Inferior vena cava (IVC) filters are prone to mechanical complications, including fracture, migration, tilt, and wall perforation; however, the underlying physiological mechanisms remain obscure. This paper employs computational fluid dynamics to investigate time-dependent hemodynamics of IVC filters under realistic clinical conditions. A patient-specific IVC geometry was subjected to physiologically pulsatile flow to evaluate flow-field dynamics, hemodynamic indices, and drag forces across varying clot burdens, heart rates, and device tilt angles. Results show that anatomical curvature inherently drives asymmetric, phase-dependent flow—an effect amplified by trapped clots and exercise-induced pulsatility. Filter tilting expands thrombogenic surfaces and spikes peak wall shear stress, raising the oscillatory shear index by up to 88%. While higher heart rates generally reduce extreme low-shear zones under mild occlusion, severe clot burdens generate new downstream stagnation regions characterized by elevated relative residence time, creating conditions favorable for secondary thrombosis. Force analysis reveals that clot burden governs force misalignment; large clots cause the resultant drag vector to deviate by approximately 60∘ from the filter axis, generating a substantial lateral moment that provides a mechanistic basis for progressive tilting and migration. Exercise heart rates further amplify pressure drop fluctuations, suggesting that patient activity level should be incorporated into post-implantation risk stratification. These findings demonstrate that the interplay between patient-specific geometry, pulsatile flow, and clot growth governs both local flow disturbances and mechanical stability, offering a pathway toward computational tools for individualized risk assessment and improved long-term management of IVC filters.

The role of complex fluid rheology and surface properties in improving electrokinetic energy conversion (EKEC) remains poorly understood. Combining numerical simulations and regular perturbation technique, we resolve the nonlinear dependence of the zeta potential on slip length and simultaneously capture the inelastic, non-Newtonian response of the working fluid. Results reveal that shear-thinning fluids (n<1) enhance the induced streaming potential (E-s & lowast;), whereas it is suppressed for shear-thickening fluids (n>1). However, rheology hardly affects E-s & lowast; beyond the optimum value of the dimensionless slip length (L-s & lowast;) owing to the contrasting mechanisms in the 'slip-dominated zone' and the 'electrokinetic retardation zone'. We report giant augmentation in EKEC efficiency owing to the coupling between L-s & lowast; and zeta potential (zeta & lowast;), with the effect being more pronounced for shear-thinning fluids, low zeta & lowast; and overlapping electrical double layers (EDLs). The maximum enhancement in efficiency occurs at a particular L-s & lowast; for a set of n and zeta & lowast;. While the gain in E-s & lowast; with n=0.5 is limited to a maximum of 50%, a maximum increase of 250% is reported for EKEC. These insights uncover new design pathways for high-performance nanofluidic energy harvesters via synergistic tuning of interfacial slip and non-Newtonian properties.

Oscillatory mechanical stimuli are prevalent in complex fluidic environments with surface charges. Flow oscillations, including high-frequency pulsations, play a significant role in a wide range of biophysical phenomena and have considerable potential for improving energy conversion efficiency. Despite their practical importance, the fundamental mechanisms governing these flow dynamics are still not fully understood. Here, we extend the work of Ding and Jian (2021) and report exclusive insights on electrokinetic transport in high-frequency, pressure-driven viscoelastic flow described using multimode Oldroyd-B constitutive models through a microchannel lined with a charged, deformable porous layer. An analytical formulation of the complex shear modulus of an Upper-Convected Maxwell fluid under oscillatory excitation reveals a transition from viscous to elastic behaviour as the frequency increases. The analysis shows that with increasing Deborah number (ratio of the relaxation time of the fluid to the characteristic timescale of flow), representing stronger viscoelastic effects, the zero-phase angle shifts toward higher frequencies, indicating an increase in the critical frequency where synchronization between flow rate and pressure gradient occurs. At lower frequencies, the system exhibits a positive phase shift characteristic of viscoelastic dominance, which reverses beyond the critical frequency as viscous effects prevail. Resonance-like amplification of flow emerges when the imposed frequency matches the natural frequency set by the balance of inertia and elastic restoring forces. Furthermore, the role of the Newtonian solvent viscosity is examined. The reported coupling between electrokinetic and viscoelastic responses emphasizes how electro-mechanical interactions govern ion transport and fluid motion, offering key insights for applications in microfluidics, physiological regulation, and soft material systems relevant to physiology and bioengineering.

