2 results
Generalized Lagrangian heterogeneous multiscale modelling of complex fluids
- Nicolas Moreno, Marco Ellero
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- Journal:
- Journal of Fluid Mechanics / Volume 969 / 25 August 2023
- Published online by Cambridge University Press:
- 10 August 2023, A2
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We introduce a fully Lagrangian heterogeneous multiscale method (LHMM) to model complex fluids with microscopic features that can extend over large spatio/temporal scales, such as polymeric solutions and multiphasic systems. The proposed approach discretizes the fluctuating Navier–Stokes equations in a particle-based setting using smoothed dissipative particle dynamics (SDPD). This multiscale method uses microscopic information derived on-the-fly to provide the stress tensor of the momentum balance in a macroscale problem, therefore bypassing the need for approximate constitutive relations for the stress. We exploit the intrinsic multiscale features of SDPD to account for thermal fluctuations as the characteristic size of the discretizing particles decreases. We validate the LHMM using different flow configurations (reverse Poiseuille flow, flow passing a cylinder array and flow around a square cavity) and fluid (Newtonian and non-Newtonian). We show the framework's flexibility to model complex fluids at the microscale using multiphase and polymeric systems. We also show that stresses are adequately captured and passed from micro to macro scales, leading to richer fluid response at the continuum. In general, the proposed methodology provides a natural link between variations at a macroscale, whereas accounting for memory effects of microscales.
Shear thickening of a non-colloidal suspension with a viscoelastic matrix
- Adolfo Vázquez-Quesada, Pep Español, Roger I. Tanner, Marco Ellero
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- Journal:
- Journal of Fluid Mechanics / Volume 880 / 10 December 2019
- Published online by Cambridge University Press:
- 18 October 2019, pp. 1070-1094
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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 $\unicode[STIX]{x1D719}=0.3$) is explored. It is found that at small Deborah numbers $De$ (based on the macroscopic imposed shear rate), relative suspension viscosities $\unicode[STIX]{x1D702}_{r}$ exhibit a plateau at every concentration investigated. By increasing $De$, shear thickening is observed, which is related to the extensional thickening of the underlying viscoelastic matrix. Under dilute conditions ($\unicode[STIX]{x1D719}=0.05$), numerical results for $\unicode[STIX]{x1D702}_{r}$ agree quantitatively with experimental data in both the $De$ and $\unicode[STIX]{x1D719}$ dependences. 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 $\unicode[STIX]{x1D719}=0.3$, despite the fact that the trend is well captured, the agreement remains qualitative with discrepancies arising in the absolute values of $\unicode[STIX]{x1D702}_{r}$ 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 average viscoelastic dissipation function $\unicode[STIX]{x1D703}^{elast}$, requiring a scaling as $\langle \unicode[STIX]{x1D703}^{elast}\rangle \sim De^{\unicode[STIX]{x1D6FC}}$ with $\unicode[STIX]{x1D6FC}\geqslant 2$ 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 for the elastic thickening are well correlated to areas with significant extensional component.