjet printing, and electrohydrodynamic manipulation of complex fluids. This study examines the deformation and breakup dynamics of a linear Phan-Thien-Tanner (LPTT) drop subjected to a uniform electric field using numerical simulations performed with the open-source solver Basilisk. Representative combinations of conductivity ratio ($\sigma_r$) and permittivity ratio ($\epsilon_r$) are chosen from six characteristic regions of the ($\sigma_r$, $\epsilon_r$) phase space, $PR_A^+$, $PR_B^+$, $PR_A^-$, $PR_B^-$, $OB^+$, and $OB^-$. In regions where the first- and second-order deformation coefficients have the same sign ($PR_A^-$, $PR_B^-$, $OB^+$), the LPTT drops exhibit deformation dynamics that negligibley deviate from the Newtonian behavior. In the $PR_A^+$ region, drops deform into prolate spheroidal shapes below a critical electric capillary number and transition to stable multi-lobed shapes or breakup beyond this threshold. Increasing elasticity of drop opposes the deformation, thereby reducing deformation and increasing critical $Ca_E$ with the Deborah number ($De$). In the $PR_B^+$ region, drops form prolate shapes below critical $Ca_E$ and develop conical ends above it. The steady-state deformation exhibits a non-monotonic dependence on $De$, increasing at low $De$ and decreasing at higher values. A similar non-monotonic variation is also observed in critical $Ca_E$. In the $OB^-$ region, LPTT drops attain oblate shapes below critical $Ca_E$ and undergo breakup beyond it. The deformation magnitude shows a non-monotonic variation with $De$, increasing initially and decreasing at higher elasticity.