SPH modeling and simulation of spherical particles interacting in a viscoelastic matrix

In this work, we extend the three-dimensional Smoothed Particle Hydrodynamics (SPH) non-colloidal particulate model previously developed for Newtonian suspending media in Vázquez-Quesada and Ellero [“Rheology and microstructure of non-colloidal suspensions under shear studied with smoothed particle hydrodynamics,” J. Non-Newtonian Fluid Mech. 233, 37–47 (2016)] to viscoelastic matrices. For the solvent medium, the coarse-grained SPH viscoelastic formulation proposed in Vázquez-Quesada, Ellero, and Español [“Smoothed particle hydrodynamic model for viscoelastic fluids with thermal fluctuations,” Phys. Rev. E 79, 056707 (2009)] is adopted. The property of this particular set of equations is that they are entirely derived within the general equation for non-equilibrium reversible-irreversible coupling formalism and therefore enjoy automatically thermodynamic consistency. The viscoelastic model is derived through a physical specification of a conformation-tensor-dependent entropy function for the fluid particles. In the simple case of suspended Hookean dumbbells, this delivers a specific SPH discretization of the Oldroyd-B constitutive equation. We validate the suspended particle model by studying the dynamics of single and mutually interacting “noncolloidal” rigid spheres under shear flow and in the presence of confinement. Numerical results agree well with available numerical and experimental data. It is straightforward to extend the particulate model to Brownian conditions and to more complex viscoelastic solvents

Planar channel flow of a discontinuous shear-thickening model fluid: Theory and simulation

In this work, an analytical solution for the pressure-driven flow of a discontinuous shear-thickening (DST) fluid in a planar channel is presented. In order to model the fluid rheology, a regularized inverse-biviscous model is adopted. This involves a region of finite thickness to model the sharp jump in viscosity, and it is consistent with momentum conservation. In the limit of vanishing thickness, the truly DST behavior is obtained. Analytical results are validated by numerical simulations under steady and start-up flow using the smoothed particle hydrodynamics method. Flow results are investigated and discussed for different values of the model parameters

Smoothed Particle Hydrodynamics simulations of integral multi-mode and fractional viscoelastic models

To capture specific characteristics of non-Newtonian fluids, during the past years fractional constitutive models have become increasingly popular. These models are able to capture in a simple and compact way the complex behaviour of viscoelastic materials, such as the change in power-law relaxation pattern during the relaxation process of some materials. Using the Lagrangian Smoothed-Particle Hydrodynamics (SPH) method we can easily track particle history; this allows us to solve integral constitutive models in a novel way, without relying on complex tasks. Hence, we develop here a SPH integral viscoelastic method which is first validated for simple Maxwell or Oldroyd-B models under Small Amplitude Oscillatory Shear flows (SAOS). By exploiting the structure of the integral method, a multi-mode Maxwell model is then implemented. Finally, the method is extended to include fractional constitutive models, validating the approach by comparing results with theory under SAOS

Investigating the causes of shear-thinning in non-colloidal suspensions: Experiments and simulations

Experiments and computations were carried out to explore the origins of shear-thinning in non-colloidal suspensions. Two grades of polydimethylsiloxane (silicone oil) and a glycerine/water mixture were used as matrices for the suspensions. The particles were 40μm diameter polystyrene (PS) and polymethyl methacrylate (PMMA) spheres. We concentrated on 40% volume fraction suspensions where shear-thinning was clear. The silicone oil matrices were nearly Newtonian: at 24o C the viscosity of the 1.15Pa-s sample showed a 2% drop in viscosity a shear rate of about 3000s−1, the 13.2 Pa-s sample showed a drop of 2% at a shear rate of approximately 100s−1, and the glycerine/water sample appeared to be Newtonian at least up to 104 s−1. Mild shear-thinning was seen with all suspensions, beginning at shear rates of order 0.1-1 s−1, followed by a rapid reduction of torque in the parallel-plate system at shear rates of 14, 150 and 1000s−1 respectively with the three matrices. These rapid reductions are ascribed to edge effects.Matching smoothed particle hydrodynamics (SPH) simulations were made. The silicone matrix viscosities were modelled by a Carreau-Yasuda (CY) fit up to shear rates of order 107 s−1. The agreement between computations and experiments is generally good for 40% volume fraction suspensions up to the shear rate where edge effects intervene in the experiments- there are no edge effects in the simulations. This confirms the suggestion [1] by Vázquez-Quesada et al [Phys. Rev. Lett,117, 108001 (2017)] that ‘hidden’ high shear rates between particles, where the non-Newtonian matrix viscosity comes into play, can result in shear-thinning at the macroscopic level. For the glycerine/water matrix at low shear rates this mechanism does not apply and a separate mechanism based on variable interparticle friction is suggested; the two mechanisms can co-exist