The viscoelastic instability of cross-slot flow was first observed experimentally almost half a century ago and reproduced numerically two decades ago, yet its physical origin remains unresolved. We revisit this problem for two-dimensional creeping flow of Oldroyd-B fluid by combining direct numerical simulations, global stability analysis, structural sensitivity analysis and energy-budget analysis. Our simulations reproduce the canonical pitchfork bifurcation, and the stability analysis consistently predicts the threshold and perturbation growth rates. The leading eigenmode consists of a chiral velocity–stress perturbation that tilts and rotates the birefringent strand generated by the extensional flow. Structural sensitivity and energy-budget analyses identify narrow high-extension-rate ridges within the extensional flow as both the spatial core and energetic source of the instability. In these ridges, the stress-based wavemaker colocalizes with large positive disturbance polymeric stress power density, indicating localized transfer of stored elastic energy to the disturbance flow. Analyses of cross-slot variants with rounded corners and with a centred cylinder further reveal that neither sharp corners nor a free central stagnation point is the essential destabilizing ingredient; rather, the instability originates from elastic-energy release in extension-dominated regions characteristic of cross-slot flow.

We investigate the dynamics of a rigid spherical particle in plane Couette flow with a viscosity that varies linearly across the channel, from the Stokes limit to non-zero Reynolds numbers, using analytical theory and immersed-boundary lattice Boltzmann simulations. In the Stokes limit, we find that the particle develops a constant, viscosity-gradient-induced translational slip, defined as the difference between the particle velocity and the undisturbed fluid velocity at its centre. The particle leads the flow when the viscosity increases towards the moving wall and lags when it decreases. Its angular velocity equals half the local, viscosity-gradient-modified fluid vorticity, experiencing no additional rotational slip. Furthermore, we show that cross-stream particle migration is strictly prohibited at any confinement ratio or gradient magnitude. At non-zero Reynolds numbers in a constant-viscosity fluid, increasing the channel Reynolds number beyond a critical value induces a supercritical pitchfork bifurcation that splits the stable centreline equilibrium into two symmetric off-centre equilibria. With a viscosity gradient, we find that for Reynolds numbers below this bifurcation point, the particle consistently settles at a single off-centre equilibrium in the less-viscous half. For Reynolds numbers exceeding this point, however, we identify a critical viscosity gradient threshold: below this limit, the particle can stabilise in either channel half depending on its initial placement; above it, the particle focuses exclusively in the less-viscous half regardless of its initial position. These findings enable predictive particle manipulation in viscosity-stratified microflows.

We examine the Poiseuille flow of viscoplastic fluids over superhydrophobic surfaces with transverse air-filled grooves, focusing on the deformation dynamics of the liquid–air interface and the resulting flow regimes. By combining a creeping-flow semianalytical model and finite Reynolds two-phase numerical simulations, we quantify how viscoplastic rheology, governed by the Bingham number ($B$), interacts with capillary and inertial forces, represented by the capillary number ($\textit{Ca}$) and Reynolds number ($R$), as well as groove geometry characterized by the aspect ratio ($d$), to dictate meniscus behaviour. The analysis covers groove aspect ratios ranging from shallow ($d \sim O(10^{-3})$) to deep ($d \sim O(1)$). The results reveal distinct interface morphologies, including flat (pinned at groove edges), deflected (pinned), depinned and collapsed states, depending on $d$, $\textit{Ca}$, $R$ and $B$. For large groove aspect ratios, the interface remains flat in the creeping-flow limit but undergoes deformation and eventually a pinned-to-depinned transition at finite inertia. This transition is well described by the effective Reynolds number $R^* = R/(1 + B)$, with $R^* \approx 30 B^{-1}$ and $R^* \approx 50 B^{-1}$ for the constant-contact-angle cases $\varTheta = 95^\circ$ and $\varTheta = 120^\circ$, respectively. With finite contact-angle hysteresis, the corresponding dynamic-contact-angle transition follows $R^* \approx 32B^{-1}$. On the other hand, for moderately shallow grooves and small $B$, interface deformation increases with $\textit{Ca}$, with depinning occurring at $\textit{Ca} \approx O(1)$; for very shallow grooves ($d \lesssim 10^{-2}$), the interface collapses at $\textit{Ca} \lesssim 1$, before depinning.

