Diffusion and rheology in crowded, 3D-confined suspensions: A model for intracellular transport

Roseanna Zia

Deparment of Chemical & Biomolecular Engineering

Cornell University

Crowded, watery compartments filled with complex fluids are ubiquitous in natural and
engineered systems, ranging from consumer products such as cosmetic products to living systems such as
biofilms and the interior of cells. They are set apart from simple fluids by the presence of microscopic
constituents embedded within the fluid that give it structure, i.e. a microstructure. Distortion of this
microstructure by externally imposed forces or fields gives rise to non-Newtonian rheological behavior
such as shear thinning, shear thickening, and time-dependent (memory) effects. A primary goal in the
study of complex fluids is the development of theoretical and computational models that relate
microstructural evolution to macroscopic material and flow properties. An important element in the
construction of such models is the accurate representation of the physical forces between the
microstructural constituents, and the influence exerted by system boundaries on such interactions.
Particle-particle and particle-boundary interactions can include electrostatic, entropic and hydrodynamic
forces, among others. While numerous models, both analytical and computational, successfully describe
microstructural evolution and its connection to macroscopic flow for unbound suspensions, the study of
suspensions enclosed by a finite boundary is an emergent area of research. In these micro-confined
systems particle-scale structure and dynamics are influenced not only by interactions between particles
themselves, but also between particles and nearby boundaries. A primary challenge in the development of
such models is the accurate and efficient representation of many-body hydrodynamic interactions and the
influence exerted on such interactions by boundaries. Such studies include systems confined by a channel
to particles confined in a droplet, but scant attention has been paid to fully three-dimensional
confinement, where flow recirculation and entropic restrictions are expected to play a special role.

In this work, we study the short- and long-time self-diffusion of hydrodynamically interacting
colloids enclosed within a spherical cavity, as a model for intracellular and other confined biophysical
transport. Prior models of such behavior began with a single enclosed particle; attempts to enlarge such
models to many particles have seen limited success owing to the challenges of accurately modeling many-
body far-field and singular near-field hydrodynamic interactions. To overcome these difficulties we have
developed a new set of hydrodynamic mobility functions to couple particle motion with hydrodynamic
force moments which, when inverted and combined with near-field resistance functions form a complete
coupling tensor that accurately captures full many-body interactions, for an arbitrary number of particles
enclosed by a spherical cavity of arbitrary relative size. The mobility functions are implemented in a
Stokesian dynamics framework, and particle motion obtained via dynamic simulation, for suspensions
from dilute to near jamming. We present results for a range of volume fractions from dilute to
concentrated, and a range of particle-to-cavity size ratios, where interplay between entropic restriction
and hydrodynamic entrainment gives rise to novel diffusive behavior. Results are compared to
experiments with excellent agreement. In some prior studies, attempts have been made to circumvent the
challenges of modeling many-body and lubrication hydrodynamics by modeling all particle interactions
as pairwise additive, and accounting only for leading-order far-field interactions (neglecting near-field
lubrication interactions entirely). A discussion of the regimes in which such approximations may be valid
is given.