Description
- Abstract:
- The force-coupling method (FCM) represents the dynamics of low Reynolds number suspension flows through a low-order, regularized multipole expansion and provides an effcient,matrix-free method to solve the grand mobility problem. In concentrated suspensions,strong short-range lubrication forces lead to ill-conditioned problems for determining hydrodynamic interactions. We present a new robust and effcient numerical scheme, lubrication-corrected FCM (LC-FCM), to solve for the hydrodynamic interactions in suspensions of a large number of hard spheres for any volume fractions under a geometric confinement. In LC-FCM, both the lubrication and far-field interactions are solved as a fully coupled system with only very small additional computation to the standard FCM. A solution procedure to expand LC-FCM for the simulation of finite-Reynolds-number suspension flows is proposed.With the goal of determining the wall effects on rheology and particle dynamics, LC-FCM simulations of suspensions of non-colloidal particles in a Couette flow at zero Reynolds number are performed. It is shown that the suspension field can be divided into three regions depending on the micro-structures; the wall region where a structured particle-layering is dominant, the core region in which the suspension field is quasi-homogeneous, and the buffer region which shows the characteristics of both the particle-layer and the shear structure. Rheological properties and suspension microstructures in each regions are presented. Due to the strong spatial coherency induced by the near-wall density fluctuations, the suspended particles exhibit anomalous diffusion. The diffusion in the wall-normal direction changes from superdiffusion for the particles next to the wall to subdiffusion for the particles near the core of the channel. The intermittent jumps and particle entrapment in near-wall particle layers are responsible for the anomalous diffusion near the wall, while the subdiffusion in the core is related to the overall confinement by the channel walls. At the volume fraction around phi = 0:48, particles near the wall assemble into strings which are organized as a simple hexagonal array. This crystal structure extends into the core of the channel as the volume fraction increases. Now, the relative viscosity becomes a function of both the volume fraction and the ordered state. It is found that the hexagonal structure can be altered by introducing an external torque applied to the suspended particles. The crystal structure is disturbed by negative torques, while positive torque has a favorable effect on the ordered state. Due to the significant changes in suspension micro-structures, rheological parameters such as the shear and vortex viscosities exhibit non-linear responses to the external torques.The dynamics of concentrated suspensions in Poiseuille flows are investigated. A statistical analysis indicates that there is an intermediate region between particle layers near the wall and a plug region in the core, in which the behavior of ensemble averaged suspension field can be approximated by a continuum theory. The particle normal stresses in the intermediate region are almost uniform, consistent with the concept of a normal-stress driven particle migration. There is a remarkable similarity between the particle-phase pressure profiles scaled by the local shear rate for different bulk volume fractions. The effective viscosity, defined by the ratio of the total shear stress to the fluid-phase shear stress, shows a good agreement with empirical viscosity relations in Couette-flow suspensions.LC-FCM for Navier-Stokes flows is employed to investigate the dynamics of concentrated suspensions in a homogeneous linear shear flow at small but finite particle Reynolds numbers. It is shown that the velocity fluctuation decreases at larger Re. However, the diffusivity is found to be an increasing function of Reynolds number as the motion of the suspended particles has a longer correlation under finite fluid inertia. The changes in rheological parameters and the pair-distribution functions with Reynolds number are presented and then discussed. It is found that the particle stresses become highly intermittent as Re increases.Finally, the dynamics of homogeneous, isotropic turbulence seeded with finite-sized particles or bubbles is investigated. Results are given on the modulation of the turbulence due to massless bubbles, neutrally buoyant particles and inertial particles. We analyze both the Eulerian statistics of the mixture and the Lagrangian statistics of the dispersed phase. The turbulent fluctuations are damped at mid-range wavenumbers by the bubbles or particles while the small-scale kinetic energy is significantly enhanced. Unexpectedly, the modulation of turbulence depends only slightly on the dispersion characteristics but is closely related to the stresslet component of the flow disturbances. The spectrum for the energy transfer by the particle phase is examined and the possibility of representing this, at large scales, through an additional effective viscosity is discussed.
- Notes:
- Thesis (Ph.D. -- Brown University (2011)
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Citation
Yeo, Kyong Min,
"Some aspects of suspension flows: Stokes to turbulent flows"
(2011).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0SJ1HVH
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Applied Mathematics Theses and Dissertations
Theses and Dissertations for the Applied Mathematics department....