Dynamics and Rheology of Non-colloidal Suspensions: Active and Soft Deformable Particles

Abstract

Classical works on the suspensions of rigid spherical and ellipsoidal particles have been carried out by Einstein and Jeffery. However, in nature and industry, we come across materials that are either deformable or active. A significant amount of work has been done on the suspensions of deformable particles, such as drops, vesicles, capsules, and biological cells, in the past few decades. Less attention is paid to the elastic particles suspended in a Newtonian fluid. Though the suspending medium is Newtonian, due to the deformability or activity of the suspended particles, these suspensions behave as non-Newtonian even in the dilute limit. Interactions are challenging to incorporate; however, significant progress can be made in the dense regime where the particle pairs interact through a thin film of intervening fluid.

The entire work towards the thesis is divided into three parts. In the first part, the work done is devoted to obtaining the dynamics of initial ellipsoidal, elastic/viscoelastic particles under externally imposed simple shear and axisymmetric extensional flows. The orientation dynamics of rigid ellipsoidal particles have been studied analytically by Jeffery and these particles are reported to exhibit tumbling. We extend this analysis to obtain orientation and extension dynamics of elastic particles. An elastic particle exhibits three different types of dynamics, known as steady-state tank-treading, tumbling, and trembling. A phase diagram is constructed to identify the different regimes of dynamics in the dimensionless stiffness and initial aspect ratio (G, ω0) parameter space. The dynamics of the particles studied initially when the particles are aligned in the plane of the shear is extended further to obtain the more complex out-of-plane dynamics.

In the second part, we obtained the dynamics of a pair of elastic particles interacting with each other in the lubrication regime under axisymmetric compression and simple shear flows. The lubrication pressure in the fluid film between the particles, the deformation features, and the film thickness profiles are captured through numerical simulations. These simulations are validated using the scaling relations obtained from a simple fluid lubricated extension to the Hertzian contact model. We also obtained the particle pair trajectories of the elastic particles compared to a pair of rigid spherical particles and studied the role played by the deformation in the observed deviations.

In the third part, the orientation dynamics of the dilute suspension of slender bacterial swimmers under externally imposed flow are studied to obtain both the linear and non-linear rheological response. The orientation distribution of the swimmers is a function of the competing mechanisms that decorrelate the orientations, such as tumbling and rotary diffusion and the imposed flow which aligns them. A dimensionless number that quantifies these competing factors is a Peclet number (Pe). We obtained through perturbative analysis, the swimmer distribution, the rheological response up to O(Pe3) and validated them through numerical simulations.