Fibers

Micron scale fibers play a fundamental role in cellar biology. These fibers could be the propulsive flagella of bacteria and sperm cells; or they could link up to form the dynamic mesh of the cellular cytoskeleton. Experimental measurements at the cellular and subcellular scales are extremely challenging to carry out, so numerical simulations are invaluable for interrogating the physics of fibrous phenomena at these scales. Still, numerical simulations at these scales have their own challenges. Biological fibers are typically inextensible, which requires strict constraints to be imposed on their dynamics. Further, the local twist in a fiber has an important effect on the way that it bends, so the way that we model the twist along a fiber is an important consideration. In addition to all of this, thermal fluctuations play a key role in biological fiber dynamics and must be carefully accounted for in simulations so that the correct equilibrium statistics are sampled.

In Biology

As a CO-PI with Aleksandar Donev and Alexander Mogilner, I've recently been funded on a three year, $300,000 NSF grant (DMS-2052515) to study the microscopic properties of the cellular cytoskeleton. The impetus for this project is a scientific need to carefully understand the microscopic dynamics in the cytoskeleton and to leverage this knowledge to predict structural and hydrodynamic behavior at the scale of the whole cell. It is not yet known if microscopic semi-flexible filaments (F-actin) can self organize into the macroscopic chiral structures responsible for the left-right asymmetry seen in some tissues, or why networks of F-actin gels are typically contractile (with or without molecular motors like myosin [*]). The goal of this project is to answer these fundamental questions in cellular biology. The stochastic nature of sub-cellular processes coupled with the ever-changing topology of cytoskeletal networks make the driving questions of this project difficult or impossible to interrogate through lab measurements or existing simulation techniques. I will lead a group to develop the novel computational tools required to close this knowledge gap; tools which carefully capture the microscopic features of cellular fiber networks at the extraordinary computational scale required to probe their macroscopic structure.

Synthetic Fibers

Swimming at low Reynolds numbers is difficult on it’s own, but navigating complex environments at this scale is extremely challenging and a fundamental issue for targeted medicine. Inspired by biological examples like bacteria and sperm, collaborators at the Colorado School of Mines assembled chains of magnetically responsive colloids to do just this: controlled navigation through complex environments at low Reynolds number [1]. Their approach was to use a percessing magnetic field to spin and twist the colloidal chains into spiraling helices or other geometries capable of movement. Once in motion, changes in the magnetic field could easily guide the swimming chain through curved channels. Our simulations of these magnetically driven colloidal chains agreed very closely with experiments [see here]. They also provided invaluable insight into the physics of these types of swimming chains. By turning on/off local twisting dynamics in the chain, we were able to show that twist in the chain is not necessary to form a helical geometry, but is absolutely essential to maintain stable swimming in this mode. We also saw that thermal fluctuations from the fluid were necessary to break the symmetry of an initially straight chain, allowing it to fold into the various morphologies seen in experiments (and replicated in our simulations). Going forward, we would like to design magnetic fields to fold a colloidal chain into a desired morphology. As a fist step, I’ve been looking at the mechanics of knots in these filaments and how entropy can untie them. I hope to use this data in conjunction with modern machine leaning techniques to `back out’ an effective, applied magnetic field which can be used to tie or untie a knot.

References

[*] “Myosin ii-independent processes in mitotic cells of dictyostelium discoideum: redistribution of the nuclei, re-arrangement of the actin system and formation of the cleavage furrow” by R. Neujahr, C. Heizer, and G. Gerisch, J Cell Sci, 110 ( Pt 2):123-37, 1997.

Publications

[1] "Reconfigurable Microbots Folded from Simple Colloidal Chains" by T. Yang, B. Sprinkle, Y. Guo, J. Qian, D. Hua, A. Donev, D. W.M. Marr, and N. Wu, PNAS, 202007255, 2020. Codes @ RigidMultiblobsWall github.

Press: https://www.minesnewsroom.com/news/snake-microbots-can-swim-through-complex-environments-mimic-human-body-targeted-drug-delivery

Colloids

The term colloidal suspensions is often used as a shorthand to mean lots of small, rigid particles (colloids), typically on the order of 1 μm wide, which are immersed in a fluid. Colloids are usually spherical (but not always! See the colloidal boomerang video on the right) and they can be active—set in motion by some outside force or torque, or passive—moved only by flows in the solvent or gravity. Colloidal suspensions make simple building blocks to study complex, emergent behavior in many body systems, and direct numerical simulation of many interacting colloids is often the only way to make any sense of their dynamics. This is particularly the case in confined environments, where things like free-energy-minimization techniques to understand colloidal interactions will typically fall short. Simulating colloidal suspensions in confinement not only difficult because one has to efficiently resolve the hydrodynamics interactions between the colloids, but also between the whole suspension and the barriers that confine it. On top of this, the colloids themselves are small enough that thermal fluctuations from the fluid can dramatically effect their dynamics. These fluctuations need to be carefully handled in simulations to ensure that thermodynamic principles like detailed balance are maintained.

