(161a) Colloidal Hydrodynamics of Particles from Biological Cells to Granular Dispersions: A Study Spanning Two Fields

Understanding the mobility of colloids or nanoparticles is central to various physical, chemical, biological as well as industrial systems [1,2]. Examples of these suspensions range from protein suspension, transport through membranes, to flow of fine particles dispersed in a fluid. Such highly concentrated suspensions under confinement can shed light into dynamics of crowded macromolecules, as such proteins inside biological cells.

Modeling colloidal hydrodynamics at low-Reynolds-number attempts to unify the disparate length scales and timescales of solvent molecules and colloidal dynamics and can be the key to operational mastery of cells. The flow behavior of such concentrated suspensions is also critical to numerous natural settings such as mud or lava flow as well as industrial settings, e.g., mixing of powder of 10- to 50-μm primary particles into a liquid.

Accurately simulating such suspensions has been proven to be a challenging issue as it requires the correct modeling of hydrodynamic interactions (both near-and-far field) and close “contact” interactions as well as coupling of such terms with Brownian fluctuations efficiently. This work roots on two recently developed diverse numerical schemes of which I have been a co-developer [3,4,5,6,7]. The first approach relies on an Immersed Boundary General geometry Ewald-like method to capture lubrication and long-range hydrodynamics and include the appropriate non-slip conditions at the confining walls [3,4]. The second approach is a Stokesian dynamics type approach that includes hydrodynamic interaction with only near-field lubrication, conservative forces such as steric repulsion and van der Waals attraction, and allows for frictional contact by lubrication breakdown [5,6,7].

The former approach has been shown to correctly reproduce the experimentally observed anomalous diffusion as observed in cells and is crucial for the understanding of diffusion of biomolecules that underpins a variety of intracellular metabolic, translational and locomotion processes [2,4]. However, no direct comparison to experimental literature was attempted. In this proposal, a first attempt will be made to compare simulation results with the experiments and that will need a thorough study and implementation of various forces present at the level of proteins. Further, this numerical scheme will be also used to study the cell jamming as observed [8], where the role of hydrodynamic interactions has not been elucidated.

The latter approach has been crucial to the recent improvements in the understanding of flow of highly concentrated suspensions of which Cornstarch in water is an archetypical example [5,6,7]. However, this numerical approach did not consider the interfaces such as walls that are an important ingredient of industrial and experimental set ups. Such interfaces are known to affect the hydrodynamic interactions [9, 10]. Based on these methods, the walls can be implemented and will answer the deeper question about the role of walls in the flow of dense suspensions. The friction plays an important role in understanding the flow behavior at very high volume fractions that are close to the jamming and it has been found that close to the jamming conditions, a system-spanning frictional contact network is formed and is in part responsible for the observed strong resistance to flow [11,12]. These approaches are disparate, and a deeper understanding of the observed flow behavior demands unification and a direct comparison of such approaches.

Bridging the gap between the disparate disciplines such as biology, fluid dynamics, contact mechanics and network theory is the motivation of proposed work. These numerical and theoretical efforts will highlight the intricate role played by hydrodynamics and colloidal-scale motion that appear in common across cell functions, types, and conditions. The proposed efforts on one hand explore not only the diffusion of a mixture of shape and size polydisperse macromolecules inside the cells but also the jamming of cells. On the other hand this work will deal with larger (granular or non-Brownian) dispersions and highlight the important role of contact mechanics at the particle level [15] and the network theory [16]. Further, establishing the relationship between network structure to the noted microscopic contact interactions is challenging in terms of the nonequilibrium statistical mechanics and will be explored.

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