Recent experiments have shown that microparticles subjected simultaneously to electrophoresis and pressure-driven flow undergo lateral migration. Although fluid inertia has been proposed to explain this phenomenon, it remains negligible in these regimes, leaving the underlying mechanism an open question. In this work, we demonstrate that concentration polarisation alone can account for this effect. By modelling a dielectric particle with finite surface conductance in a shear flow, we show that the flow breaks the symmetry of the ionic cloud in the direction perpendicular to the applied electric field. The resulting asymmetry induces lateral migration through coupled electrophoretic and diffusiophoretic mechanisms. Our analytical expression predicts migration velocities of the order of ${\unicode{x03BC}}\mathrm{m\,s}^{-1}$ and reveals a reversal in the migration direction for Dukhin numbers of order unity.

Filtration flows through nanoporous membranes play a crucial role in a range of cutting-edge technologies, including water purification, osmotic power generation and targeted drug delivery. Molecular dynamics (MD) simulations are currently considered the state-of-the-art approach for modelling nano-filtration processes. However, their high computational cost makes simulating large-scale filtration systems impractical, limiting the ability to conduct extensive parametric studies and optimise design strategies. In the present paper, we merge a molecular analysis of the nano-filtration problem with a homogenisation technique, to upscale the filtration flow from the single nanopore description to the whole membrane scale phenomenon. The homogeneous model allows replacing the detailed description of the flow through the whole membrane with a simplified flow description, where the membrane is an effective smooth interface between two macroscopic fluid regions. The model rigorously quantifies jumps in the macroscopic solvent velocity and stresses across the homogeneous membrane via a set of tensorial quantities computed once and for all via MD simulations, enabling us to predictively quantify the membrane properties in the presence of nanoscopic pores. Finally, we validate the MD-homogenisation model by comparison with MD simulations of a water flow through arrays of pores, assessing the computational efficiency of the novel methodology.

The development of organic biosignature analysis instruments with picomolar (pM) sensitivity is necessary for meaningfully exploring our solar system for habitability and for organic chemical biomarkers. To address this challenge, the Microfluidic Organic Analyzer (MOA) prototype has been redesigned and reengineered in a compact, low-mass, space-flight ready format. To evaluate the performance of the flight-format MOA instrument, we performed a series of Zero-G parabolic aircraft flights to test the microfluidic fluid processing, capillary electrophoresis (CE) separation, and detection systems in a diverse range of micro- and hyper-gravity environments. Amino acid CE separations were performed in flight to assess the protocols and to determine the dependence of the separation quality on large variations in gravitational potential. We present here amino acid separations performed as the gravitational potential varied from 0.16 to 1.7 g during the separation. When the flight profile enabled proper preparation, the separation was indistinguishable from separations performed in a constant 1 g environmental control with the same reagents. This work advances the technology readiness of the MOA for performing in situ organic analyses relevant to habitability and biosignatures — an important step toward deploying picomolar sensitivity in the search for extraterrestrial biomarkers.

This study develops a general theory for analysing a three-dimensional (3-D) acoustofluidic system, which consists of a cavity sandwiched by parallel piezoelectric substrates. The cavity is filled with a fluid and microparticle mixture, whose movements are actuated by surface acoustic waves (SAW) generated by the piezoelectric substrates. In contrast to the formulations based on the velocity potential and streamfunction, we developed a frequency-domain perturbation method to solve the compressible Navier–Stokes equations to obtain the acoustofluidic fields for both inviscid and viscous fluids. These solutions allow for the accurate prediction of the pressure nodal positions within the sandwiched cavity, and the effects of the microfluidic cavity geometry on the pressure nodal position are examined. Our analysis shows that the in-plane pressure-node distribution is controlled by phase modulation, whereas the out-of-plane distribution is governed by the amplitude ratio of the standing SAWs produced by the two parallel substrates. For viscous fluids, a coordinated amplitude–phase modulation strategy is proposed to achieve the desirable wave node distribution. The present theoretical derivations are validated against numerical simulations and laboratory experiments, in terms of both the velocity and pressure fields. This work provides guidelines for the fabrication and operation of acoustofluidic devices, extending current 2-D acoustic control to fully 3-D manipulation of microparticles suspended in the fluid.

