Elasto-inertial turbulence (EIT) offers a mechanism to tune fundamental flow processes using elastic instabilities by the addition of polymer to the fluid. Here, we extend this emerging paradigm to elastoviscoplastic (EVP) materials, where the interplay of elasticity and a yield stress dictates the flow dynamics. Through direct numerical simulations of channel flow, we demonstrate that a yield stress does not suppress EIT but rather reorganizes it, with the flow maintaining an EIT-like characteristic even when most of the domain is nominally unyielded. Plasticity promotes the formation of solid-like plugs and patches, weakens near-wall streaks, and non-monotonically modifies drag, while elastic stresses continue to drive fluctuations in yielded shear layers. Detailed analysis of solid-fraction statistics, first-normal-stress fields, turbulent kinetic energy spectra and budgets jointly reveal a robust elastic turbulent core where EVP stresses transition from net sinks to net sources of turbulent kinetic energy as elasticity of the material increases. The turbulent kinetic energy spectra retain inertial and elastic scaling ranges, and flow topology collapses towards quasi-two-dimensional, sheet-like structures for large elasticity of the EVP material. Together the present results identify EIT in EVP fluids as an elastic turbulent state  modified by plasticity, bridging the gap between viscoelastic EIT and high–Reynolds-number EVP turbulence and providing mechanistic insight directly relevant to controlling drag, mixing and transport in yield-stress fluids.

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.

This study investigates the impact of elasticity and plasticity on two-dimensional flow past a circular cylinder at Reynolds number Re=100. Ten direct numerical simulations were performed using the Saramito-Herschel–Bulkley model to represent viscoelastic and elastoviscoplastic (EVP) fluids. The flow evolves from a periodic von Kármán vortex street to chaotic-like regimes. Proper Orthogonal Decomposition (POD) and Higher Order Dynamic Mode Decomposition (HODMD) are applied to extract dominant flow structures and their temporal dynamics. For viscoelastic fluids, increasing the Weissenberg number Wi elongates the recirculation bubble and shifts it downstream, resulting in more intricate but still periodic behavior. In EVP fluids, seven cases explore variations in Bingham number Bn, solvent viscosity ratio βs, and power law index n, aiming to qualitatively assess their influence rather than determine critical thresholds. Results indicate that stronger plastic effects, especially with n≥1, lead to increased flow complexity. Three dynamic regimes are identified: (i) periodic; (ii) transitional, with elongated recirculation and disrupted periodicity; and (iii) fully complex, with breakdown of recirculation. Overall, the study highlights the interplay between inertia, elasticity, and yield stress in non-Newtonian flows past obstacles and identifies key parameters driving the transition from periodic to complex regimes.

Experimental studies of natural convection in yield stress fluids have revealed transient behaviours that contradict predictions from viscoplastic models. For example, at a 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 the transient natural convection of elastoviscoplastic (EVP) fluids in a square cavity with differentially heated side walls, 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 an asymptotic behaviour similar to the Kelvin-Voigt model as, 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.

Yield stress fluids are ubiquitous in our environment and industrial processes - from food, cosmetics and hygiene products to paper pulp processing and geophysical flows of magma, mudslides and avalanches. The flow behaviour of these fluids is qualitatively different from water and other simple fluids, for instance because they behave as soft solid materials before starting to flow. Therefore it is important for applications to be able to understand and model yield stress fluid flow.

Bingham formulated his seminal model for yield stress fluids already in the beginning of 20\textsuperscript{th} century, but in the recent years experiments have shown that many flow phenomena cannot be explained by the Bingham model. A new central insight is that the elasticity of the material plays a role, and results in behaviours similar to viscoelastic fluids. To capture such effects in computer simulations, one has to use an elastoviscoplastic model that combines yield stress and elasticity of the fluid.

This thesis consists of computer simulations of flows of elastoviscoplastic fluids in fundamental canonical flow configurations of relevance for industries. Also multiphase flows are studied – suspensions of particles, droplets and bubbles – with specialised numerical methods.  In suspensions of bubbles or droplets in planar shear flow, we show how rheology and droplet dynamics is affected by yield stress and elasticity of the surrounding material.  Fluid elasticity makes the droplets migrate towards channel walls, while yield stress increases the effective viscosity of the fluid, slowing down this migration. When two bubbles come close to each other in shear flow, they either attract or repel each other in the vorticity direction depending on their relative separation.

Particle suspensions are analysed in a three-dimensional channel with a quadratic cross-section. We observe, similarly to experiments, that spherical particles move towards the four corners of the channel, and we explain this phenomenon by analysing the stress fields obtained from our simulations. Non-spherical particles on the other hand can obtain several distinct stable orientations, and precessing or tumbling motions, when interacting with the solid part of the material, the ``central plug region".

Building on the studies of multiphase flows comprising elastoviscoplastic carrier fluids under laminar flow conditions, attention was turned to the behaviour of viscous droplets suspended in such fluids under turbulent flow conditions. The elasticity and yield stress of the carrier fluid are found to play a central role in droplet break-up and coalescence. As elasticity and yield stress increase, droplet break-up is suppressed, leading to the formation of large droplets and an accompanying skewness in the size distribution of droplets. The elasticity of the carrier fluid generates lift forces across the channel that drive droplet migration towards the centre. This migration depletes droplet layers near the walls, hence no significant variations in drag are observed.