We present a thin film theory to unveil the interaction between the non-Newtonian effects and the Marangoni flow for a thermally actuated drop on a solid surface. Our numerical simulations with different equilibrium contact angles (θ _e) , shear-dependent viscosities (n), and dimensionless thermocapillary strengths (β ) reveal a nonlinear influence of the fluid rheology on Marangoni stress and disjoining pressure. For non-Newtonian droplets, we have identified three distinct spreading regimes. The behavior of the Marangoni film regime can be characterized by certain conditions. At lower values of θ _e , higher values of β , and a specific range of n, the film exhibits a distinct linear drop shape. Additionally, for the shear-thickening drops, the thermocapillary time scale occurs early, and the advancing front becomes steeper, while drops with shear-thinning properties maintain a noticeable curvature for an extended period. On the other hand, when θ _e is higher, and (β , n) are lower, the droplets display a consistent shape and move at a uniform speed denoted as (U), which is identified as droplet regime. The droplets of this regime have a complex interaction of n and β , which leads to a considerable rise in U for shear-thinning fluids. Regardless of the regime, the shear-thinning droplet spreading is slower than that of Newtonian droplets, while the shear-thickening droplet spreading is faster in comparison. These findings can be employed in microfluidics to gain control over the spreading of non-isothermal biofluid droplets.

The complex rheology of biofluids and industrial fluids is a decisive factor in their deformation and spreading on a heated substrate. However, the intervening role of gravity forces remains unexplored. Here, we apply the lubrication approximation to the momentum equation and the power-law constitutive relation for inelastic non-Newtonian fluids, with the intermolecular forces being accounted for within the continuum hypothesis. The derived evolution equation for droplet height has been solved numerically using the finite element method. The Marangoni stress dominates the conjoining-disjoining pressure in the 'Marangoni film regime'. The gravity effect causes a significant curvature of the rear edge, leading to a pancake-like droplet shape and reduced capillary ridge height near advancing fronts. Furthermore, increasing capillary ridge height with shear-thinning and faster-moving advancing fronts with either enhanced Marangoni stress or shear-thickening are both dampened by gravity. The droplet regime, previously observed in microgravity conditions, no longer exists under gravity. The drop deviates from its initial shape as dictated by its rheology but maintains the same shape afterwards, leading to a new regime named 'transition without breakup.' The gravity effect weakens after initial deformation, and the dominant conjoining-disjoining pressure results in a constant migration speed without further deformation. The 'transition with breakup regime', where droplets break apart into smaller droplets, is influenced by a critical interaction between Marangoni stress, intermolecular force, and gravity force. The onset of rupture strongly depends on the fluid rheology and the thermocapillary strength. The presented regime maps provide the critical parameters for switching regimes and highlight exclusive spreading states under gravity. These insights on the critical interaction between gravity, shear-dependent rheology, and thermocapillary actuation for partially wetting droplets could lead to more versatile microfluidic devices for handling complex biofluids.

The spreading of sessile droplets under thermocapillary actuation has been extensively studied; however, the interplay between nonlinear thermocapillary effects and shear-dependent rheology remains largely unexplored. Here, we present a theoretical framework to unravel this complex physics by considering a self-rewetting droplet that is subjected to a uniform temperature gradient, whereas the generalized Newtonian model captures the rheology of both shear-thinning and shear-thickening fluids. Departing from linear surface tension assumptions, we consider a nonlinear temperature dependence, revealing a different scaling law for droplet spreading. Three distinct spreading regimes emerge: degenerated Marangoni film, accelerated droplet, and a transition zone. The combined interplay between the nonlinear thermocapillary effect and the shear-dependent viscous nature of the fluid plays a critical role in determining the existence and characteristics of these regimes. Shear-thickening fluids flatten curvature but enhance spreading, while shear-thinning fluids delay entry into the nonlinear regime. Self-rewetting droplets show accelerated movement due to position-dependent Marangoni stress and may fragment under high stress in shear-thickening cases. The nonlinear relationship between viscous resistance and shear rate modifies the force balance governing spreading. These findings may enable new microfluidic methods for precise droplet control, mixing, and targeted delivery.

