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.

We study the role of the capillary number, Ca and of the surface wettability on the dynamics of the interface between an invading and a defending phase in a porous medium by means of numerical simulations. We employ a hybrid phase field-immersed boundary approach to successfully model the contact line dynamics over the solid objects. Using a phase-field method which naturally incorporates dynamic wetting we eliminate the need for empirical contact line models to address contact line singularity. We map the two dominant modes governing the motion of the interface, namely, capillary fingering, and stable penetration, in the (Ca - theta) plane, with theta the static contact angle prescribed at the solid pores. Capillary fingering dominates at lower values of Ca and pores hydrophobic to the invading phase, while a stable penetration is observed on hydrophillic surfaces. We present new measurements and analyses, including curvature probability density functions and average curvature. We also show that the pressure needed for the invading phase to advance at constant flow rate decreases with the capillary number, and increases with the contact angle at the capillary numbers considered. The latter is due to a significant increase in the length of the interface in the case of capillary fingering. Finally, we show that it is possible to identify the different interfacial modes by measuring the penetration length and velocity during the medium filling.

We present a fully Eulerian hybrid immersed-boundary/phase-field model to simulate wetting and contact line motion over any arbitrary geometry. The solid wall is described with a volume-penalisation ghost-cell immersed boundary whereas the interface between the two fluids by a diffuse-interface method. The contact line motion on the complex wall is prescribed via slip velocity in the momentum equation and static/dynamic contact angle condition for the order parameter of the Cahn-Hilliard model. This combination requires accurate computations of the normal and tangential gradients of the scalar order parameter and of the components of the velocity. However, the present algorithm requires the computation of averaging weights and other geometrical variables as a preprocessing step. Several validation tests are reported in the manuscript, together with 2D simulations of a droplet spreading over a sinusoidal wall with different contact angles and slip length and a spherical droplet spreading over a sphere, showing that the proposed algorithm is capable to deal with the three-phase contact line motion over any complex wall. The Eulerian feature of the algorithm facilitates the implementation and provides a straight-forward and potentially highly scalable parallelisation. The employed parallelisation of the underlying Navier-Stokes solver can be efficiently used for the multiphase part as well. The procedure proposed here can be directly employed to impose any types of boundary conditions (Neumann, Dirichlet and mixed) for any field variable evolving over a complex geometry, modelled with an immersed-boundary approach (for instance, modelling deformable biological membranes, red blood cells, solidification, evaporation and boiling, to name a few). 

We propose and validate a novel experimental technique to measure two-point statistics of turbulent flows. It consists of spreading rigid fibers in the flow and tracking their position and orientation in time and is therefore named “fiber tracking velocimetry.” By choosing different fiber lengths, i.e., within the inertial or dissipative range of scales, the statistics of turbulence fluctuations at the selected length scale can be probed accurately by simply measuring the fiber velocity at its two ends and projecting it along the transverse-to-fiber direction. By means of fully resolved direct numerical simulations and experiments, we show that these fiber-based transverse velocity increments are statistically equivalent to the (unperturbed) flow transverse velocity increments. Moreover, we show that the turbulent energy-dissipation rate can be accurately measured exploiting sufficiently short fibers. The technique is tested against standard particle tracking velocimetry (PTV) of flow tracers with excellent agreement. Our technique overcomes the well-known problem of PTV to probe two-point statistics reliably because of the fast relative diffusion in turbulence that prevents the mutual distance between particles to remain constant at the length scale of interest. This problem, making it difficult to obtain converged statistics for a fixed separation distance, is even more dramatic for natural flows in open domains. A prominent example is oceanic currents, where drifters (i.e., the tracer-particle counterpart used in field measurements) disperse quickly, but at the same time their number has to be limited to save costs. Inspired by our laboratory experiments, we propose pairs of connected drifters as a viable option to solve the issue.

We study the effect of isotropic porous walls on a plane Couette flow laden with spherical and rigid particles. We perform a parametric study varying the volume fraction between 0 and 30%, the porosity between 0.3 and 0.9 and the non-dimensional permeability between 0 and 7.9×10-3 We find that the porous walls induce a progressive decrease in the suspension effective viscosity as the wall permeability increases. This behavior is explained by the weakening of the wall-blocking effect and by the appearance of a slip velocity at the interface of the porous medium, which reduces the shear rate in the channel. Therefore, particle rotation and the consequent velocity fluctuations in the two phases are dampened, leading to reduced particle interactions and particle stresses. Based on our numerical evidence, we provide a closed set of equations for the suspension viscosity, which can be used to estimate the suspension rheology in the presence of porous walls.