Micro-droplets are extensively used in chemical, biological and medical research, primarily for conducting various tests on samples, including living organisms, using a microfluidic framework. Recent studies have shown that the physiology of bacteria can be significantly altered when subjected to shear and/or extensional stresses. With this motivation, we perform experiments to understand the vortex dynamics involved during the pinch-off process in a cross-flow droplet generator, using particle image velocimetry to visualise the vortical structures and to quantitatively measure the associated stresses developed inside droplets. The process of pinching off inherently leads to bi-directional acceleration of fluid in the rapidly thinning capillary bridge, resulting in a vortex in the separated droplet as well as in the retracting ligament. We propose scaling laws for the vortical flow inside the droplet post pinch-off and predict the maximum circulation production inside the droplet. Further, we discuss the vortex dynamics inside the droplet, the retracting ligament and the advancing ligament and examine the stress fields associated with this transient phenomenon.

The dynamics of carboxyl-modified polystyrene colloidal particles of varying size and zeta potential were investigated in a microfluidic junction device where merging electrolyte streams generated a steady-state salt concentration gradient. The device featured a long microchannel downstream of the junction, enabling the particle dynamics to be analysed over a time scale comparable to the relaxation time of the salt gradient. In the bulk of the channel, particles migrate outwards through a diffusive-like process arising from the additive contributions of particle diffusiophoresis and wall diffusioosmosis. An analytical expression is derived for the effective diffusion coefficient, and a microfluidic approach is proposed to estimate particle diffusiophoretic mobility. Particles accumulated at the walls also displace sideways but the direction of their motion depends on the counter-acting effects of particle diffusiophoresis and wall diffusioosmosis. This motion is sub-diffusive at short distances from the junction, but either ceases or reverses further downstream. The intensity of the accumulation peaks exhibits a non-monotonic dependence on the distance from the junction and, after calibration, can serve for the microfluidic measurement of particle size or zeta potential, when one property is known a priori. The influence of electric double layer polarisation on diffusiophoretic mobility is also examined.

Fluid transport through compliant microchannels is widely observed in both natural and engineered systems, including the transport of nutrients through xylem, mechano-chemically sensitive valves, hydrogel-based drug delivery systems and filter-paper-based diagnostic kits. In such flows, the two-way coupled interaction between fluid stresses and compliance of the bounding walls gives rise to a rich flow dynamics. These soft solid walls can absorb fluid and swell, and the resulting coupling between swelling kinetics and wall compliance further complicates the flow evolution, which can be observed in water flow through hydrogel microchannels or toluene flow through polydimethylsiloxane microchannels. Here, we develop a mathematical framework to investigate the spatio-temporal evolution of a Newtonian fluid flowing through a shallow rectangular microchannel bounded by soft, swelling walls. Using lubrication approximations, we derive a nonlinear diffusion equation for fluid pressure and channel height, which reveals a non-monotonic flow dynamics arising from the competition between swelling-induced collapse and fluid-pressure-induced restraint. A simplified analytical solution of the nonlinear diffusion equation, validated through fully coupled numerical simulations, identifies distinct regimes of flow evolution, and captures the transition from swelling-dominated to fluid-pressure-dominated behaviour, governed by the interplay between the swelling ratio and wall compliance. These results elucidate non-intuitive, yet fundamental flow responses in swelling, compliant channels, and highlight their implications for passive flow generation and flow control via mechano-chemical interactions.

