We investigate the rheology of biphasic emulsions composed of an elastoviscoplastic (EVP) matrix and viscous, initially spherical monodisperse droplets via interface-resolved numerical simulations. The droplet interface is captured using a level-set method, and the EVP phase is modelled with the Saramito constitutive equation. We explore the effects of the volume fraction, Capillary, Weissenberg, and Bingham numbers, considering both dilute and semi-dilute regimes (volume fractions from 0.16% to 20%) at two density and viscosity ratios. The constitutive curve shows a negative curvature, consistent with previous studies on emulsion rheology with coalescing drops. Increasing the Capillary and Bingham numbers show qualitatively similar trends: increasing drop deformation with both results in a decrease of the emulsion's relative viscosity. This is further supported by stress budget analysis, which shows that yield stress increases the effective viscosity of the matrix fluid, thereby increasing the effective Capillary number and reducing the effective viscosity ratio. The emulsion rheology shows a complex relationship with the Weissenberg number (Wi). In dilute systems, droplet deformation increases with Wi, while bubbles exhibit a non-monotonic trend. Relative viscosity rises with Wi for droplet emulsions up to Wi = 1.75 due to localised EVP shear stress, then slightly decreases. For bubbly emulsions, viscosity remains nearly constant at low Wi but decreases at larger values. At semi-dilute concentrations, similar trends emerge with EVP stresses dominating and dictating the emulsion's relative viscosity. At high Wi, increased EVP stress, reduced coalescence, larger interfacial stress, and near-wall migration collectively increase the relative viscosity.

We study the interaction-induced migration of bubbles in shear flow and observe that bubbles suspended in elastoviscoplastic emulsions organize into chains aligned in the flow direction, similarly to particles in viscoelastic fluids. To investigate the driving mechanism, we perform experiments and simulations on bubble pairs, using suspending fluids with different rheological properties. First, we notice that, for all fluids, the interaction type depends on the relative position of the bubbles. If they are aligned in the vorticity direction, then they repel, if not, then they attract each other. The simulations show a similar behavior in Newtonian fluids as in viscoelastic and elastoviscoplastic fluids, as long as the capillary number is sufficiently large. This shows that the interaction-related migration of the bubbles is strongly affected by the bubble deformation. We suggest that the cause of migration is the interaction between the heterogeneous pressure fields around the deformed bubbles, due to capillary pressure.

The transport of particles in elastoviscoplastic (EVP) fluids is of significant interest across various industrial and scientific domains. However, the physical mechanisms underlying the various particle distribution patterns observed in experimental studies remain inadequately understood in the current literature. To bridge this gap, we perform interface-resolved direct numerical simulations to study the collective dynamics of spherical particles suspended in a pressure-driven EVP duct flow. In particular, we investigate the effects of solid volume fraction, yield stress, inertia, elasticity, shear-Thinning viscosity, and secondary flows on particle migration and formation of plug regions in the suspending fluid. Various cross-streamline migration patterns are observed depending on the rheological parameters of the carrier fluid. In EVP fluids with constant plastic viscosity, particles aggregate into a large cluster at the duct centre. Conversely, EVP fluids with shear-Thinning plastic viscosity induce particle migration towards the duct walls, leading to formation of particle trains at the corners. Notably, we observe significant secondary flows (compared to the mean velocity) in shear-Thinning EVP suspensions, arising from the interplay of elasticity, shear-Thinning viscosity and particle presence, which further enhances corner-ward particle migration. We elucidate the physical mechanism by which yield stress augments the first normal stress difference, thereby significantly amplifying elastic effects. Furthermore, through a comprehensive analysis of various EVP suspensions, we identify critical thresholds for elasticity and yield stress necessary to achieve particle focusing at the duct corners.

Elastoviscoplastic (EVP) fluids, characterized 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 influence 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 microfluidics applications.