Microscale swimming strategies of bodies with different shapes in the presence of external flow have been studied extensively in previous literatures. However, the behaviour of the microswimmer near a wall with complex surface wettability conditions is still unexplored. To bridge this gap in literature, we consider a spherical microswimmer and illustrate its dynamic behaviour with an analytical-numerical approach near a slippery wall. The coupled effect of self-propulsion and external shear presents some new characteristics in the presence of wall slip. Intending to observe different types of possible mobility of a puller-type microswimmer, we illustrate the trajectories. Additionally, we present phase portraits to illustrate the dependence of the squirmer parameter with the background shear and slippery wall. The primary findings of the study are the combinations of external flow and slip length causing the squirmer to escape from, collide against the wall and exhibit rheotactic motion, which are summarised in the regime map. Our results reveal that a slippery wall additionally introduces a critical limit of shear strength, beyond which puller microswimmers escape for lower values of slip length followed by a band of the rheotactic and an annihilation zone against the wall at higher values of wall slip.

Understanding the effect of intricate surface wettability conditions on microswimmers is crucial for precisely navigating them across narrow microcirculatory networks. Here, we adopt the spherical squirmer model and Navier slip condition to delineate the microswimmer locomotion under a Poiseuille flow in a slit microchannel. Through a combined analytical-numerical approach utilizing bispherical coordinates and the superposition technique, we resolve the slip-modulated simultaneous hydrodynamic interaction with substrate boundaries. Phase portraits reveal that slip significantly alters propulsion mechanisms, destabilizing centreline stable oscillations of pullers beyond a threshold slip length. Superhydrophobic surfaces suppress near-wall rheotaxis states but preserve centreline focusing, facilitating slip-assisted directed transport without surface accumulation. Under strong background flows, subcritical Hopf bifurcation emerges for pullers at a critical slip length, transitioning dynamics from coexisting stable and unstable states to purely unstable behaviour. Contrastingly, for pushers, slip causes a transition from unstable to either stable or fixed-amplitude oscillations. Increased slip length reduces hydrodynamic repulsion on pullers from the walls by enhancing rotational velocity near the walls, whereas it counteracts the torque that causes unstable oscillations of pushers. Three-dimensional analysis of the trajectories reveals the significant role of the out-of-plane orientation of the microswimmer in its transitions between different swimming states. The presented regime maps offer parametric combinations for specific motion behaviours, guiding the development of smart microfluidic drug delivery systems and preventing biofilm deposition in biomedical devices.

BACKGROUND AND OBJECTIVE:Stenosis or narrowing of arteries due to the buildup of plaque is a common occurrence in atherosclerosis and coronary artery disease (CAD), limiting blood flow to the heart and posing substantial cardiovascular risk. While the role of geometric irregularities in arterial stenosis is well-documented, the complex interplay between the abnormal hemorheology and asymmetric shape in flow characteristics remains unexplored. METHODS:This study investigates the influence of varying hematocrit (Hct) levels, often caused by conditions such as diabetes and anemia, on flow patterns in an idealized eccentric stenotic artery using computational fluid dynamics simulations. We consider three physiological levels of Hct, 25%, 45%, and 65%, representing anemia, healthy, and diabetic conditions, respectively. The numerical simulations are performed for different combinations of shape eccentricity and blood rheological parameters, and hemodynamic indicators such as wall shear stress (WSS), oscillatory shear index (OSI), are relative residence time (RRT) are calculated to assess the arterial health. RESULTS:Our results reveal the significant influence of Hct level on stenosis progression. CAD patients with anemia are exposed to lower WSS and higher OSI, which may increase the propensity for plaque progression and rupture. However, for CAD patients with high Hct level - as is often the case in diabetes - the WSS at the minimal lumen area increases rapidly, which may also lead to plaque rupture and cause adverse events such as heart attacks. These disturbances promote endothelial dysfunction, inflammation, and thrombus formation, thereby intensifying cardiovascular risk. CONCLUSIONS:Our findings underscore the significance of incorporating hemorheological parameters, such as Hct, into computational models for accurate assessment of flow dynamics. We envision that insights gained from this study will inform the development of tailored treatment strategies and interventions in CAD patients with common comorbidities such as diabetes and anemia, thus mitigating the adverse effects of abnormal hemorheology and reducing the ever-growing burden of cardiovascular diseases.

