Thermally modulated cross-stream migration of a surfactant-laden deformable drop in a Poiseuille flow

Abstract

In the present study, we investigate the cross-stream migration of a deformable droplet suspended in a non-isothermal Poiseuille flow in the presence of bulk-insoluble surfactants.Owing to the non-linearity present in the system of governing equations, an asymptotic approach is adopted, in an effort to capture the intricate and non-trivial coupling between the various influencing parameters. With the assumption of negligible inertia in fluid flow and convective transport of thermal energy, we obtain the droplet migration velocity through small-deformation perturbation analysis for two different limiting cases, namely, convection-driven-surfactant transport and surface-diffusion-dominated surfactant transport. Under each of these limiting cases, the cross-stream migration of droplet is studied for a constant temperature gradient applied in the same direction as well as in a direction opposite to the imposed flow. For the former limiting case, the droplet is always migrates towards the centerline of flow. For a highly viscous droplet, the direction of its cross-stream migration reverses. When the temperature decreases in the direction of the imposed flow, cross-stream migration velocity reduces with increase in the applied temperature gradient till a critical point is reached at which there is no cross-stream migration. Beyond the critical point, there is a gradual increase in the magnitude of the crossstream velocity. The droplet, below the critical temperature gradient, migrates towards the flow centerline; however, above it the droplet moves away from the centerline. For the other limiting case of surfactant transport dominated by surface convection, the magnitude of the cross-stream velocity is found to be significantly larger and at the same time independent of the droplet-carrier phase viscosity ratio. a E-mail address for correspondence: suman@mech.iitkgp.ernet.in

Steering a thermally activated micromotor with a nearby isothermal wall

“…drop manipulation (Das et al. 2017; Das & Chakraborty 2018; Das, Mandal & Chakraborty 2018), electrothermal flows (Kunti et al. 2018, 2019) and capillary transport (Chaudhury & Chakraborty 2015; Bandopadhyay & Chakraborty 2018).…”

Thermotaxis of a deformable droplet in a confined Poiseuille flow

“…In this section, we present a direct one-to-one comparison between the results obtained from the present study and the analytical study by Das & Chakraborty (2018), where they computed the migration velocity of a droplet by considering small deviations of the shape from a sphere and a one-way coupling between the thermal field and fluid flow.…”

“…Conversely, a linearly decreasing temperature field in the flow direction was found to slow down the droplet migration along both the axial as well as cross-streamline directions. In a related work by the same authors, the effect of asymptotically small shape deformation was also taken into account (Das & Chakraborty 2018), and it was observed that when the temperature decreases along the direction of flow, a reversal in the direction of cross-streamline migration of the droplet occurs beyond a certain magnitude of the temperature gradient.…”

“…Despite offering significant insights on thermally modulated droplet transport, the above results appear to be physically somewhat restrictive because of the following simplifications made for analytical tractability: ( a ) shape deformation of the droplet during its dynamic evolution is neglected (Das et al. 2018) or at the best considered to be asymptotically small (Das & Chakraborty 2018); and ( b ) the externally imposed thermal field is directly super-imposed on the droplet, obviating a possible two-way coupling mediated by the balance of viscous stress and capillary stress at the dynamically evolving interface.…”

Cross-stream migration of a Brownian droplet in a polymer solution under Poiseuille flow

“…[8][9][10] Such cross-stream migration could be desirable if a separation is needed but undesirable if a homogeneous distribution is preferred, and it is important to understand and design the conditions under which migration occurs. Multiple mechanisms exist for cross-stream migration in microchannels, [11][12][13][14][15] but in this article we will focus on particle migration that is passively controlled by a pressure-or gravity-driven flow, 16,17 which is attractive from an engineering perspective for its potential as a scalable, high-throughput technology.…”