We investigate the diffusiophoresis of a non-polarizable droplet laden with soluble ionic surfactant, in which the surface charge arises from the adsorption of surfactant at the fluid–fluid interface. Unlike previous studies which assume either a fixed surface charge or instantaneous equilibrium between the interface and the adjacent electrolyte, we formulate the interfacial transport based on the mass-balance framework, incorporating Langmuir adsorption–desorption kinetics and finite surface diffusivity. The coupled electrokinetic problem is solved using a perturbation approach with imposed ionic concentration as a perturbation parameter. Analytical expressions for the droplet mobility and interfacial velocity are derived based on the Debye–Hückel approximation as well as the thin layer consideration for the insoluble surfactant, which are found to agree with the numerical results in the corresponding limits. We demonstrate that consideration of a uniform, immobile surface charge leads to an unphysical singular mobility, whereas allowing the surface charge to evolve through interfacial surfactant redistribution yields continuous and physically consistent droplet diffusiophoresis. Increasing the desorption rate enhances surfactant redistribution and Marangoni stress, which weakens the negative mobility created by the electrophoresis part, reverses the direction of motion by enhancing the chemiphoretic contribution, and subsequently leads to a strong enhancement of positive mobility before eventual saturation in the transport-limited regime. The dependence of mobility on viscosity ratio and electrolyte composition further reveals how mixed electrolytes provide a robust means of tuning droplet motion. This study underscores the crucial role of adsorption–desorption dynamics and interfacial transport of soluble ionic surfactants in governing the diffusiophoresis of fluid particles, with implications for droplet manipulation in microfluidic system in imposed salinity gradients.

Via asymptotics and numerics, we develop a semi-analytical procedure to capture the effect of slowly varying (streamwise) meniscus curvature on the flow resistance of the adiabatic section of an axial-groove heat pipe (AGHP). The small parameter is the pitch of the grooves divided by the length of the section. The geometry of the AGHP, its orientation with respect to gravity and relevant thermophysical properties (and, thus, the maximum capillary pressure) are prescribed. The deviation of the radius of curvature of the menisci from that of the lands (raised ridges protruding into the heat pipe bounding the axial grooves through which liquid flows) is captured numerically. (Alternatively, a boundary perturbation approach using a second small parameter, a protrusion angle of the meniscus into the groove, is outlined.) A local analysis ensures that the singularities at the triple-contact lines are resolved. Our procedure enables more accurate prediction of the capillary limit of an AGHP and the thermal resistance of its adiabatic section because, as shown, it causes the flow resistance in the adiabatic section in an AGHP representative of a commercial one to change by as much as 70 %. Instructions to access our code to semi-analytically compute the capillary limit when the radii of the menisci and lands are equal but, unlike in previous literature, shear stress and velocity are matched along the meniscus in the adiabatic section, are provided.

Two-fluid capillary flows in channels and pipes form a fundamental problem in fluid mechanics with widespread applications in physical, biological and microfluidic systems. A key phenomenon in such flows is the generation of long capsular bubbles, known as Taylor bubbles. A simple configuration that forms Taylor bubbles is coflow, where two fluids (one viscous, the other inviscid) are injected concurrently into a pipe or channel, producing a periodic pinch-off of inviscid bubbles at a regular frequency. By considering a lubrication theory for the necking region between the bubble injection nozzle and the developing Taylor bubble, we conduct a mathematical study of the formation of two-dimensional Taylor bubbles, yielding analytical insight into injection-driven pinch-off dynamics and the parametric control of its frequency. A key result is to demonstrate a quasi-static limiting theory of the necking dynamics for small capillary numbers. The theory is based on coupling an outer near-static regime of the pinching film with an apparent dynamic contact line that matches the necking zone to the film surrounding the Taylor bubble. This asymptotic structure, which becomes more refined in the limit of small capillary number, reveals a fundamental link between capillary pinch-off dynamics and the quasi-static regimes underlying spreading droplets. The theory yields a prediction for the dimensionless pinch-off time, $t_* \propto d^{7/3} / q_F^{4/3}$, where $q_F$ represents the flux of viscous fluid and $d$ the size of the capillary. The study thereby yields new mathematical understanding of flow regimes that underlie bubble generation in capillary systems from first principles, and the first step towards application of quasi-static analysis to more complex axisymmetric and three-dimensional examples of capillary pinch-off.