What I’m working on

In past works I’ve studied emergent phenomena in colloidal suspensions driven by an applied, magnetically induced torque [1,3]. My collaborators and I were able to match experimental measurements of theses suspensions with simulated statistics and see exceptional agreement. Still the natural next question is: what happens to the suspension if you apply a force instead of a torque? We use a combination of experimental measurements and detailed simulations to interrogate the dynamics of a colloidal suspension sedimenting down an inclined plane. This work is in preparation, to be submitted in the coming month.

What I’ve done

The foundation for much of my work on colloidal suspensions was done in [1], where my collaborators and I described linear scaling algorithms (in the sense that the overall complexity scaled linearly with the number of particles in the suspension) to simulate the Brownian dynamics of arbitrarily shaped colloids above a wall. The methods we developed in [1] are quite general and could easily be applied to most types of constrained Brownian dynamics. This work was extended in [2] to simulate arbitrarily shaped colloids in any kind of confinement (i.e slit channels, cuboids, etc …) by explicitly simulating the fluctuating solvent. Inspired by experiments from the authors of [*], we used our new method to interrogate interesting wave patterns in a colloidal monolayer being hydrodynamically forced through a slit channel with `egg carton’ like corrugations. As a testament to the fundamental importance of fluctuations, and to the utility of numerical methods, we could simply `turn off’ the stochastic component in our simulations to find that no motion in the suspension is observed at all without thermal fluctuations from the solvent. In [3] my collaborators and I investigated an interesting observation that a uniformly dense (in the sense of packing density) suspension of magnetic microrollers (spherical colloids driven by an applied, rotating magnetic field) will tend to self separate into an upper layer of fast particles and a lower layer of slow particles. My collaborators in this work were able to make extremely precise measurements of velocity statistics in these types of suspensions. To interrogate these measurements, we developed a novel numerical method which used minimally resolved, nearfield `lubrication’ corrections to very accurately and efficiently simulate the densely packed suspensions from the experiments. The agreement we saw between measurements and simulations was remarkable and we used this to discern important physical mechanisms for these types of active suspensions.

References

[*] “Observation of kinks and antikinks in colloidal monolayers driven across ordered surfaces”, T. Bohlein, J. Mikhael, C. Bechinger, Nat Mater. 2011 Dec 18;11(2):126-30.

Publications

[1] "Large Scale Brownian Dynamics of Confined Suspensions of Rigid Particles", by B. Sprinkle, F. Balboa Usabiaga, N. A. Patankar and A. Donev, J. Chem. Phys., 147, 244103, 2017. Codes @ RigidMultiblobsWall github.

[2] "Brownian Dynamics of Fully Confined Suspensions of Rigid Particles Without Green's Functions", by B. Sprinkle, A. Donev, A. Pal Singh Bhalla and N. Patankar, J. Chem. Phys., 150, 164116, 2019. Codes @ IBAMR github

[3] "Driven dynamics in dense suspensions of microrollers" by B. Sprinkle, E. B. van der Wee and Y. Luo and M. Driscoll, and A. Donev,  Soft Matter, 16, 7982 - 8001, 2020. Codes @ RigidMultiblobsWall github.

CFD

In addition to all the low Reynolds number projects that I work on, I also like to occasionally dip into the moderate Reynolds number side of fluid-stucture interaction. I’m an ardent follower of the immersed boundary (IB) framework for fluid structure interaction and I’ve developed some functionality for the IBAMR software infrastructure.

What I’m working on

Recently some collaborators in the Applied Math Lab at Courant build a beautiful device to carefully examine Feynman’s reverse sprinkler. Richard Feynman famously asked: if a classic garden sprinkler with curved arms is placed in a bath and sucks water in instead of pushing it out, which way will it spin? After a number of long, careful experiments they believe that they have an answer. I’ve been working with them by running IB simulations of their experimental setup to pin down the physics behind what they observe.

What I’ve done

In [1] my colloaborators and I used IBAMR to interogate the swimming efficiency of certain kinds of fish who hold their bodies rigid and propel themselves using an elongated, undulating fin (gymnotiform swimmers). We showed that the classical theory on these swimmers due to J. Lighthill was insufficient to explain their swimming efficiency. Using simulations we were able to argue that the efficiency these types of swimmers enjoy is largely due to the flow structures generated by their undulating fin. Using a simplified `rigid plate’ model for a fish, we were also able to find some optimal `design parameters’ for these types of swimmers and validate them with data collected from real fish.

Publications

[1] “Hydrodynamic Optimality of Balistiform and Gymnotiform Locomotion”, by B. Sprinkle, R. Bale, A. Pal Singh Bhalla, M. A. MacIver and N. A. Patankar, Euro. J. Comp. Mech., 26, 1–2, 31–43, 2017.