[Paper Review] Electrohydrodynamic migration of a surfactant-coated deformable drop in Poiseuielle flow

Antarip Poddar, Shubhadeep Mandal+2 more|arXiv (Cornell University)|Jun 26, 2018

Electrohydrodynamics and Fluid Dynamics52 references4 citations

TL;DR

This study investigates the electrohydrodynamic migration of a surfactant-coated, deformable drop in a Poiseuille flow using a leaky dielectric model and a double asymptotic perturbation method under small electric Reynolds number and capillary number. The results reveal a highly non-linear coupling between surfactant-induced Marangoni stresses, electrohydrodynamic forces, and flow curvature, enabling selective control over drop migration direction and speed through tailored electrical and surfactant properties, offering new degrees of freedom in microfluidic droplet actuation.

ABSTRACT

In this study we attempt to explore the consequences of surfactant coating on the electrohydrodynamic manipulation of a drop motion in a plane Poiseuielle flow. In addition we consider bulk insoluble surfactants and a linear dependency of the surface tension on the surfactant concentration. Subsequently a double asymptotic perturbation method is used in terms of small electric Reynolds number and capillary number in the limit of a diffusion-dominated surfactant transport mechanism. Also going beyond the widely employed axisymmetric framework, the coupled system of governing differential equations in three dimensions are then solved by adopting the `generalized Lamb solution technique'. The expressions of key variables suggest that the flow curvature of the external flow, the electric field effects and the surfactant effects are coupled in a non-trivial manner, well beyond a linear superposition. A careful investigation shows that surfactant-induced Marangoni stresses interacts with the electrohydrodynamic stresses in a highly coupled fashion. Owing to this, under different combinations of electrical conductivity and permittivity ratios, the Mason number and the applied electric field direction, the surfactants affect differently on the longitudinal as well as cross-stream migration velocity of the drop. The present results may be of utmost importance in providing a deep insight to the underlying complex physical mechanisms. Most importantly the ability of surfactants in selectively controlling the drop motion in different directions, makes them suitable for achieving a new degree of freedom in the electrical actuation of droplets in the microfluidic devices.

Motivation & Objective

• To understand the coupled effects of surfactant coating, electrohydrodynamic forces, and Poiseuille flow on the migration and deformation of a deformable drop.
• To extend beyond axisymmetric models by solving the 3D governing equations using the generalized Lamb solution technique.
• To quantify how surfactant-induced Marangoni stresses interact with electrohydrodynamic stresses in altering cross-stream and longitudinal migration velocities.
• To identify conditions under which surfactants can be used to direct droplets toward or away from the channel centerline via electrical actuation.

Proposed method

• Employed a leaky dielectric model to solve the electric potential field in the presence of an external electric field.
• Applied a double asymptotic perturbation method in terms of small electric Reynolds number and capillary number, assuming diffusion-dominated surfactant transport.
• Used a linear dependence of surface tension on surfactant concentration and modeled bulk insoluble surfactants.
• Solved the coupled system of 3D governing equations using the generalized Lamb solution technique to handle non-axisymmetric flow configurations.
• Validated results by recovering known limiting cases, including clean drop motion in Poiseuille flow and surfactant effects without electric fields.
• Conducted parametric studies on Mason number, electric field direction, conductivity and permittivity ratios, and surfactant sensitivity to assess migration behavior.

Experimental results

Research questions

• RQ1 How does surfactant coating alter the electrohydrodynamic migration of a deformable drop in a Poiseuille flow beyond linear superposition?
• RQ2 In what way do Marangoni stresses from surfactant gradients interact with electrohydrodynamic stresses to influence cross-stream and longitudinal migration velocities?
• RQ3 Can the direction of droplet migration (toward or away from the channel centerline) be controlled by tuning electrical conductivity and permittivity ratios in combination with surfactant effects?
• RQ4 How does the sensitivity of surface tension to surfactant concentration affect drop deformation and its resulting migration speed?
• RQ5 What role does flow curvature play in modifying the electrohydrodynamic response of a surfactant-coated drop?

Key findings

• The surfactant-induced Marangoni stress and electrohydrodynamic stress are coupled in a non-trivial, non-linear manner, leading to complex migration dynamics not predictable by linear superposition.
• For specific combinations of electrical conductivity and permittivity ratios, surfactants can be used to direct the droplet toward or away from the channel centerline.
• The cross-stream migration velocity is significantly altered by the interplay between drop deformation and surfactant concentration sensitivity, with 'tip stretching' phenomena playing a key role.
• The longitudinal migration velocity is modulated by the competition between electrohydrodynamic flow modification and Marangoni-induced surface flows, with sensitivity increasing at higher surfactant concentration gradients.
• The model accurately recovers known results from prior studies—such as Chan & Leal (1979) for clean drops and Das et al. (2017a) for surfactant-coated drops—validating the approach under limiting conditions.
• Parametric analysis shows that the correction to migration velocity due to surfactants and electric fields is strongly dependent on the Mason number, field direction, and surfactant distribution parameter β.