Understanding the hydrodynamics of microswimmers in viscoelastic fluids and confined environments is crucial for interpreting their behaviour in natural settings and designing synthetic microswimmers for practical applications like cargo transport. In this study, we explore the hydrodynamics of a concentric active compound particle - a model microswimmer (a squirmer) positioned at the centre of a viscoelastic fluid droplet (a model cargo) suspended in another viscoelastic medium. We consider the Oldroyd-B constitutive model to characterize the fluids and employ a perturbative approach in the Deborah number to analyze viscoelastic effects analytically, assuming a small Capillary number so that the droplet remains spherical and does not deform. We examine three cases: (i) a squirmer confined within a viscoelastic fluid droplet suspended in a Newtonian fluid, (ii) a squirmer confined within a Newtonian fluid droplet suspended in a viscoelastic fluid, and (iii) a squirmer confined within a viscoelastic fluid droplet suspended in another viscoelastic fluid. Our findings reveal that the swimming speeds of the squirmer and the droplet are determined by the complex interplay of viscoelasticity, the size ratio of the droplet to the squirmer (confinement strength), and the viscosity ratio of the surrounding fluid to the droplet fluid. A critical aspect of this interaction is the positioning of stagnation points within the fluid flow, which governs the distribution of polymeric stress. This distribution, in turn, plays a crucial role in determining the influence of viscoelasticity on the squirmer's dynamics. Our analysis suggests that viscoelastic effects can either enhance or hinder the swimming speed of the squirmer when confined in a droplet, depending on the specific configuration of the system.

Tissue homeostasis, the biological process of maintaining a steady state in tissue via control of cell proliferation and death, is essential for the development, growth, maintenance, and proper function of living organisms. Disruptions to this process can lead to serious diseases and even death. In this study, we use the vertex model for the cell-level description of tissue mechanics to investigate the impact of the tissue environment and local mechanical properties of cells on homeostasis in confined epithelial tissues. We find a dynamic steady state, where the balance between cell divisions and removals sustains homeostasis, and characterise the homeostatic state in terms of cell count, tissue area, homeostatic pressure, and the cells’ neighbour count distribution. This work, therefore, sheds light on the mechanisms underlying tissue homeostasis and highlights the importance of mechanics in its control.

Controlled navigation of self-propelled active matter in complex biological environments has remained a significant challenge in engineering owing to a multitude of interactions that persist in the process. Active droplets, being some of the several synthetic active matters, have garnered significant attention owing to their ability to exhibit dynamic shape changes, self-sustained motion, interact with external stimuli such as flows, and mimic biological active matter. Here, we explore the dynamics of a self-propelled active droplet powered by the oscillatory Belousov–Zhabotinsky (BZ) reaction in the presence of a shear flow. We adapt a multicomponent lattice Boltzmann method (LBM) in conjunction with the phase-field model to simulate the droplet's interaction with the surrounding fluid. We unravel the collective effect of droplet deformation, reaction kinetics, and strength of the surrounding shear flow on droplet dynamics. Our findings depict that the shear flow disrupts the initial isotropic surface tension, and produces concentration nucleation spots in the droplet. The asymmetry thus generated produces Marangoni flow that ultimately propels the droplet. Our findings provide valuable insights into the mechanisms governing active droplet behavior and open new avenues for designing controllable synthetic active matter systems with potential applications in microfluidics, targeted delivery, and biomimetic technologies. In addition, our framework can potentially be integrated with the physics-informed machine learning framework to develop more efficient mesh-free methods.

Complex tissue flows in epithelia are driven by intra- and inter-cellular processes that generate, maintain, and coordinate mechanical forces. There has been growing evidence that cell shape anisotropy, manifested as nematic order, plays an important role in this process. Here we extend an active nematic vertex model by replacing substrate friction with internal viscous dissipation, dominant in epithelia not supported by a substrate or the extracellular matrix, which are found in many early-stage embryos. When coupled to cell shape anisotropy, the internal viscous dissipation allows for long-range velocity correlations and thus enables the spontaneous emergence of flows with a large degree of spatiotemporal organisation. We demonstrate sustained flow in epithelial sheets confined to a channel, providing a link between the cell-level vertex model of tissue dynamics and continuum active nematics, whose behaviour in a channel is theoretically understood and experimentally realisable. Our findings also show a simple mechanism that could account for collective cell migration correlated over distances large compared to the cell size, as observed during morphogenesis.