Despite significant advances in the field of man-made micro- and nanomotors, it remains a challenge to precisely control their motion in bounded environments. Here, we present a theoretical analysis of a thermally activated micromotor near a plane wall under the action of a background linear temperature field. The coupling between the autonomous and field-directed motions has been resolved using a combined analytical–numerical framework comprising general solutions in bispherical coordinates and the reciprocal theorem for creeping flows. Results reveal giant augmentation in swimming speeds, the controlling parameter zones for positive and negative thermotaxes and the flexibility of steering perpendicular to the field gradient for an isolated micromotor. Boundary-instigated thermo-fluidic modulations at different levels of confinements and preferential orientations cause directional switching of both the vertical translation and rotation parallel to the wall, thereby drastically altering the phase portraits of the swimmer dynamics. Contrasting trajectory characteristics, e.g. escape, attraction, are partitioned by unstable separatrices in the phase portraits, while competitive repulsion (attraction) after attraction (repulsion) characteristics emerge for different relative field strengths$\mathcal {S}$and gradient orientations$\theta _T$. Below$\mathcal {S}=0.25$, highly counter-intuitive trajectories result when the micromotor is initially launched from an overlapping escape zone. Moreover, external-field-assisted microswimming can uniquely tune the directionality of wall-parallel translation, broadening the scope of dynamic regulation of self-propulsion. Thus, providing insights into a precisely controlled fuel-free actuation of micromotors near a physical obstacle, the present study stands as a step toward addressing the increasing demand for successful implementation of micromotors in futuristic clinical and environmental applications.

Eccentric compound drops, which are ubiquitous in many naturally inspired and engineering systems, can migrate under the sole presence of a uniform electric field, unlike the case of isolated single drops. Here, we report the migration of eccentric compound drops under a uniform electric field, imposed parallel to the line of centres of the constituting drops, by developing an approximate analytical model that applies to low Reynolds number limits under negligible droplet deformation, following axisymmetric considerations. In contrast to the sole influence of the electrohydrodynamic forces that has thus far been established to be emphatic for the eccentric configuration, here we report the additional effects induced by the dielectrophoretic forces to result in decisive manipulation in the drop migration. We show that the relative velocity between the inner and outer drops, which is a function of the eccentricity itself, dictates the dynamical evolution of the eccentricity variation under the competing electrohydrodynamic and dielectrophoretic interactions. This brings out four distinct regimes of the migration characteristics of the two drops based on their relative electro-physical properties. Our results reveal that an increase in eccentricity and the size ratio of the inner and outer droplets may induce monotonic or non-monotonic variation in the drop velocities, depending on the operating regime. We show how the interplay of various properties holds the control of selectively increasing or suppressing the eccentricity with time. These findings open up various avenues of electrically manipulative motion of encapsulated fluidic phases in various applications encompassing engineering and biology.

The near-surface locomotion of microswimmers under the action of background flows has been studied extensively, whereas the intervening effects of complex surface properties remain hitherto unknown. Intending to delineate the shear-driven dynamics near a planar slippery wall, we adopt the squirmer model of microswimmers and employ a three-dimensional analytical-numerical framework in bispherical coordinates. It is interpreted that both the self-propulsion and the external shear flow are redistributed due to hydrodynamic slippage, followed by modulations in the thrust torque on the microswimmer. Phase portraits of the quasi-steady dynamics indicate that the stable upstream swimming states, known as ‘rheotaxis’, are significantly modulated by the slip length compared with the no-slip case. For puller swimmers, an intricate interplay among the modulated interfacial friction near a slippery surface, velocity gradients of the shear flow and the strength of the squirmer parameter promotes a critical shear rate beyond which a wide range of new rheotactic states exist. Consequently, an escaping microswimmer may exhibit rheotaxis or an existing rheotactic state annihilates due to crashing. Although stable states are absent for pushers without steric interactions, transitions from escaping and undamped oscillations to ‘rheotaxis’ occur in the presence of wall repulsion, but only until the other characteristics are overwhelmed by escape due to enhanced shear. Disclosing the ability of hydrodynamic slippage in broadening the scope of migration against a background flow for a wide range of parameters, the present work paves the way for investigations on the entrapment of microswimmers near complex pathways or sorting using selective rheotaxis.

The fabrication of self-propelling micromotors and the study of their propulsion strategies have gained attention due to their wide range of applications in the medical, engineering, and environmental fields. The role of a background temperature field in the precise navigation of a self-thermophoretic micromotor near an insulated wall has been investigated by employing exact solutions to the energy equation and creeping flow. We report bound states for half-coated micromotors appearing as steady-state sliding, damped, and periodic oscillations when the dimensionless external temperature gradient (S) is in the range of 0.15≤S<0.26. The sliding height is lower with S but remains insensitive to the thermal conductivity contrast. Moreover, the stationary states for the self-propelled, asymmetrically coated micromotors transform into scattering trajectories. We highlight the combinations of S and coating coverage needed for guided swimming up or against the field along with a broad spectrum of counter-intuitive temporal variations of its navigating locations. These unique observations have been ascribed to a confinement-mediated dynamic coupling between the passive and active propulsion mechanisms.

