Normal lubrication force between spherical particles immersed in a shear-thickening fluid

In this work, the inverse bi-viscous model [Physics of Fluids 29, 103104 (2017)] is used to describe a shear-thickening fluid. An analytical velocity profile in a planar Poiseuille flow is utilized to calculate an approximate solution to the generalized lubrication force between two close spheres interacting hydrodynamically in such a medium. This approximate analytical expression is compared to the exact numerical solution.The flow topology of the shear-thickening transition within the interparticle gap is also shown and discussed in relation to the behaviour of the lubrication force. The present result can allow in the future to perform numerical simulations of dense particle suspensions immersed in a shear-thickening matrix based on an effective lubrication force acting between pairwise interacting particles. This model may find additional value in representing experimental systems consisting of suspensions in shear thickening media, polymer coated suspensions, and industrial systems such as concrete

A conservative lubrication dynamics method for the simulation of dense non-colloidal suspensions with particle spin

In this paper, a novel Fast Lubrication Dynamics method that can efficiently simulate dense non-colloidal suspensions is proposed. To reduce the computational cost in the presented methodology, interparticle lubrication-based forces and torques alone are considered together with a short-range repulsion to enforce finite inter-particle separation due to surface roughness, Brownian forces or other excluded volume effects. Given that the lubrication forces are singular, i.e. scaling inversely with the inter-particle gap, the strategy to expedite the calculations is severely compromised if explicit integration schemes are used, especially at high concentrations. To overcome this issue, an efficient semi-implicit splitting integration scheme to solve for the particles translational and rotational velocities is presented. To validate the proposed methodology, a suspension under simple shear test is simulated in three dimensions and its rheology is compared against benchmark results. To demonstrate the stability/speed-up in the calculations, performance of the proposed semi-implicit scheme is compared against a classical explicit Velocity-Verlet scheme. The predicted viscometric functions for a non-colloidal suspension with a Newtonian matrix are in excellent agreement with the reference data from the literature. Moreover, the presented semi-implicit algorithm is found to be significantly faster than the classical lubrication dynamics methods with Velocity-Verlet integration schemes

Numerical investigation of the rheological behavior of a dense particle suspension in a biviscous matrix using a lubrication dynamics method

This paper presents a numerical approach to predict the rheology of dense non-colloidal suspensions with a biviscous matrix. A biviscous matrix is characterized as a fluid with two shear rate dependent viscosities i.e. one above and below a critical shear rate $\dot{\gamma}_c$ . The methodology is based on the lubrication dynamics which dominantly influence the suspension properties at high values of particle concentration. To efficiently handle the singular lubrication forces in the dense suspensions, a semi-implicit splitting integration scheme is employed. Using the presented approach, three dimensional simulations were performed and the predicted rheology of the suspension with a biviscous matrix is discussed under two regimes: (a) $\dot{\gamma}_c$ larger than the macroscopic applied shear rate where fluid slippage effect can be modeled in terms of the non-Newtonian properties of the matrix, and (2) $\dot{\gamma}_c$ smaller than the macroscopic applied shear rate where a biviscous model can be seen as a regularization of an apparent yield stress matrix. The results obtained at high $\dot{\gamma}_c$ show that the shear thinning of the biviscous matrix in the inter-particle gaps, which can be interpreted as an apparent fluid slipping on the particle surface, provides an alternative mechanism to explain the experimentally observed shear-thinning of non-colloidal suspension with Newtonian matrices. At low γ̇c values, the predicted suspension properties and its microstructure corroborates the available experimental results on suspensions with yield stress fluids

Apparent slip mechanism between two spheres based on solvent rheology: Theory and implication for the shear thinning of non-Brownian suspensions

Analytical results for the apparent slip between two spheres in a simple biviscous model of a shear thinning fluid are presented. Velocity profiles and apparent slip lengths along the surfaces are analyzed in order to characterize the physical mechanism. It is shown that in this non-Newtonian model, the effect of shear-thinning limited to high-shear rates in the interstitial regions between close spheres can be alternatively interpreted as the onset of an apparent shear-rate dependent slippage effect. The results of the theory compare well with experiments from the literature showing the presence of surface slip on a particle approaching a planar wall. In terms of implications on suspensions rheology, the present results bridge the ’hidden’ solvent shear-thinning theory [A. Va ́zquez-Quesada et al. , Phys. Rev. Lett., 117, 108001-5 (2016)] with slip-based models presented recently in [M. Kroupa et al., Phys. Chem. Chem. Phys. 19, 5979-5984 (2017)] as a possible explanation on the mechanism behind the shear-thinning in hard-sphere non-Brownian suspensions