The classical problem of steady streaming induced by an oscillating object has been studied extensively, but prior work has focused almost exclusively on single-frequency oscillations, which result in symmetric, quadrupole-like flows. Here we demonstrate that dual-frequency oscillations induce asymmetric steady streaming with a non-zero net flux in a direction determined by the polarity of the oscillation – the oscillator serves as a pump. We use numerical simulations and asymptotic analysis at small amplitude to examine two-dimensional steady streaming around a cylinder, first focusing on frequency ratio 2. The computational experiments show asymmetrical streaming and pumping, i.e. net flux downstream. It is well known from asymptotic analysis that steady streaming is second order in amplitude, and we show that pumping occurs at third order. We then extend the analysis to general frequency ratios, where we give necessary conditions for pumping, and predict the order in amplitude at which pumping occurs. Finally, we corroborate the theoretical results with computational simulations for different frequency ratios, and we discuss the implications for using dual-mode vibrations to pump fluids in lab-on-a-chip and other applications.

Microfluidic systems integrated with magnetic manipulation of microparticles, serving as a functional component, have been extensively used in various applications, including biomedical diagnostics and targeted drug delivery. Microparticle dynamics in confined microchannels is governed by hydrodynamic viscous effects, magnetic dipole interactions and enhanced interactions with microchannel boundaries, while an in-depth understanding of the underlying mechanisms is still evolving. This work presents a systematic investigation on the dynamic response of microparticles suspended in a quasi-stationary liquid within a microchannel under an external magnetic field using a three-dimensional lattice Boltzmann model (LBM). The hydrodynamic viscous effects and the two-way fluid–structure interaction are fully resolved in this model. A dimensionless analysis of the microparticle dynamic equation is performed first, leading to the identification of two key characteristic parameters central to this work: the magnetic number $N_{\textit{mag}}$, which characterises the synergy of the hydrodynamic viscous effect and the magnetic dipole interaction, and the particle–wall separation distance $R/l$, which accounts for the microchannel wall interaction. Further, a series of LBM simulations with different $N_{\textit{mag}}$ and $R/l$ are carried out. The results suggest that the spatial trajectories of microparticles remain unaffected in response to variation in $N_{\textit{mag}}$, while their aggregation times demonstrate a linear dependence on the reciprocal of $N_{\textit{mag}}$ when released from the same initial position. Moreover, vortices generated by the motion of microparticles within microchannels tend to migrate toward the microparticles themselves as they approach the microchannel walls. As a result, microparticles experience an enhanced hydrodynamic viscous effect, which prolongs their aggregation time and leads to slight deviations in their spatial trajectories. A predictive model for the aggregation time is established, accounting for the effects of the external magnetic field, the microchannel wall interaction, as well as the initial positions of microparticles. The findings in this work provide significant insights into the optimisation of microparticle-based microfluidic technologies, thereby promoting their development in biomedical and chemical analytical applications.

In recent years, lubricant-infused superhydrophobic microfluidic surfaces have attracted significant attention for their potential to reduce drag. Motivated by the need to examine how non-Newtonian rheology influences hydrodynamic resistance in such systems, an analytical model for apparent slip is developed for pressure-driven flow of a non-Newtonian primary fluid over a non-Newtonian secondary infused fluid. For analytical tractability, Poiseuille flow in a non-Newtonian liquid-infused microchannel is modelled as two adjacent, immiscible power-law fluids co-flowing between infinite parallel plates under a constant pressure gradient. By enforcing continuity of velocity and tangential shear stress at the flat interface, closed-form expressions are obtained for the velocity distribution and interfacial slip velocity. Indeed, auxiliary two-phase full-field simulations for representative cases are consistent with the analytical predictions of interfacial shear stress and slip velocity. A quantitative analysis of the classical effective slip length reveals that it is governed by the slip-layer thickness, the infused fluid rheology and the interfacial apparent viscosity ratio. Generalised expressions are further obtained for the slip flow-rate ratio and the pressure-drop ratio relative to the classical no-slip channel. Within the present two-layer model, for fixed interfacial apparent viscosity ratio and slip-layer thickness, combinations involving shear-thinning primary and secondary fluids yield better slip-enhancement and drag-reduction trends. These results provide a reduced analytical framework for interpreting rheology-dependent apparent slip behaviour in non-Newtonian liquid-infused microchannels.

