Understanding and modulating the cross-stream motion of a surfactant-coated droplet in pressure driven flow has great implications in many practical applications. A combination of interfacial viscosity and Marangoni stress acting over a surfactant-coated droplet in pressure driven flow offers greater flexibility to modulate the cross-stream motion of it. Despite the intense theoretical and numerical research towards manipulating the surfactant-laden Newtonian droplets in Poiseuille flow, the experimental investigations are seldom explored. Herein, we report our study on understanding the influence of interfacial viscosity on the cross-stream motion of a surfactantcoated Newtonian droplet in both isothermal and non-isothermal Poiseuille flow from a theoretical as well as an experimental perspective. A theoretical model has been developed to understand the effect of interfacial viscosity on the lateral migration of a droplet under the assumptions of no shape deformation and negligible fluid inertia or thermal convection. Theoretical analysis is performed under two limiting conditions: (i) when the transport of surfactants is dominated by surface-diffusion and (ii) when the transportation of surfactants is dominated by surface-convection. Our theoretical analysis shows that both the dilatational as well as the shear surface viscosities suppress the lateral migration velocity of the droplet. Experiments have been performed to validate the theoretically predicted droplet trajectories and to understand the influence of channel confinement on the lateral migration of the droplet. It has been observed from the experiments that the droplet travels faster towards the centerline of the flow in a highly confined domain. The results presented in this study could provide new vistas in designing and analyzing various droplet-based microfluidic, biomedical and bio-microfluidic devices.

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The present study deals with the effect of surfactant distribution on the deformation of a viscoelastic droplet suspended in another viscoelastic medium, subjected to a uniaxial extensional flow. Under the assumption of negligible fluid inertia and small shape deformation, an asymptotic approach is adopted to solve the flow field. The Oldroyd-B model is used to represent both the carrier and droplet phases. The dynamics of the droplet is studied for the limiting cases of surface diffusion as well as surface convection mode of surfactant transport. The presence of an imposed flow results in a non-uniform distribution of surfactants which generates a surface tension gradient or Marangoni stress that is significantly found to affect the deformation of a viscoelastic droplet. The present analysis is performed for the general scenario where either of the phases may exhibit Newtonian or viscoelastic behavior. Upon comparison with the special case where both the phases are Newtonian, noteworthy differences in the effect of Marangoni stress on the dynamics of droplets are observed. It is found that increase in the Marangoni stress along the droplet surface reduces the effect of viscoelasticity on the shape deformation of the droplet. It is also found that a critical viscosity ratio can be defined for a viscoelastic droplet at which the effect of Marangoni stress on its shape deformation is the maximum.

A droplet under a thermal gradient is known to migrate in a preferential direction, as governed by the variation of its interfacial tension with temperature. Contradicting the outcome of reported asymptotic analysis, here we show that the calculation of the droplet migration by considering the variation of interfacial tension with the imposed thermal field alone may be fundamentally incorrect. This error is attributed to the dynamically evolving interfacial temperature field due to a two-way coupling between the thermal field and the flow field, mediated by the droplet deformation and thermal diffusion. By directly capturing an inherent nonlinear coupling between the thermal field and the flow field using explicit interface tracking in a three-dimensional space, our boundary integral based analysis reveals that a linearly decreasing temperature profile imposed along the direction of a plane Poiseuille flow enhances the migration speed of the droplet in both the axial and cross-stream directions. This is in sharp contrast to a prediction of decelerated motion of the droplet under the same imposed thermal field, as obtained from asymptotic theory. We attribute this discrepancy to an alteration of the surface tension mediated interfacial stress due to the locally evolving temperature field, and a consequent concomitant alteration in the interfacial viscous stress to realize a tangential force balance at the interface. From scaling arguments, we show that the resulting change in the viscous drag force may occur over an order of magnitude, disrupting the outcome as compared to that obtained from asymptotic analysis. These results are likely to bear significant implications in controllable separation and sorting of deformable entities in confined fluidic media.

Constriction in the flow passage in the physiological circulatory system is central to the occurrence of several diseased conditions such as thrombosis and is also pivotal towards the understanding of several regulatory processes in the human microvasculature. It is, therefore, imperative to advance a mechanistic insight on the dynamics of the transiting cellular encapsulations in a physiologically-mimicking micro-confinement, with particular focus on deciphering the role of its mechano-physical properties. Here we bring out a quantitative depiction on the role of the membrane fluidity and the initial deflation (shape deviation from sphericity) of a lipid vesicle during its morphological transition from stretching to tumbling via rolling as it migrates across a microfluidic constriction. Based on our experimental observations as well as theoretical insights, we construct a regime map to elucidate the range of the key dimensionless parameters orchestrating the dynamic transition. Our results further bring out the role of the initial position of the lipid vesicle on its subsequent stretching dynamics, exhibiting characteristic nonlinearities and non-monotonic trends. In addition, our observations on the vesicles stretching dynamics emerge from mapping selectively with the viscosity contrast between the encapsulated and the suspending fluid medium, offering potential physiologically relevant cues on the impact of the aging of a cellular moiety on its deformability as it transits through a constricted path. Such mechanistic insights may potentially enable establishing quantitative correlations between the dynamical transition of a cellular encapsulation and its mechano-physical properties, which may in turn, have decisive implications in various states of health and disease while circulating across microvascular fluidic pathways.