Shear-thickening of a non-colloidal suspension with a viscoelastic matrix

In this work we study the rheology of a non-colloidal suspension of rigid spherical particles interacting with a viscoelastic matrix. Three-dimensional numerical simulations under shear flow are performed using the smoothed particle hydrodynamics method and compared with experimental data available in the literature using different constant- viscosity elastic Boger fluids. The rheological properties of the Boger matrices are matched in simulation under viscometric flow conditions. Suspension rheology under dilute to semi-concentrated conditions (i.e. up to solid volume fraction φ = 0.3) is explored. It is found that at small Deborah numbers (based on the macroscopic imposed shear rate), relative suspension viscosities ηr exhibit a plateau at every concentration investigated. By increasing the Deborah number De shear-thickening is observed which is related to the extensional-thickening of the underlying viscoelastic matrix. Under dilute conditions (φ = 0.05) numerical results for ηr agree quantitatively with experimental data both in the De- and φ-dependencies. Even under dilute conditions, simulations of full many-particle systems with no ’a priori’ specification of their spatial distribution need to be considered to recover precisely experimental values. By increasing the solid volume fraction towards φ = 0.3, despite the fact that the trend is well captured, the agreement remains qualitative with discrepancies arising in the absolute values of ηr obtained from simulations and experiments but also with large deviations existing among different experiments. With regard to the specific mechanism of elastic thickening, the microstructural analysis shows that elastic thickening correlates well with the averaged viscoelastic dissipation function θ_elast, requiring a scaling as θ_elasti ∼De^α with α > 2 to take place. Locally, despite the fact that regions of large polymer stretching (and viscoelastic dissipation) can occur everywhere in the domain, flow regions uniquely responsible of the elastic thickening are well correlated to areas with significant extensional component

Dynamics and rheology of a suspension of super-paramagnetic chains under the combined effect of a shear flow and a rotating magnetic field

This study presents an analysis of the dynamics of a single and multiple chains of spherical super-paramagnetic beads suspended in a Newtonian fluid under the combined effect of an external rotating magnetic field and a shear flow. Viscosity results depend on two main non-dimensional numbers: the ratio between the shear rate and the magnetic rotation frequency and the ratio between the hydrodynamic and magnetostatic interactions (the Mason number). When the shear rate is smaller than the magnetic frequency, the chain rotation accelerates the surrounding fluid, reducing the value of the measured suspension viscosity even below the solvent one. In this regime, shear-thickening is observed. For values of the shear rates comparable to the rotation magnetic frequency, the viscosity reaches a maximum and non-linear coupling effects come up. If the shear rate is increased to values above the rotation frequency, the viscosity decreases and a mild shear-thinning is observed. In terms of the Mason number, the suspension viscosity reduces in line with literature results reported for fixed magnetic fields, whereas the shear-rate/magnetic-frequency ratio parameters induces a shift of the viscosity curve towards larger values. Results at larger concentrations and multiple chains amplify the observed effects

Tribological variable-friction coefficient models for the simulation of dense suspensions of rough polydisperse particles

The rheology of concentrated suspensions of particles is complex and typically exhibits a shear-thickening behavior in the case of repulsive interactions. Despite the recent interest arisen, the causes of the shear-thickening remain unclear. Frictional contacts have been able to explain the discontinuous shear thickening in simulations. However, the interparticle friction coefficient is considered to be constant in most simulations and theoretical works reported to date despite the fact that tribological experiments demonstrate that the friction coefficient can not only be constant (boundary regime) but also decrease (mixed regime) or even increase (full-film lubrication regime), depending on the normal force and the relative velocity between the particles and the interstitial liquid between them. Interestingly, the transition between the boundary regime and the full-lubrication regime is governed by the particle average roughness. Particle-level simulations of suspensions of hard spheres were carried out using short-range lubrication and roughness-dependent frictional forces describing the full Stribeck curve. Suspensions with different particle's roughness were simulated to show that the particle roughness is a key factor in the shear-thickening behavior; for sufficiently rough particles, the suspension exhibits a remarkable shear-thickening, while for sufficiently smooth particles, the discontinuous shear-thickening disappears

