| dc.description.abstract | This work focuses on two problems in complex fluids, namely collective dynamics of suspensions of self-propelled particles and the rheology of dry granular materials. In both systems, interaction between the particles is of utmost importance in determining their dynamics and rheology.
Self-propelled particles such as micro-organisms propel themselves by using waving, undulating, or rotating motion of their flagella or cilia. Swimming speeds range up to 250 ?m/s and their size lies in the range of 1 to 200 ?m. The Reynolds number based on swimming speed and diameter of the swimmers is usually very small. We propose a model for self-propulsion and incorporate the full hydrodynamic interactions between the particles. We extend the Stokesian Dynamics technique (Brady et al., 1988; Brady and Bossis, 1988; Durlofsky et al., 1987) to incorporate self-propulsion and carry out dynamic simulations for a range of particle concentrations. Irrespective of the propulsion mechanism, our model captures the salient features of the active suspensions. Our model treats each active particle as a sphere with a dipole S? which acts slightly away from the center. The velocity is then determined by the orientation vector p, and the magnitude of the dipole S?. The problem is further simplified by placing the force dipole at the particle center and introducing a self-propulsive force F? in the direction of p. We track the motion of every particle as a function of time and extract the relevant statistical and microstructural properties. We find interesting and unexpected aspects of the collective dynamics reflected in the distribution of particle velocity and the position and orientation correlations (Mehandia and Nott, 2008).
The other two problems we study relate to the slow flow of dense granular materials. In this regime of flow, the particles are in enduring contact which occurs during sliding and rolling of particles relative to each other.
The first problem on slow granular flows is the application of the Cosserat plasticity model of Mohan et al. (1999) to two-dimensional flows. The Cosserat plasticity theory was developed to overcome a deficiency of the classical plasticity theories, namely the lack of a material length scale in the constitutive relations (Muhlhaus, 1986, 1989; Tejchman and Gudehus, 1993; Tejchman and Wu, 1993). A simple Cosserat plasticity model was successfully used by Mohan et al. (1999) to study the fully developed flow through a vertical channel. Our aim in the present work is to use their model for two-dimensional flows, such as flow past an obstacle and the flow through hoppers. A finite difference method with a nonlinear solver is used to numerically solve the governing equations for the flow through a vertical channel and a hopper.
The second problem is experimental measurement of the stress in a granular material sheared in a cylindrical Couette cell. The stress profiles in static and sheared granular beds are measured using a multi-axis force transducer. A modified Couette device, with an arrangement to place the transducer at any vertical position on the outer cylinder, is used to study the variation of stress with respect to depth in a sheared granular material. We have used glass beads and mustard seeds as model granular materials. Our results show a dramatic change in the stress profiles when the material is sheared at constant rate. The behavior differs qualitatively from that of a static granular bed, a sheared Newtonian fluid, and the predictions of all available theories for slow granular flows. This experimental study reveals some fundamental aspects of the rheology of granular materials which have thus far not been explored. | |