Experimental studies of natural convection in yield stress fluids have revealed transient behaviours that contradict predictions from viscoplastic models. For example, at sufficiently large yield stress, these models predict complete motionlessness; below a critical value, yielding and motion onset can be delayed in viscoplastic models. In both cases, however, experiments observe immediate motion onset. We present numerical simulations of transient natural convection of elastoviscoplastic (EVP) fluids in a square cavity with differentially heated sidewalls, exploring the role of elasticity in reconciling theoretical predictions with experimental observations. We consider motion onset in EVP fluids under two initial temperature distributions: (i) a linear distribution characteristic of steady pure conduction, and (ii) a uniform distribution representative of experimental conditions. The Saramito EVP model exhibits asymptotic behaviour similar to the Kelvin-Voigt model as t→ 0⁺, where material behaviour is primarily governed by elasticity and solvent viscosity. The distinction between motion onset and yielding, a hallmark of EVP models, is the key feature that bridges theoretical predictions with experimental observations. While motion onset is consistently immediate (as seen in experiments), yielding occurs with a delay (as predicted by viscoplastic models). Scaling analysis suggests that this delay varies logarithmically with the yield stress and is inversely proportional to the elastic modulus. The intensity of the initial pre-yield motion increases with higher yield stress and lower elastic modulus. The observed dynamics resemble those of under- and partially over-damped systems, with a power-law fit providing an excellent match for the variation of oscillation frequency with the elastic modulus.

We present interface-resolved direct numerical simulations of turbulent channel flow of elastoviscoplastic (EVP) fluids laden with viscous droplets. The simulations are conducted at Re_bulk = 2800 for differnet Weissenberg numbers (Wi) in viscoelastic FENE-P fluids and different Bingham numbers (Bn) in elastoviscoplastic Saramito FENE-P fluids, in order to examine the influence of elasticity and yield stress of the carrier fluid on multiphase turbulent flow dynamics. The drag-reducing effects associated with fluid elasticity observed in classical viscoelastic turbulence, as well as in prior studies of single-phase elastoviscoplastic channel flows, are found to persist in the present study. Introducing viscous droplets into the carrier fluid does not produce significant variations in overall drag relative to the single-phase cases, with a clear absence of near-wall droplet layers as the droplets preferentially migrate towards the channel centre. The normal stress gradient generated by the mean flow drives this centre-ward migration, leading to a depletion of droplets in the near-wall region. Both elasticity and yield stress are found to have a strong influence on the droplet size distribution. Increasing either Wi or Bn tends to promote the formation of larger droplets by suppressing breakup through the stabilisation of interfacial instabilities.

The flow of complex fluids past a circular cylinder is a canonical flow configuration of broad industrial and scientific interest. We present numerical simulations investigating the flow of Boger fluids (modelled with the Oldroyd-B constitutive equation), viscoelastic shear-thinning fluids with anisotropic mobility (using the Giesekus model), and elastoviscoplastic fluids (using Saramito's model) past a circular cylinder in a channel of height twice the cylinder diameter. Through direct numerical simulations, we investigate for the first time the onset of the three-dimensional elastic wake instability discovered by McKinley et al. [Philos. Trans., Math. Phys. Eng. Sci. vol. 334, no. 1671 (1993)], and its development with increasing Deborah number. Our results for Boger fluids show the onset of a steady three-dimensional cellular structure above a critical Deborah number, with a wavelength and appearance consistent with experiments. When the Deborah number increases, both simulations and experiments show a transition to time-dependent behaviour. Further, we show that increasing shear-thinning and anisotropic drag through the Giesekus mobility parameter, α, rapidly suppresses the instability, an effect we attribute to the shear-thinning first-normal stress coefficient of the Giesekus model. Finally, our simulations predict onset of the three-dimensional wake instability in elastoviscoplastic fluids, with velocity perturbations in the wake extending smoothly into the surrounding un-yielded regions. Parametric studies in Deborah-Bingham (De-Bn) space reveal that increasing De increases the instability amplitude and non-linearity, and shows transition to time-dependent behaviour, while increasing Bn primarily increases the volume of un-yielded regions and the instability amplitude.