Direct numerical simulations are carried out to study the effect of finite Weissenberg number up to Wi = 16 on laminar and turbulent channel flows of an elastoviscoplastic (EVP) fluid, at a fixed bulk Reynolds number of 2800. The incompressible flow equations are coupled with the evolution equation for the EVP stress tensor by a modified Saramito model that extends both the Bingham viscoplastic and the finite extensible nonlinear elastic-Peterlin (FENE-P) viscoelastic models. In turbulent flow, we find that drag decreases with both the Bingham and Weissenberg numbers, until the flow laminarises at high enough elastic and yield stresses. Hence, a higher drag reduction is achieved than in the viscoelastic flow at the same Weissenberg number. The drag reduction persists at Bingham numbers up to 20, in contrast to viscoplastic flow, where the drag increases in the laminar regime compared with a Newtonian flow. Moreover, elasticity affects the laminarisation of an EVP flow in a non-monotonic fashion, delaying it at lower and promoting it at higher Weissenberg numbers. A hibernation phenomenon is observed in the EVP flow, leading to large changes in the unyielded regions. Finally, plasticity is observed to affect both low- and high-speed streaks equally, attenuating the turbulent dissipation and the fragmentation of turbulent structures.

In this numerical and theoretical work, we study the turbulent channel flow of Newtonian and elastoviscoplastic fluids. The coherent structures in these flows are identified by means of higher order dynamic mode decomposition (HODMD), applied to a set of data non-equidistant in time, to reveal the role of the near-wall streaks and their breakdown, and the interplay between turbulent dynamics and non-Newtonian effects. HODMD identifies six different high-amplitude modes, which either describe the yielded flow or the yielded-unyielded flow interaction. The structure of the low- and high-frequency modes suggests that the interaction between high- and low-speed streamwise velocity structures is one of the mechanisms triggering the streak breakdown, dominant in Newtonian turbulence where we observe shorter near-wall streaks and a more chaotic dynamics. As the influence of elasticity and plasticity increases, the flow becomes more correlated in the streamwise direction, with long streaks disrupted for short times by localised perturbations, reflected in reduced drag. Finally, we present streamwise-periodic dynamic mode decomposition modes as a viable tool to describe the highly complex turbulent flows, and identify simple well-organised groups of travelling waves.

The dynamics of a single elastoviscoplastic drop immersed in plane shear flow of a Newtonian fluid is studied by three-dimensional direct numerical simulations using a finite-difference and level-set method combined with the Saramito model for the elastoviscoplastic fluid. This model gives rise to a yield stress behavior, where the unyielded state of the material is described as a Kelvin-Voigt viscoelastic solid and the yielded state as a viscoelastic Oldroyd-B fluid. Yielding of an initially solid drop of Carbopol is simulated under successively increasing shear rates. We proceed to examine the roles of nondimensional parameters on the yielding process; in particular, the Bingham number, the capillary number, the Weissenberg number, and the ratio of solvent and total drop viscosity are varied. We find that all of these parameters, and not only the Bingham number, have a significant influence on the drop dynamics. Numerical simulations predict that the volume of the unyielded region inside the droplet increases with the Bingham number and the Weissenberg number, while it decreases with the capillary number at low Weissenberg and Bingham numbers. A new regime map is obtained for the prediction of the yielded, unyielded, and partly yielded modes as a function of the Bingham and Weissenberg numbers. The drop deformation is studied and explained by examining the stresses in the vicinity of the drop interface. The deformation has a complex dependence on the Bingham andWeissenberg numbers. At low Bingham numbers, the droplet deformation shows a nonmonotonic behavior with an increasing drop viscoelasticity. In contrast, at moderate and high Bingham numbers, droplet deformation always increases with drop viscoelasticity. Moreover, it is found that the deformation increases with the capillary number and with the solvent to total drop viscosity ratio. A simple ordinary differential equation model is developed to explain the various behaviours observed numerically. The presented results are in contrast with the heuristic idea that viscoelasticity in the dispersed phase always inhibits deformation.

The effects of soluble surfactant on the lateral migration of a bubble in a pressure-driven channel flow are examined by interface-resolved numerical simulations. The interfacial and bulk surfactant concentration evolution equations are solved fully coupled with the incompressible Navier-Stokes equations. A non-linear equation of state is used to relate interfacial surface tension to surfactant concentration at the interface. Extensive computations are performed to investigate the bubble dynamics for a wide range of parameters. It is found that surfactant dramatically changes the bubble dynamics. In the clean case, the bubble position depends on its deformability, characterized by the Eotvos (Eo) and the capillary (Ca) numbers. The spherical bubble moves towards the wall, while the deformable one migrates away from it. On the other hand, in the presence of the surfactant, even the spherical bubble moves away from the wall. It is also found that the contaminated bubble stays away from the wall for Eo = 0.1 and Eo = 1.5 while it migrates towards the wall for 0.1 < Eo < 1.5. Also, at high Eo, the onset of path instability is observed for both the clean and the contaminated cases. However, adding surfactant to the system triggers the path instability earlier and amplifies the oscillations afterwards.