We study the pinch-off dynamics of a fluid surrounded by a significantly more viscous one during fluid–fluid displacement in straight, cylindrical capillary tubes, where the interface evolves under the influence of a moving contact line. We investigate the influence of insoluble surfactants on the dynamics of both the contact line and pinch-off. We focus on a visco-capillary displacement regime where the imposed flow rate exceeds a critical threshold, beyond which the contact-line velocity is governed by the partial wettability of the confined geometry, becoming independent of the flow rate. Under these conditions, the fluid–fluid meniscus forms an advancing axial finger, leaving behind a thin film of the defending fluid. This unstable film retracts along the partially wetting walls, forming a dewetting rim that grows with the steady contact-line motion. Eventually, a surface-tension-driven Rayleigh–Plateau instability dominates, triggering pinch-off at the rim neck. For a surfactant-free interface, our results show that the early-stage evolution of the neck diameter follows a power law $\tau ^\alpha$, where $\tau$ is the time to the pinch-off singularity and the scaling exponent $\alpha$ depends on the contact-line velocity determined by the wettability. Over the range resolved in the present simulations, $\alpha$ decreases from values near $1/2$ at large contact-line velocity towards values close to $1/5$ as the contact-line velocity is reduced. We demonstrate that, in the presence of insoluble surfactants, the contact-line velocity, at a given wettability, scales linearly with surfactant elasticity due to Marangoni stresses along the dewetting rim interface, which affect the timing and location of the pinch-off. Despite these effects, at the early-time regime, the pinch-off dynamics exhibits the same self-similar scaling behaviour as in the surfactant-free case.

Elastoviscoplastic (EVP) fluids, characterised by the coexistence of elastic, viscous and yield-stress properties, play a central role in diverse applications, including drug delivery, 3D printing and hydraulic fracturing. These fluids often transport non-spherical particles whose migration dynamics strongly influences flow behaviour. In this work, we employ interface-resolved direct numerical simulations to investigate the migration and orientation dynamics of finite-size spheroidal particles suspended in EVP duct flows across a wide range of governing parameters. Our results show that the equilibrium position and orientation of the particles are influenced significantly by both their aspect ratio and the carrier fluid rheology. In Saramito fluids, spheroidal particles migrate towards the duct centre and align along the duct diagonals in the presence of inertia. At sufficiently high elasticity, they penetrate the central plug and reach the duct core, irrespective of their initial position or shape. At lower elasticities, where larger plug regions persist, interactions with the plug alter the angular dynamics of the particles, leading to unsteady, quasi-periodic tumbling and spinning motions. In contrast, in Saramito–Giesekus fluids, the interplay between inertial forces, shear-thinning plastic viscosity and yield stress drives particles towards the duct corners, aligning them perpendicular to the duct diagonals. In semi-dilute suspensions, flattened particles maintain a greater distance from the walls, whereas their spherical counterparts tend to cluster directly at the corners. These findings reveal complex migration and orientation behaviours unique to EVP media and suggest new opportunities for geometry-based particle separation in microfluidic applications.

We present an experimental and theoretical investigation of steady Taylor cone-jetting of highly viscous liquids at the minimum flow rate required for steady jetting. To achieve a steady cone-jet, the viscous liquid is flown through a conducting needle under the action of a strong electric field acting between the needle and a flat collector plate. Experiments reveal that the minimum flow rate and the corresponding jet diameter depend on both the needle diameter and the electrical conductivity of the liquid. Subsequently, we used the experimental measurements to formulate correlations among the minimum flow rate, the needle diameter and the physical properties of the liquid, including the electrical conductivity. To elucidate the underlying physics and experimental observations, we performed an order-of-magnitude analysis. The scaling analysis reveals that in the cone region, the viscous and interfacial tension forces are of comparable magnitude, while in the current transfer region, the viscous and electrostatic suction forces are the dominant resisting and driving forces, respectively. Subsequently, we theoretically derived the scaling relations for the minimum flow rate and the corresponding jet diameter by considering the balance of forces at the cone-tip and in the current transfer region. The empirical and theoretical scaling laws for the minimum flow rate and the corresponding jet diameter agree well for highly viscous liquids with electrical conductivity spanning over four orders of magnitude. Lastly, we present the limits that describe the regime for which the minimum flow rate depends on the needle diameter, and the derived scaling laws are applicable.