Collectively moving cellular systems often contain a proportion of dead cells or non-motile genotypes. When mixed, nematically aligning motile and non-motile agents are known to segregate spontaneously. However, the role that topological defects and active stresses play in shaping the distribution of the two phases remains unresolved. In this study, we investigate the behaviour of a two-dimensional binary mixture of active and passive nematic fluids to understand how topological defects are transported between the two phases and, ultimately, how this leads to the segregation of topological charges. When the activity of the motile phase is large, and the tension at the interface of motile and non-motile phases is weak, we find that the active phase tends to accumulate  +1/2 defects and expel  −1/2 defects so that the motile phase develops a net positive charge. Conversely, when the activity of the motile phase is comparatively small and interfacial tension is strong, the opposite occurs so that the active phase develops a net negative charge. We then use these simulations to develop a physical intuition of the underlying processes that drive the charge segregation. Lastly, we quantify the sensitivity of this process on the other model parameters, by exploring the effect that anchoring strength, orientational elasticity, friction, and volume fraction of the motile phase have on topological charge segregation. As  +1/2 and  −1/2 defects have very different effects on interface morphology and fluid transport, this study offers new insights into the spontaneous pattern formation that occurs when motile and non-motile cells interact.

Generating core–shell particles with a well-controlled morphology is of great interest due to the interdependence between the morphology and different properties of these structures. These particles are often generated in microfluidic devices in a background quadratic flow. Therefore, in this study, we investigate the hydrodynamics and morphology of a concentric active compound particle, an active particle encapsulated in a fluid droplet, in an imposed quadratic flow. Governing equations for fluid flow are analytically solved in the inertia-less limit assuming that the surface tension force dominates the viscous forces (capillary number, Ca ≪ 1). Poiseuille flow deforms the compound particle into a three-lobe structure governed by the hexapolar component of the Poiseuille flow. Activity deforms the compound particle into a prolate shape owing to the velocity field of a force dipole. For an active compound particle in a Poiseuille flow, morphology is sensitive to the orientations and relative strengths of the activity and Poiseuille flow. Primarily, the presence of activity breaks the three-lobe symmetry of the drop shape and makes it more asymmetric and elongated. Moreover, the active compound particle becomes more susceptible to breakup in a quadratic flow when (i) the strength of activity is much stronger than the imposed flow strength, (ii) the active particle is oriented along the symmetry axes of the quadratic flow, (iii) the size ratio of the confining droplet to the encapsulated active particle is small and (iv) the viscosity ratio of the outer fluid to the inner fluid is small. Finally, we demonstrate that imposing the pulsatile quadratic flow prevents the breakup of an active compound particle during its generation and transport, and further assists in tuning the morphology.

Self-sustained locomotion of synthetic droplet swimmers has been of great interest due to their ability to mimic the behavior of biological swimmers. Here we harness the Belousov-Zhabotinsky (BZ) reaction to induce Marangoni stresses on the fluid-droplet interface and elucidate the spontaneous locomotion of active BZ droplets in a confined two-dimensional channel. Our approach employs the lattice Boltzmann method to simulate a coupled system of multiphase hydrodynamics and BZ-reaction kinetics. Our investigation reveals the mechanism underlying the propulsion of active BZ droplets, in terms of convective and diffusive fluxes and deformation of the droplets. Furthermore, we demonstrate that by manipulating the degree of confinement, strength, and nature of coupling between surface tension and active species’ concentration, the motion of the BZ droplet can be directed. In addition, we are able to capture two different kinds of droplet behaviors, namely, sustained and stationary, and establish conditions for the sustained long-time motion. We envisage that our findings can be used not only to understand the mechanics of biological swimmers but also to design reaction-driven self-propelled systems for a variety of biomimetic applications.

Microorganisms navigate through fluid, often confined by complex environments, to survive and sustain life. Inspired by this fact, we consider a model system and seek to understand the wall curvature driven dynamics of a squirmer, a mathematical model for a microswimmer, using (i) lattice Boltzmann simulations and (ii) analytical theory by D. Papavassiliou and G. P. Alexander [Eur. Phys. Lett. 110, 44001 (2015)]. The instantaneous dynamics of the system is presented in terms of fluid velocity fields, and the translational and angular velocities of the microswimmer, whereas the long time dynamics is presented by plotting the squirmer trajectories near curved boundaries in physical and dynamical space, as well as characterizing them in terms of fixed points and experimentally relevant measures, namely, (i) proximity parameter, (ii) retention time, (iii) swimmer orientation and (iv) tangential velocity near the boundary, and (v) scattering angle during the collision. Our detailed analysis shows that irrespective of the type and strength, microswimmers exhibit a greater affinity towards a concave boundary due to hydrodynamic interactions compared to a convex boundary. In the presence of additional repulsive interactions with the boundary, we find that pullers (propel by forward thrust) have a slightly greater affinity towards the convex-curved walls compared to pushers (propel by backward thrust). Our study provides a comprehensive understanding of the consequence of hydrodynamic interactions in a unified framework that encompasses the dynamics of pullers, pushers, and neutral swimmers in the neighborhood of flat, concave, and convex walls. In addition, the combined effect of oppositely curved surfaces is studied by confining the squirmer in an annulus. The results presented in a unified framework and insights obtained are expected to be useful to design geometrical confinements to control and guide the motion of microswimmers in microfluidic applications.