Interface-resolved direct numerical simulations are performed to examine the combined effects of soluble surfactant and viscoelasticity on the structure of a bubbly turbulent channel flow. The incompressible flow equations are solved fully coupled with the FENE-P viscoelastic model and the equations governing interfacial and bulk surfactant concentrations. The latter coupling is achieved through a non-linear equation of state which relates the surface tension to the surfactant concentration at the interface. The two-fluid Navier-Stokes equations are solved using a front-tracking method, augmented with a very efficient FFT-based pressure projection method that allows for massively parallel simulations of turbulent flows. It is found that, for the surfactant-free case, bubbles move toward the wall due to inertial lift force, resulting in formation of wall layers and a significant decrease in the flow rate. Conversely, a high-enough concentration of surfactant changes the direction of lateral migration of bubbles, i.e., the contaminated bubbles move toward the core region and spread out across the channel. When viscoelasticity is considered, viscoelastic stresses counteract the Marangoni stresses, promoting formation of bubbly wall-layers and consequently strong decrease in the flow rate. The formation of bubble wall-layers for combined case depends on the interplay of the inertial and elastic, and Marangoni forces. 

A numerical and theoretical study of yield-stress fluid flows in two types of model porous media is presented. We focus on viscoplastic and elastoviscoplastic flows to reveal some differences and similarities between these two classes of flows. Small elastic effects increase the pressure drop and also the size of unyielded regions in the flow which is the consequence of different stress solutions compare to viscoplastic flows. Yet, the velocity fields in the viscoplastic and elastoviscoplastic flows are comparable for small elastic effects. By increasing the yield stress, the difference in the pressure drops between the two classes of flows becomes smaller and smaller for both considered geometries. When the elastic effects increase, the elastoviscoplastic flow becomes time-dependent and some oscillations in the flow can be observed. Focusing on the regime of very large yield stress effects in the viscoplastic flow, we address in detail the interesting limit of 'flow/no flow': yield-stress fluids can resist small imposed pressure gradients and remain quiescent. The critical pressure gradient which should be exceeded to guarantee a continuous flow in the porous media will be reported. Finally, we propose a theoretical framework for studying the 'yield limit' in the porous media.

Despite significant progress, cell viability continues to be a central issue in droplet-based bioprinting applications. Common bioinks exhibit viscoelastic behavior owing to the presence of long-chain molecules in their mixture. We computationally study effects of viscoelasticity of bioinks on cell viability during deposition of cell-loaded droplets on a substrate using a compound droplet model. The inner droplet, which represents the cell, and the encapsulating droplet are modeled as viscoelastic liquids with different material properties, while the ambient fluid is Newtonian. The model proposed by Takamatsu and Rubinsky ["Viability of deformed cells," Cryobiology 39(3), 243-251 (1999)] is used to relate cell deformation to cell viability. We demonstrate that adding viscoelasticity to the encapsulating droplet fluid can significantly enhance the cell viability, suggesting that viscoelastic properties of bioinks can be tailored to achieve high cell viability in droplet-based bioprinting systems. The effects of the cell viscoelasticity are also examined, and it is shown that the Newtonian cell models may significantly overpredict the cell viability. Published under license by AIP Publishing.

We investigate the elastoviscoplastic flow through porous media by numerical simulations. We solve the Navier–Stokes equations combined with the elastoviscoplastic model proposed by Saramito for the stress tensor evolution [1]. In this model, the material behaves as a viscoelastic solid when unyielded, and as a viscoelastic Oldroyd-B fluid for stresses higher than the yield stress. The porous media is made of a symmetric array of cylinders, and we solve the flow in one periodic cell. We find that the solution is time-dependent even at low Reynolds numbers as we observe oscillations in time of the unyielded region especially at high Bingham numbers. The volume of the unyielded region slightly decreases with the Reynolds number and strongly increases with the Bingham number; up to 70% of the total volume is unyielded for the highest Bingham numbers considered here. The flow is mainly shear dominated in the yielded region, while shear and elongational flow are equally distributed in the unyielded region. We compute the relation between the pressure drop and the flow rate in the porous medium and present an empirical closure as function of the Bingham and Reynolds numbers. The apparent permeability, normalized with the case of Newtonian fluids, is shown to be greater than 1 at low Bingham numbers, corresponding to lower pressure drops due to the flow elasticity, and smaller than 1 for high Bingham numbers, indicating larger dissipation in the flow owing to the presence of the yielded regions. Finally we investigate the effect of the Weissenberg number on the distribution of the unyielded regions and on the pressure gradient.

We present numerical simulations of laminar and turbulent channel flow of an elastoviscoplastic fluid. The non-Newtonian flow is simulated by solving the full incompressible Navier-Stokes equations coupled with the evolution equation for the elastoviscoplastic stress tensor. The laminar simulations are carried out for a wide range of Reynolds numbers, Bingham numbers and ratios of the fluid and total viscosity, while the turbulent flow simulations are performed at a fixed bulk Reynolds number equal to 2800 and weak elasticity. We show that in the laminar flow regime the friction factor increases monotonically with the Bingham number (yield stress) and decreases with the viscosity ratio, while in the turbulent regime the friction factor is almost independent of the viscosity ratio and decreases with the Bingham number, until the flow eventually returns to a fully laminar condition for large enough yield stresses. Three main regimes are found in the turbulent case, depending on the Bingham number: for low values, the friction Reynolds number and the turbulent flow statistics only slightly differ from those of a Newtonian fluid; for intermediate values of the Bingham number, the fluctuations increase and the inertial equilibrium range is lost. Finally, for higher values the flow completely laminarizes. These different behaviours are associated with a progressive increases of the volume where the fluid is not yielded, growing from the centreline towards the walls as the Bingham number increases. The unyielded region interacts with the near-wall structures, forming preferentially above the high-speed streaks. In particular, the near-wall streaks and the associated quasi-streamwise vortices are strongly enhanced in an highly elastoviscoplastic fluid and the flow becomes more correlated in the streamwise direction.