Dynamics of elastoviscoplastic filament stretching.

We study theoretically the stretching dynamics of a yield stress material that exhibits both elastic and viscoplastic behavior. The material is confined between two coaxial disks, forming initially a cylindrical liquid bridge and then a neck when the disks are pulled apart. The material follows the Saramito-Herschel-Bulkley constitutive model and yields according to the von Mises criterion. We find that an elongated thin neck is formed when elasticity prevails, connecting the upper and lower parts of the filamentous bridge. This neck has been observed in breakup experiments of yield stress bridges, but this is the first theoretical study that predicts it. Earlier numerical and theoretical studies of filament stretching of yield stress materials failed to do so, because they excluded elasticity from the constitutive model they used in the simulations. Our results indicate that increasing elasticity leads to shorter pinching times and filament length than the viscoplastic case. This is caused by the fact that larger areas of the filament remain unyielded, while they undergo small deformation even before yielding, and only the remaining smaller yielded areas carry the burden of visible deformation. Our findings suggest that the value of the yield strain, defined as the ratio of the yield stress to the elastic modulus, should be used with caution to determine whether elastic effects will affect the filament stretching procedure or not.

Shear stress and intravascular pressure effects on vascular dynamics: two-phase blood flow in elastic microvessels accounting for the passive stresses.

We study the steady hemodynamics in physiological elastic microvessels proposing an advanced fluid-structure interaction model. The arteriolar tissue is modeled as a two-layer fiber-reinforced hyperelastic material representing its Media and Adventitia layers. The constitutive model employed (Holzapfel et al. in J Elast 61:1-48, 2000) is parametrized via available data on stress-strain experiments for arterioles. The model is completed by simulating the blood/plasma flow in the lumen, using the thixotropic elasto-viscoplastic model in its core, and the linear Phan-Thien and Tanner viscoelastic model in its annular part. The Cell-Free Layer (CFL) and the Fåhraeus and Fåhraeus-Lindqvist effects are considered via analytical expressions based on experimental data (Giannokostas et al. in Materials (Basel) 14:367, 2021b). The coupling between tissue deformation and blood flow is achieved through the experimentally verified pressure-shear hypothesis (Pries et al. Circ Res 77:1017-1023, 1995). Our calculations confirm that the increase in the reference inner radius produces larger expansion. Also, by increasing the intraluminal pressure, the thinning of the walls is more pronounced and it may reach 40% of the initial thickness. Comparing our predictions with those in rigid-wall microtubes, we conclude that apart from the vital importance of vasodilation, there is an up to 25% reduction in wall shear stress. The passive vasodilation contributes to the decrease in the tissue stress fields and affects the hemodynamic features such as the CFL thickness, reducing the plasma layer when blood flows in vessels with elastic walls, in quantitative agreement with previous experiments. Our calculations verify the correctness of the pressure-shear hypothesis but not that of the Laplace law.

How viscoelastic is human blood plasma?

Blood plasma has been considered a Newtonian fluid for decades. Recent experiments (Brust et al., Phys. Rev. Lett., 2013, 110) revealed that blood plasma has a pronounced viscoelastic behavior. This claim was based on purely elastic effects observed in the collapse of a thin plasma filament and the fast flow of plasma inside a contraction-expansion microchannel. However, due to the fact that plasma is a solution with very low viscosity, conventional rotational rheometers are not able to stretch the proteins effectively and thus, provide information about the viscoelastic properties of plasma. Using computational rheology and a molecular-based constitutive model, we predict accurately the rheological response of human blood plasma in strong extensional and constriction complex flows. The complete rheological characterization of plasma yields the first quantitative estimation of its viscoelastic properties in shear and extensional flows. We find that although plasma is characterized by a spectrum of ultra-short relaxation times (on the order of 10-3-10-5 s), its elastic nature dominates in flows that feature high shear and extensional rates, such as blood flow in microvessels. We show that plasma exhibits intense strain hardening when exposed to extensional deformations due to the stretch of the proteins in its bulk. In addition, using simple theoretical considerations we propose fibrinogen as the main candidate that attributes elasticity to plasma. These findings confirm that human blood plasma features bulk viscoelasticity and indicate that this non-Newtonian response should be seriously taken into consideration when examining whole blood flow.

Yielding the yield-stress analysis: a study focused on the effects of elasticity on the settling of a single spherical particle in simple yield-stress fluids.

The sedimentation of a single particle in materials that exhibit simultaneously elastic, viscous and plastic behavior is examined in an effort to explain phenomena that contradict the nature of purely yield-stress materials. Such phenomena include the loss of the fore-and-aft symmetry with respect to an isolated settling particle under creeping flow conditions and the appearance of the "negative wake" behind it. Despite the fact that similar observations have been reported in studies involving viscoelastic fluids, researchers conjectured that thixotropy is responsible for these phenomena, as the aging of yield-stress materials is another common feature. By means of transient calculations, we study the effect of elasticity on both the fluidized and the solid phase. The latter is considered to behave as an ideal Hookean solid. The material properties of the model are determined under the isotropic kinematic hardening framework via Large Amplitude Oscillatory Shear (LAOS) measurements. In this way, we are able to predict accurately the unusual phenomena observed in experiments with simple yield-stress materials, irrespective of the appearance of slip on the particle surface. Viscoelasticity favors the formation of intense shear and extensional stresses downstream of the particle, significantly changing the entrapment mechanism in comparison to that observed in viscoplastic fluids. Therefore, the critical conditions under which the entrapment of the particle occurs deviate from the well-known criterion established theoretically by Beris et al. (1985) and verified experimentally by Tabuteau et al. (2007) for similar materials under conditions that elastic effects are negligible. Our predictions are in quantitative agreement with published experimental results by Holenberg et al. (2012) on the loss of the fore-aft symmetry and the formation of the negative wake in Carbopol with well-characterized rheology. Additionally, we propose simple expressions for the Stokes drag coefficient, as a function of the gravity number, Yg (related to the Bingham number), for different levels of elasticity and for its critical value, under which entrapment of particles occurs. These criteria are in agreement with the results found in the recent work by Ahonguio et al. (2014). Finally, we propose a method to quantify experimentally the elastic effects in viscoplastic particulate systems.

Direct numerical simulation of a 2D-stented aortic heart valve at physiological flow rates.

We study the nonlinear interaction of an aortic heart valve, composed of hyperelastic corrugated leaflets of finite density attached to a stented vessel under physiological flow conditions. In our numerical simulations, we use a 2D idealised representation of this arrangement. Blood flow is caused by a time-varying pressure gradient that mimics that of the aortic valve and corresponds to a peak Reynolds number equal to 4050. Here, we fully account for the shear-thinning behaviour of the blood and large deformations and contact between the leaflets by solving the momentum and mass balances for blood and leaflets. The mixed finite element/Galerkin method along with linear discontinuous Lagrange multipliers for coupling the fluid and elastic domains is adopted. Moreover, a series of challenging numerical issues such as the finite length of the computational domain and the conditions that should be imposed on its inflow/outflow boundaries, the accurate time integration of the parabolic and hyperbolic momentum equations, the contact between the leaflets and the non-conforming mesh refinement in part of the domain are successfully resolved. Calculations for the velocity and the shear stress fields of the blood reveal that boundary layers appear on both sides of a leaflet. The one along the ventricular side transfers blood with high momentum from the core region of the vessel to the annulus or the sinusoidal expansion, causing the continuous development of flow instabilities. At peak systole, vortices are convected in the flow direction along the annulus of the vessel, whereas during the closure stage of the valve, an extremely large vortex develops in each half of the flow domain.