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We investigate theoretically the buoyancy-driven motion of a viscous drop in a yield-stress material, incorporating elastic effects represented by the Saramito–Herschel–Bulkley constitutive equation. We solve the governing equations using an open-source finite volume solver and utilizing the volume of fluid technique to accurately capture the interface between the two fluids. To validate our numerical approach, we compare our results with data from previous experimental and numerical studies. We find quantitative agreement in terms of terminal velocities and drop shapes, affirming the accuracy of our model and its numerical solution. Notably, we observe that incorporating elastic effects into the modeling of the continuous phase is essential for predicting phenomena reported in experiments, such as the inversion of the flow field behind the sedimenting drop (i.e., the negative wake) or the formation of a teardrop shape. Due to the elastoviscoplastic nature of the continuous phase, we observe that small drops remain entrapped because the buoyancy force is insufficient to fluidize the surrounding material. We investigate entrapment conditions using two different protocols, which yield different outcomes due to the interplay between capillarity and elastoplasticity. Finally, we conduct an extensive parametric analysis to evaluate the impact of rheological parameters (yield stress, elastic modulus, and interfacial tension) on the dynamics of sedimentation. [ABSTRACT FROM AUTHOR]

We propose an enhanced model for the rheological characterization of human blood that accounts for thixotropy, viscoelasticity, and yield-stress. Blood plasma is assumed to act as a Newtonian solvent. We introduce a scalar variable, λ , to macroscopically describe the structure of blood. The temporal evolution of λ is governed by an equation that accounts for aggregation of red blood cells and breakdown of rouleaux structures. We introduce a Gaussian function that qualitatively describes experimental findings on rouleaux restructuring and the expression that was proposed by Stephanou and Georgiou for the breakdown term. The constitutive equation for stresses is based on the elastoviscoplastic formalism by Saramito. However, the max term of the viscoplastic deformation rate has been replaced by a continuous function of λ to account for smooth solid-fluid transition, following the experimental evidence. The continuous yielding description provides improved rheological predictions, especially in small amplitude oscillatory shear. The model predicts finite viscous dissipation at small amplitude oscillation, as we would expect from a gel material-like human blood. Overall, it has nine adjustable parameters that are fitted simultaneously to experimental data by nonlinear regression. The model can accurately predict numerous flow conditions: steady shear, step shear, hysteresis loops, and oscillatory shear. We compare this model (TEVP 9) to our previous formulation for human blood (TEVP 11), and we show that the predictions of the new model are more accurate, despite using fewer parameters. We provide additional predictions for uniaxial elongation, which include finite normal stress difference, extensional hardening at large values of the extensional rate, and extensional thinning at extremely large extensional rates. [ABSTRACT FROM AUTHOR]

We present a systematic analysis of the predictions of two tube-theory based constitutive models: Marrucci and Ianniruberto and Rolie-Poly models. These models are tested in their single-mode form in rheometric flows and in their multimode form in transient, one-dimensional channel flow and steady, two-dimensional, contraction-expansion slit flow. Monodisperse and polydisperse polymers are considered, respectively. As these models predict infinite elongational viscosity, a finite chain extensibility factor is necessary to obtain physically meaningful results in uniaxial extension. A thorough investigation of Warner and Cohen nonlinear spring laws revealed that the latter law may lead to a nonphysical solution multiplicity, where two stable solutions, with a positive definite conformation tensor, arise. All the numerical results are compared with experimental observations and the predictions of Giesekus and Phan-Thien and Tanner models. Characteristic features measured experimentally in the benchmark flows are described well by all models although the tube-theory models perform, in general, more satisfactorily with respect to both the rheological data and the inhomogeneous flow data. [ABSTRACT FROM AUTHOR]