SPH simulations of thixo-viscoplastic fluid flow past a cylinder

Thixotropic materials are complex fluids that display time-dependent viscosity and/or yield-stress response upon the application of a fixed deformation, while recovering their original structured-state when the deformation is discontinued. Thixotropic effects are presents in many different systems and applications, ranging from food products, such as ketchup, to metals, such as molten aluminum. In this work we present a first attempt to simulate the rheological properties of thixo-viscoplastic flows using a Smoothed Particle Hydrodynamic (SPH) method. The study set up is a 2D flow around a circular cylinder as well as a simple shear flow between parallel plates to validate our numerical results. SPH solutions are compared with simulations performed using the open-source Finite Volume Method solver RheoTool, based on OpenFOAM. The viscoplastic model used in this work is the Papanastasiou model combined with a recently developed microstructural one, in order to include thixotropy. In this thixo-viscoplastic framework, we analyze the flow properties in terms of yield-fronts, streamlines and structure-parameter fields at different Bingham and Thixotropy numbers, through microstructural thixotropic and yield-stress parameters variation. Obtained results show an important novelty: an asymmetry in the thixo-viscoplastic flow around the cylinder

Multifunctional P-Doped TiO2 Films: A New Approach to Self-Cleaning, Transparent Conducting Oxide Materials

Multifunctional P-doped TiO2 thin films were synthesized by atmospheric pressure chemical vapor deposition (APCVD). This is the first example of P-doped TiO2 films with both P5+ and P3– states, with the relative proportion being determined by synthesis conditions. This technique to control the oxidation state of the impurities presents a new approach to achieve films with both self-cleaning and TCO properties. The origin of electrical conductivity in these materials was correlated to the incorporation of P5+ species, as suggested by Hall Effect probe measurements. The photocatalytic performance of the films was investigated using the model organic pollutant, stearic acid, with films containing predominately P3– states found to be vastly inferior photocatalysts compared to undoped TiO2 films. Transient absorption spectroscopy studies also showed that charge carrier concentrations increased by several orders of magnitude in films containing P5+ species only, whereas photogenerated carrier lifetimes—and thus photocatalytic activity—were severely reduced upon incorporation of P3– species. The results presented here provide important insights on the influence of dopant nature and location within a semiconductor structure. These new P-doped TiO2 films are a breakthrough in the development of multifunctional advanced materials with tuned properties for a wide range of applications

Charge Transport Phenomena in Heterojunction Photocatalysts: The WO₃/TiO₂ System as an Archetypical Model

Recent studies have demonstrated the high efficiency through which nanostructured core–shell WO3/TiO2 (WT) heterojunctions can photocatalytically degrade model organic pollutants (stearic acid, QE ≈ 18% @ λ = 365 nm), and as such, has varied potential environmental and antimicrobial applications. The key motivation herein is to connect theoretical calculations of charge transport phenomena, with experimental measures of charge carrier behavior using transient absorption spectroscopy (TAS), to develop a fundamental understanding of how such WT heterojunctions achieve high photocatalytic efficiency (in comparison to standalone WO3 and TiO2 photocatalysts). This work reveals an order of magnitude enhancement in electron and hole recombination lifetimes, respectively located in the TiO2 and WO3 sides, when an optimally designed WT heterojunction photocatalyst operates under UV excitation. This observation is further supported by our computationally captured details of conduction band and valence band processes, identified as (i) dominant electron transfer from WO3 to TiO2 via the diffusion of excess electrons; and (ii) dominant hole transfer from TiO2 to WO3 via thermionic emission over the valence band edge. Simultaneously, our combined theoretical and experimental study offers a time-resolved understanding of what occurs on the micro- to milliseconds (μs–ms) time scale in this archetypical photocatalytic heterojunction. At the microsecond time scale, a portion of the accumulated holes in WO3 contribute to the depopulation of W5+ polaronic states, whereas the remaining accumulated holes in WO3 are separated from adjacent electrons in TiO2 up to 3 ms after photoexcitation. The presence of these exceptionally long-lived photogenerated carriers, dynamically separated by the WT heterojunction, is the origin of the superior photocatalytic efficiency displayed by this system (in the degradation of stearic acid). Consequently, our combined computational and experimental approach delivers a robust understanding of the direction of charge separation along with critical time-resolved insights into the evolution of charge transport phenomena in this model heterojunction photocatalyst