In the present work, within the framework of thin film theory, we delineate the interaction between the interfacial dynamics of thermal Marangoni flow and non-Newtonian rheology by considering a spreading droplet over a non-isothermal substrate. The numerical simulations, performed at different equilibrium contact angles $(\theta _e)$ , dimensionless thermocapillary strengths $(\beta )$ and shear-dependent viscosities $(n)$ , reveal that the fluid rheology nonlinearly influences the mechanisms of disjoining pressure and Marangoni stress. Accordingly, three distinct spreading regimes for non-Newtonian drops arise. Results indicate that the Marangoni film regime, having an approximate linear drop shape, sustains at lower $\theta _e$ , higher $\beta$ and $n$ ranges. Also, shear-thickening drops display an early onset of thermocapillary time scale and a steeper advancing front, while their shear-thinning counterparts retain a significant curvature for a much longer time. Contrastingly, the droplet regime is identified by fixed shape and uniform speed $(U)$ at higher $\theta _e$ and lower $(\beta$ , $n)$ combinations. Here, an intricate interplay between $\beta$ and $n$ realizes a sharp increase in $U$ for shear thinning compared with its invariance for shear-thickening droplets. The transition regime appears as an intermediate regime between the other two and involves multiple ruptured droplets. In all the regimes, we observe slower (faster) spreading of shear-thinning (thickening) droplets than the Newtonian droplets. In addition, the variations in $n$ cause intense characteristic modulations to spreading attributes like droplet morphology and transient spreading behaviour, and also act as a switching mechanism between different spreading regimes. These unique results may be utilized for superior control of non-isothermal biofluid droplets in microfluidics.

Selective heating of a microparticle surface had been observed to cause its autonomous movement in a fluid medium due to self-generated temperature gradients. Here, we theoretically investigate the response of such an auto-thermophoretic particle near an isothermal planar wall. We derive an exact solution of the energy equation and employ the Lorentz reciprocal theorem to obtain the translational and rotational swimming velocities in the creeping-flow limit. We report fixed points for vertical movement of the micromotor for its specific orientations relative to the wall. The critical wall gap for fixed points shows unique non-monotonic dependence on the metallic coating coverage on the particle. Also, the micromotor trajectories can be switched either from wall-bound sliding or stationary state to escape from the near-wall zone by tuning the particle and the surrounding fluid pair thermal conductivity contrast. The scenario holds several exclusive distinguishing features from the otherwise extensively studied self-diffusiophoresis phenomenon near an inert wall, despite obvious analogies in the respective constitutive laws relating the fluxes with the gradients of the concerned forcing parameters. The most contrasting locomotion is the ability of a self-thermophoretic micromotor with a large heated cap to migrate towards the wall even if it is initially directed away from the wall. During the stationary states of swimming, the cold portion on the micromotor surface faces away from the wall under all conditions. Such unique aspects hold the potential of being harnessed in practice towards achieving intricate control over the autonomous motion of microparticles in thermally regulated fluidic environments.

Interaction of motile microrganisms with a nearby solid substrate is a well studied phenomenon. However, the effects of hydrodynamic slippage on the substrate have received a little attention. In the present study, within the framework of the squirmer model, we impose a tangential velocity at the swimmer surface as a representation of the ciliatory propulsion and subsequently obtain exact solution of the Stokes equation based on a combined analytical-numerical approach. We illustrate how the near-wall swimming velocities are non-trivially altered by the interaction of wall slip and hydrodynamic forces. We report a characteristic transition of swimming trajectories for both puller and pusher type microswimmers by hydrodynamic slippage if the wall-slip length crosses a critical value. In case of puller microswimmers that are propelled by a breast-stroke like action of their swimming apparatus ahead of their cell body, the wall slip can cause wall-bound trapping swimming states, either as periodic or damped periodic oscillations which would otherwise escape from a no slip wall. The associated critical slip length has a non-monotonic dependence on the initial orientation of the swimmer which is represented by novel phase diagrams. Pushers, which get their propulsive thrust from posterior flagellar action, also show similar swimming state transitions but in this case the wall slip mediated reorientation dynamics and the swimming modes compete in a different fashion to that of the pullers. The present results pave the way for understanding the motion characteristic of biological microswimmers near confinements with hydrophobic walls or strategize the design of microfluidic devices used for sorting and motion rectification of artificial swimmers by tailoring their surface wettability.