Next, the first study of heat transfer by natural convection in elastoviscoplastic fluids is performed. The findings show that material elasticity can account for experimentally observed behaviour in Carbopol, such as the immediate onset of motion when a temperature gradient is applied in fluids with sufficiently low yield stress. In fluids with higher (super-critical) yield stress, the solid-like material is found to undergo elasto-inertial vibrations, resembling the behaviour of a damped spring-mass system.

Finally, three-dimensional computer simulations are conducted to successfully reproduce for the first time a classical wake instability in the flow viscoelastic fluids past a confined, circular cylinder in both steady and time-dependent regimes. The influence of different fluid behaviours is examined - in particular, the impact of shear-thinning in viscoelastic liquids and the role of yield stress in elastoviscoplastic materials. The results show that a small degree of shear-thinning in the first normal stress coefficient of viscoelastic liquids can rapidly suppress the instability. In elastoviscoplastic fluids, the characteristic instability is found to persist, with velocity fluctuations remarkably extending into the surrounding un-yielded regions of the material - which behave like soft solids - through elastic deformation.

Flytspänningsvätskor är vanligt förekommande i vår omgivning och i industriella processer – från livsmedel, kosmetika och hygienprodukter till processering av pappersmassa och geofysiska flöden av till exempel magma, jordskred och laviner. Flödesbeteendet av dessa vätskor skiljer sig markant från flödet av vatten och andra enkla vätskor, bland annat för att de beter sig som mjuka fasta material innan de börjar flöda, vilket ger lavinartade beteenden. Därför är det viktigt för tillämpningarna att  kunna förstå och modellera deras flöden.

Bingham formulerade sin banbrytande modell för flytspänningsvätskor redan i början av 1900-talet, men de senaste åren har experiment visat att många strömningsfenomen för dessa vätskor inte kan förklaras av Bingham-modellen. En ny central insikt är att materialens elasticitet spelar roll, och resulterar i flödesfenomen som liknar viskoelastiska vätskor. För att kunna fånga dessa effekter måste man använda en elastoviskoplastisk modell som kombinerar flytspänning och elasticitet.

Denna avhandling består av datorberäkningar av elastoviskoplastiska vätskeflöden i grundläggande flödeskonfigurationer av relevans för industrierna. Också flerfasflöden studeras – suspensioner av partiklar, droppar och bubblor – med specialiserade numeriska metoder. I suspensioner av bubblor och droppar i plan skjuvströmning visar vi hur reologin och dropparnas dynamik påverkas av flytspänning och elasticitet av materialet. Vätskans elasticitet leder till att dropparna flyttar sig mot kanalväggarna, medan flytspänning ökar den effektiva viskociteten och saktar ner deras förflyttning. När två bubblor kommer nära varandra i skjuvströmning så rör de sig mot eller ifrån varandra i vorticitetsriktningen.

Partikelsuspensioner analyseras i tredimensionella kanaler av kvadratiskt tvärsnitt. Vi observerar likt experiment att runda (sfäriska) partiklar flyttar sig mot kanalens fyra hörn och förklarar detta fenomen genom att studera spänningsfält från simuleringarna. Icke-sfäriska partiklar däremot kan anta flera stabila orienteringar och jämviktstillstånd, och partiklarna utför flera olika precesserande och tumlande rörelser, när de interagerar med den fasta delen av materialet, den ``centrala pluggregionen".

Med utgångspunkt i studierna av droppar, bubblor och partiklar i elastoviskoplastiska vätskor under laminära strömningsförhållanden riktas uppmärksamheten mot beteendet hos viskösa droppar suspenderade i sådana vätskor under turbulenta strömningsförhållanden. Elasticiteten och flytspänning hos bärarvätskan visar sig spela en central roll för droppars sönderfall och koalescens. När elasticitet och flytgräns ökar motverkas droppars sönderfall, vilket leder till bildandet av stora droppar och en åtföljande skevhet i storleksfördelningen. De stora dropparnas deformerbarhet, tillsammans med bärarvätskans elasticitet, genererar lyftkrafter tvärs över kanalen som driver droppmigration mot centrum. Denna migration tunnar ut droppskikten nära väggarna, och därför observeras inga betydande variationer i friktion.

Nästa del av arbetet utgörs av den första studien av värmeöverföring genom naturlig konvektion i elastoviskoplastiska vätskor. Resultaten visar att materialets elasticitet kan förklara experimentellt observerat beteende i Carbopol, såsom det omedelbara påbörjandet av rörelse när en temperaturgradient appliceras i vätskor med tillräckligt låg flytgräns. I vätskor med högre (superkritisk) flytgräns uppvisar det fastliknande materialet elasto-inertiella vibrationer, vilka påminner om beteendet hos ett dämpat fjäder-mass-system.

Avslutningsvis utförs tredimensionella datorsimuleringar där man för första gången framgångsrikt reproducerar en klassisk vakinstabilitet i strömningen av viskoelastiska vätskor kring en innesluten, cirkulär cylinder under både stationära och tidsberoende förhållanden. Olika vätskeegenskapers inverkan undersöks – särskilt effekten av skjuvtunnande i viskoelastiska vätskor och flytgränsens roll i elastoviskoplastiska material. Resultaten visar att en liten grad av skjuvtunnande i den första normala spänningskoefficienten hos viskoelastiska vätskor snabbt kan dämpa instabiliteten. I elastoviskoplastiska vätskor kvarstår den karakteristiska instabiliteten, och hastighetsfluktuationer sträcker sig påtagligt in i de omgivande, ej uppflytna områdena av materialet – som beter sig som mjuka fasta kroppar – genom elastisk deformation.

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.

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.

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.

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.