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.

This article identifies the main coherent structures driving the flow dynamics in the turbulent channel flow over anisotropic porous walls. Two different cases have been analyzed where the drag increases or decreases with respect to a channel with isotropic porous walls. Higher order dynamic mode decomposition (HODMD) is applied to analyze these data, identifying 20 and 15 high amplitude modes in the drag increasing (DI) and drag reducing (DR) cases, respectively, which well reflects the largest flow complexity in the former case. The frequency of 13 modes and the three-dimensional structure of the modes are similar in the DR and DI cases, suggesting the need of using more complex analyses to deepen our physical insight of these flows. The spatio-temporal HODMD analysis identifies a periodic solution along the spanwise direction (as imposed by the boundary conditions). The wavenumbers related to the modes with highest amplitude are β = 0 and β = 3 (Lz = 2 3 π ). The rollers, groups of spanwise correlated structures, are mostly identified in the DI case near the wall, with β = 0, while the presence of the streaks, streamwise correlated structures are mostly identified in the DR case. Although, in areas far away from the wall it is possible to identify these two types of structures with β = 3 in both cases, depending on the temporal frequency of the DMD modes, the rollers and the streaks are related to high and low frequency DMD modes, respectively. Finally, a model is constructed to predict the temporal evolution of the wall shear, using the 6 most relevant DMD modes interacting near the channel wall: 6 low frequency modes for DR and 3 low and 3 high frequency modes for DI. In the DR case the wall shear is predicted for almost 300 time units with relative error ∼ 2%, however, this error is larger in the DI case, ∼ 6%, suggesting the need of using a larger number of modes to represent this more complex flow.

The flapping states of a flexible fiber fully coupled to a three-dimensional turbulent flow are investigated via state-of-the-art numerical methods. Two distinct flapping regimes are predicted by the phenomenological theory recently proposed by Rosti et al. (Phys. Rev. Lett. 121:044501, 2018) the under-damped regime, where the elasticity strongly affects the fiber dynamics, and the over-damped regime, where the elastic effects are strongly inhibited. In both cases we can identify a critical value of the bending rigidity of the fiber by a resonance condition, which further provides a distinction between different flapping behaviors, especially in the under-damped case. We validate the theory by means of direct numerical simulations and find that, both for the over-damped regime and for the under-damped one, fibers are effectively slaved to the turbulent fluctuations and can therefore be used as a proxy to measure various two-point statistics of turbulence. Finally, we show that this holds true also in the case of a passive fiber, without any feedback force on the fluid.

We study the effect of spherical particles on the turbulent flow of a viscoelastic fluid and find that the drag reducing effect of polymer additives is completely lost for semidense suspensions, with the drag increasing more than for suspensions in Newtonian fluids. This different behavior is due to three separate effects. First, polymer stretching is reduced by the presence of rigid particles, thus canceling the drag reducing benefit of the viscoelastic fluid. Second, drag increase is provided by the growth of the particle and polymeric shear stresses with the particles, due to larger shear rates in the vicinity of the particle surface. Third, particles migrate towards the wall due to the shear-thinning property of the fluid, thus enhancing the particle near-wall layer and further increasing the drag.

We perform three-dimensional numerical simulations to investigate the sedimentation of a single sphere in the absence and presence of a simple cross-shear flow in a yield stress fluid with weak inertia. In our simulations, the settling flow is considered to be the primary flow, whereas the linear cross-shear flow is a secondary flow with amplitude 10 % of the primary flow. To study the effects of elasticity and plasticity of the carrying fluid on the sphere drag as well as the flow dynamics, the fluid is modelled using the elastoviscoplastic constitutive laws proposed by Saramito (J. Non-Newtonian Fluid Mech., vol. 158 (1-3), 2009, pp. 154-161). The extra non-Newtonian stress tensor is fully coupled with the flow equation and the solid particle is represented by an immersed boundary method. Our results show that the fore-aft asymmetry in the velocity is less pronounced and the negative wake disappears when a linear cross-shear flow is applied. We find that the drag on a sphere settling in a sheared yield stress fluid is reduced significantly compared to an otherwise quiescent fluid. More importantly, the sphere drag in the presence of a secondary cross-shear flow cannot be derived from the pure sedimentation drag law owing to the nonlinear coupling between the simple shear flow and the uniform flow. Finally, we show that the drag on the sphere settling in a sheared yield stress fluid is reduced at higher material elasticity mainly due to the form and viscous drag reduction.