Recent findings of possible applications of bio-friendly synthetic self-phoretic swimmers, have motivated the researchers in investigating the various motion-generating mechanisms to optimize the operating characteristics of the same. In this paper we model the auto-electrophoretic motion of a bimetallic (Au-Pt) spherical swimmer in a non-Newtonian medium. In view of the fact that many bio-fluids closely follow the generalized Newtonian rheology, the rheology of the surrounding swimming medium is considered to follow the Carreau-Yasuda viscosity model. Further to capture the experimentally observed effects of peroxide concentration and feedback of generated proton concentration on the surface cation flux, we incorporate a Michaelis-Menten like surface reaction kinetics. The electrocatalytic efficiency defined as a ratio between the cost of swimming of an equivalent passively dragged particle and the input chemical energy via surface reaction, is utilized to assess the influence of the rheological parameters on the swimmer performance. The results indicate that the shear thinning and shear thickening nature of the surrounding fluid causes an enhancement and reduction in swimmer velocity, respectively. However, an increase in the shear thinning effect does not always guarantee an efficient operation of the microswimmer. A competition between the particle velocity and reduction in the drag force on the particle, decides whether the propulsion efficiency will have a relative augmentation or attenuation with varying power law index. We further report the existence of maximum efficiency points for some specific range of Weissenberg number and optimum power law indices. Moreover the behaviour of such optimum operating conditions strongly depends on the non-trivial and highly coupled interplay among the rheology and electrocatalytic parameters.

Electrical effects can impart a cross-stream component to drop motion in a pressure-driven flow, due to either an asymmetric charge distribution or shape deformation. However, surfactant-mediated alterations in such migration characteristics remain unexplored. By accounting for three-dimensionality in the drop motion, we analytically demonstrate here a non-trivial switching of drop migration with the aid of a surfactant coating on its surface. We establish this phenomenon as controllable by exploiting an interconnected interplay between the hydrodynamic stress, electrical stress and Marangoni stress, manifested so as to achieve a net interfacial force balance. Our results reveal that under different combinations of electrical conductivity and permittivity ratios, the relative strength of the electric stress with respect to the hydrodynamic stress, the applied electric field direction and the surfactants alter the longitudinal and cross-stream velocity components of the droplets differently. The effect of drop deformation on its speed is found to be altered with the increased sensitivity of the surface tension to the surfactant concentration, depending on the competing effects of the electrohydrodynamic flow modification and the tip stretching phenomenon. Further, with a suitable choice of electrical property ratios, the Marangoni effects can be exploited to direct the drop in reaching a final transverse position towards or away from the channel centreline. These results may turn out to be of immense consequence in providing an insight to the underlying complex physical mechanisms dictating an intricate control on the drop motion in different directions.

We investigate the effects of surfactant coating on a deformable viscous drop under the combined action of shear flow and a uniform electric field. Employing a comprehensive three-dimensional approach, we analyse the non-Newtonian shearing response of the bulk emulsion in the dilute suspension regime. Our results reveal that the location of the peak surfactant accumulation on the drop surface may get shifted from the plane of shear to a plane orthogonal to it, depending on the tilt angle of the applied electric field and strength of the electrical stresses relative to their hydrodynamic counterparts. The surfactant non-uniformity creates significant alterations in the flow perturbation around the drop, triggering modulations in the bulk shear viscosity. Overall, the shear-thinning or shear-thickening behaviour of the emulsion appears to be greatly influenced by the interplay of surface charge convection and Marangoni stresses. We show that the balance between electrical and hydrodynamic stresses renders a vanishing surface tension gradient on the drop surface for some specific shear rates, rendering negligible alterations in the bulk viscosity. This critical condition largely depends on the electrical permittivity and conductivity ratios of the two fluids and orientation of the applied electric field. Also, the physical mechanisms of charge convection and surface deformation play their roles in determining this critical shear rate. As a consequence, we obtain new discriminating factors, involving electrical property ratios and the electric field configuration, which govern the same. Consequently, the surfactant-induced enhancement or attenuation of the bulk emulsion viscosity depends on the electrical conductivity and permittivity ratios. The concerned description of the drop-level flow physics and its connection to the bulk rheology of a dilute emulsion may provide a fundamental understanding of a more complex emulsion system encountered in industrial practice.

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.