Chemically active Janus particles generate tangential concentration gradients along their surface for self-propulsion. Although this is well studied in unbounded domains, the analysis in biologically relevant environments such as confinement is scarce. In this work, we study the motion of a Janus sphere in weak confinement. The particle is placed at an arbitrary location, with arbitrary orientation between the two walls. Using the method of reflections, we study the effect of confining planar boundaries on the phoretic and hydrodynamic interactions, and their consequence on the Janus particle dynamics. The dynamical trajectories are analyzed using phase diagrams for different surface coverage of activity and solute-particle interactions. In addition to near wall states such as ‘sliding’ and ‘hovering’, we demonstrate that accounting for two planar boundaries reveals two new states: channel-spanning oscillations and damped oscillations around the centerline, which were characterized as ‘scattering’ or ‘reflection’ by earlier analyses on single wall interactions. Using phase-diagrams, we highlight the differences in inert-facing and active-facing Janus particles. We also compare the dynamics of Janus particles with squirmers for contrasting the chemical interactions with hydrodynamic effects. Insights from the current work suggest that biological and artificial swimmers sense their surroundings through long-ranged interactions, that can be modified by altering the surface properties.

Compound particles are a class of composite systems in which solid particles encapsulated in a fluid droplet are suspended in another fluid. They are encountered in various natural and biological processes, for e.g. nucleated cells, hydrogels, microcapsules etc. Generation and transportation of such multiphase structures in microfluidic devices is associated with several challenges because of the poor understanding of their structural stability in a background flow and the rheological characteristics of their dispersions. Hence, in this work, we analyse the flow in and around a concentric compound particle and investigate the deformation dynamics of the confining drop and its stability against breakup in imposed linear flows. In the inertia-less limit (Reynolds number, $Re \ll 1$) and assuming that the surface tension force dominates the viscous forces (low capillary number, $Ca$, limit), we obtain analytical expressions for the velocity and pressure fields up to ${O}(Ca)$ for a compound particle subjected to a linear flow using a domain perturbation technique. Simultaneously, we determine the deformed shape of the confining drop correct up to ${O}(Ca^2)$, facilitating the following. (i) Since ${O}(Ca^2)$ calculations account for the rotation of the anisotropically deformed interface, the reorientation dynamics of the deformed compound particles is determined. (ii) Calculations involving the ${O}(Ca^2)$ shape of the confining interface are found to be important for compound particles as ${O}(Ca)$ calculations make qualitatively different predictions in generalised extensional flows. (iii) An ${O}(Ca)$ constitutive equation for the volume-averaged stress for a dilute dispersion of compound particles was developed to study both shear and extensional rheology in a unified framework. Our analysis shows that the presence of an encapsulated particle always enhances all the measured rheological quantities such as the effective shear viscosity, extensional viscosity and normal stress differences. (iv) Moreover, linear viscoelastic behaviour of a dilute dispersion of compound particles is characterised in terms of complex modulus by subjecting the dilute dispersion to a small-amplitude oscillatory shear (SAOS) flow. (v) Various expressions pertaining to a suspension of particles, drops, and particles coated with a fluid film are also derived as limiting cases of compound particles.

Active particles encapsulated in a droplet are called active compound particles. In addition to the activity induced fluid flows, these multiphase structures may experience imposed flows in the process of generating and manipulating them in microfluidic devices or in their natural habitats. Therefore, we investigate the deformation dynamics and stability of a drop encapsulating a model microswimmer, a spherical squirmer (shaker) concentrically placed in a drop, when subjected to an imposed shear flow. Using Lamb’s general solution, Stokes equations are solved to determine the flow field and consequently the shape of the droplet interface. Shear flow always deforms the drop and the flow induced by the active particle may enhance or impede this deformation based on its orientation. The extent of deformation also depends on (i) the size of the active particle and the droplet, (ii) the viscosity of the droplet fluid and the fluid in which it is dispersed, (iii) the orientation of the active particle, and (iv) the relative strength of activity and imposed shear. Finally we find that the presence of an imposed vorticity field has a stabilizing effect on the active compound particle as it rotates the encapsulated swimmer and the drop undergoes a time periodic deformation.

Particles confined in droplets are called compound particles. They are encountered in various biological and soft matter systems. Hydrodynamics can play a decisive role in determining the configuration and stability of these multiphase structures during their preparation and use. Therefore, we investigate the dynamics and stability of a concentric compound particle under external forces and imposed flows. The governing equations are solved analytically in the inertia-less limit using the standard technique of superposition of vector harmonics and the solutions obtained are reported in terms of steady state flow fields, the viscous drag on the particle and the time evolution of the confining drop shape. The limiting form of a compound particle as a thin film coated rigid particle is analyzed in each case. We find that the concentric configuration of a rotating compound particle is a steady state solution, and we calculate the extra force required to stabilize the concentric configuration of a translating compound particle. A comprehensive comparison of drop deformations in various linear ambient flows is also provided. Based on the findings, we propose pulsatile flow as a reliable method to transport compound particles without breakup of the confining drop. Thus, our analysis provides useful guidelines for preparation and transportation of stable compound particles in the context of nucleated cells, aerosols, droplet-based encapsulation of motile organisms and polymer microcapsules.