Migration of a surfactant-laden droplet in non-isothermal Poiseuille flow

Das, Sayan; Mandal, Sumantra; Som, S. K.; Chakraborty, Suman

doi:10.1063/1.4973663

Cited by 31 publications

(26 citation statements)

References 56 publications

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“…We have obtained the droplet velocity in low s Pe limit as (53), we obtain the axial velocity of a surfactant-laden droplet in non-isothermal Poiseuille flow which was previously obtained by Das et al (2016). A closer look into equation (53) The effect of Marangoni stress diminishes in the limit λ → ∞ which is due to the fact that the droplet surface becomes more rigid and the interfacial tension plays no role in governing the hydrodynamics.…”

Section: Effect Of Marangoni Stress In the Low S Pe Limitmentioning

confidence: 80%

“…In a recent work, we have investigated the axisymmetric motion of a surfactant-laden droplet in combined presence of linearly varying temperature field and imposed Poiseuille flow (Das et al 2016). However, there is no study present in the literature which investigates the combined effect of temperature and imposed Poiseuille flow on the cross-stream migration characteristics of a droplet in the presence of bulk-insoluble surfactants.…”

Section: Introductionmentioning

confidence: 99%

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Effect of temperature gradient on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow

2017

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The motion of a viscous droplet in unbounded Poiseuille flow under the combined influence of bulk-insoluble surfactant and linearly varying temperature field aligned in the direction of imposed flow is studied analytically. Neglecting fluid inertia, thermal convection and shape deformation, asymptotic analysis is performed to obtain the velocity of a force-free surfactantladen droplet. The droplet speed and direction of motion are strongly influenced by the interfacial transport of surfactant which is governed by surface Péclet number. The present study is focused on the following two limiting situations of surfactant transport: (i) surface diffusion dominated surfactant transport considering small surface Péclet number, and (ii) surface convection governed surfactant transport considering high surface Péclet number. Thermocapillary-induced Marangoni stress, strength of which relative to viscous stress is represented by thermal Marangoni number, has strong influence on the distribution of surfactant on the droplet surface. Temperature field not only affects the axial velocity of the droplet but also has significant effect on the cross-stream velocity of the droplet in spite of the fact that the temperature gradient is aligned with the Poiseuille flow direction. When the imposed temperature increases in the direction of Poiseuille flow, the droplet migrates towards the flow centerline. The magnitude of both axial and crossstream velocity components increases with the thermal Marangoni number. However, when the imposed temperature decreases in the direction of Poiseuille flow, the magnitude of both axial and cross-stream velocity components may increase or decrease with the thermal Marangoni number. Most interestingly, the droplet moves either towards the flow centerline or away from it. Present study shows a critical value of the thermal Marangoni number beyond which the droplet moves away from the flow centerline which is in sharp contrast to the motion of a surfactant-laden droplet in isothermal flow for which droplet always moves towards the flow centerline.

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Section: Effect Of Marangoni Stress In the Low S Pe Limitmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Effect of temperature gradient on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow

2017

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“…where, ( ) The local surfactant concentration is governed by a convection-diffusion equation along the surface of the droplet, which is given by [33,56] ( )…”

Section: Governing Equations and Boundary Conditionsmentioning

confidence: 99%

“…Deformation of droplet induces a lift force that significantly affects the cross-stream migration of the droplet. However, a significant number of studies have also analyzed the migration characteristics of a non-deformable surfactant laden droplet [32,33]. The presence of a non-uniform distribution of surfactants generates a Marangoni stress along the interface of the droplet.…”

Section: Introductionmentioning

confidence: 99%

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

Das

Chakraborty

2018

Phys. Rev. Fluids

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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

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“…So, for a better control over the relevant technological processes, it is important to know the underlying hydrodynamics of these processes as well as to identify different actuating forces that can control the droplets motion. Common factors influencing droplet dynamics include the fluid inertia (Ho and Leal, 1974;Mortazavi and Tryggvason, 2000;, surface deformation (Goldsmith and Mason, 1962;Chaffey, Brenner and Mason, 1965;Haber and Hetsroni, 1971;Wohl and Rubinow, 1974;Stan et al, 2011;, presence of surfactants (Hanna and Vlahovska, 2010;Pak, Feng and Stone, 2014;Das et al, 2017;Das, Mandal and Chakraborty, 2017a), magnetic fields (Zhang et al, 2009), acoustic waves (Franke et al, 2009) and thermo capillary stresses (Baroud et al, 2007;Das, Mandal and Chakraborty, 2017b). Apart from these, externally applied electric fields (Hase, Watanabe and Yoshikawa, 2006;Ristenpart et al, 2009;Zagnoni and Cooper, 2009;Kurimura et al, 2013;Mhatre and Thaokar, 2013;Vajdi Hokmabad et al, 2014) can also act as a means for controlling droplet motion.…”

Section: Introductionmentioning

confidence: 99%

Electrohydrodynamic interaction between droplet pairs in a confined shear flow

et al. 2019

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The present study deals with the numerical as well as asymptotic analysis of the electrohydrodynamic interaction between two deformable droplets in a confined shear flow. Considering both the phases as leaky dielectric, we have performed numerical simulations to study the effect of channel confinement on the drop trajectories in the presence of a uniform electric field. Two important varieties of motion are identified in the present analysis, namely (i) the reversing motion and (ii) the passing over motion. The study suggests that conversion of the passing over motion to the reversing motion or vice versa is possible via modulating the strength of the imposed electric field. Such a conversion of the pattern of droplet migration is also possible in a confined domain due to change in different electrical properties of the system (for instance conductivity). The present numerical model is also able to predict the pattern of the trajectory of individual droplets depending on the initial distance separating the two. For example, a smaller initial distance results in a reversing motion whereas a passing over motion is predicted when the distance between the droplets is significantly large. However, the final positions of the droplets are found to be independent of their initial positions. Interestingly, presence of electric field is found to prevent droplet coalescence to a certain extent depending on its strength, thus rendering the emulsion stable. A small deformation asymptotic model is also developed under the assumption of negligible fluid inertia to support the numerical results for the limiting case of an unbounded flow. The current investigation successfully presents a novel technique to predict the precise positions of a system of droplets in a micro-channel and how electric field can be used as a tool to modulate droplet trajectories in an emulsion. Such a study has a wide potential towards application in design and functionalities of several modern-day droplet based micro fluidics devices.

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Migration of a surfactant-laden droplet in non-isothermal Poiseuille flow

Cited by 31 publications

References 56 publications

Effect of temperature gradient on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow

Effect of temperature gradient on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow

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

Electrohydrodynamic interaction between droplet pairs in a confined shear flow

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