When a charged particle translates through an electrolyte solution, the electric double layer around it deforms in response to the fluid motion and creates an electric force opposite the direction of motion, decreasing the settling velocity. This is a multidisciplinary phenomenon that combines fluid mechanics and electrodynamics, differentiating it from the classical problem of an uncharged sedimenting particle. It has many applications varying from mechanical to biomedical, such as in drug delivery in blood through charged microparticles. Related studies so far have focused on Newtonian fluids, but recent studies have proven that many biofluids, such as human blood plasma, have elastic properties. To this end, we perform a computational study of the steady sedimentation of a spherical, charged particle in human blood plasma due to the centrifugal force. We used the Giesekus model to describe the rheological behavior of human blood plasma. Assuming axial symmetry, the governing equations include the momentum and mass balances, Poisson's equation for the electric field, and the species conservation. The finite size of the ions is considered through the local-density approximation approach of Carnahan-Starling. We perform a detailed parametric analysis, varying parameters such as the ζ potential, the size of the ions, and the centrifugal force exerted upon the particle. We observe that as the ζ potential increases, the settling velocity decreases due to a stronger electric force that slows the particle. We also conduct a parametric analysis of the relaxation time of the material to investigate what happens generally in viscoelastic electrolyte solutions and not only in human blood plasma. We conclude that elasticity plays a crucial role and should not be excluded from the study. Finally, we examine under which conditions the assumption of point-like ions gives different predictions from the Carnahan-Starling approach.

The appearance of surface distortions on polymer melt extrudates, often referred to as sharkskin instability, is a long-standing problem. We report results of a simple physical model, which link the inception of surface defects with intense stretch of polymer chains and subsequent recoil at the region where the melt detaches from the solid wall of the die. The transition from smooth to wavy extrudate is attributed to a Hopf bifurcation, followed by a sequence of period doubling bifurcations, which eventually lead to elastic turbulence under creeping flow. The predicted flow profiles exhibit all the characteristics of the experimentally observed surface defects during polymer melt extrusion.

The present work focuses on the in-silico investigation of the steady-state blood flow in straight microtubes, incorporating advanced constitutive modeling for human blood and blood plasma. The blood constitutive model accounts for the interplay between thixotropy and elasto-visco-plasticity via a scalar variable that describes the level of the local blood structure at any instance. The constitutive model is enhanced by the non-Newtonian modeling of the plasma phase, which features bulk viscoelasticity. Incorporating microcirculation phenomena such as the cell-free layer (CFL) formation or the Fåhraeus and the Fåhraeus-Lindqvist effects is an indispensable part of the blood flow investigation. The coupling between them and the momentum balance is achieved through correlations based on experimental observations. Notably, we propose a new simplified form for the dependence of the apparent viscosity on the hematocrit that predicts the CFL thickness correctly. Our investigation focuses on the impact of the microtube diameter and the pressure-gradient on velocity profiles, normal and shear viscoelastic stresses, and thixotropic properties. We demonstrate the microstructural configuration of blood in steady-state conditions, revealing that blood is highly aggregated in narrow tubes, promoting a flat velocity profile. Additionally, the proper accounting of the CFL thickness shows that for narrow microtubes, the reduction of discharged hematocrit is significant, which in some cases is up to 70%. At high pressure-gradients, the plasmatic proteins in both regions are extended in the flow direction, developing large axial normal stresses, which are more significant in the core region. We also provide normal stress predictions at both the blood/plasma interface (INS) and the tube wall (WNS), which are difficult to measure experimentally. Both decrease with the tube radius; however, they exhibit significant differences in magnitude and type of variation. INS varies linearly from 4.5 to 2 Pa, while WNS exhibits an exponential decrease taking values from 50 mPa to zero.

This work focuses on the advanced modeling of the thixotropic nature of blood, coupled with an elasto-visco-plastic formulation by invoking a consistent and validated model for TEVP materials. The proposed model has been verified for the adequate description of the rheological behavior of suspensions, introducing a scalar variable that describes dynamically the level of internal microstructure of rouleaux at any instance, capturing accurately the aggregation and disaggregation mechanisms of the RBCs. Also, a non-linear fitting is adopted for the definition of the model's parameters on limited available experimental data of steady and transient rheometric flows of blood samples. We present the predictability of the new model in various steady and transient rheometric flows, including startup shear, rectangular shear steps, shear cessation, triangular shear steps and LAOS tests. Our model provides predictions for the elasto-thixotropic mechanism in startup shear flows, demonstrating a non-monotonic relationship of the thixotropic index on the shear-rate. The intermittent shear step test reveals the dynamics of the structural reconstruction, which in turn is associated with the aggregation process. Moreover, our model offers robust predictions for less examined tests such as uniaxial elongation, in which normal stress was found to have considerable contribution. Apart from the integrated modeling of blood rheological complexity, our implementation is adequate for multi-dimensional simulations due to its tensorial formalism accomplished with a single time scale for the thixotropic effects, resulting in a low computational cost compared to other TEVP models., Competing Interests: The authors declare no conflict of interest.