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1. Shear rheology of a dilute suspension of thin rings

   https://doi.org/10.1122/8.0000628  

   Borker, Neeraj S.; Koch, Donald L. (April 2023, Journal of Rheology)

   The rheology of suspensions of rings (tori) rotating in an unbounded low Reynolds number simple shear flow is calculated using numerical simulations at dilute particle number densities ( n ≪ 1 ). Suspensions of non-Brownian rings are studied by computing pair interactions that include hydrodynamic interactions modeled using slender body theory and particle collisions modeled using a short-range repulsive force. Particle contact and hydrodynamic interactions were found to have comparable influences on the steady-state Jeffery orbit distribution. The average tilt of the ring away from the flow-vorticity plane increased during pairwise interactions compared to the tilt associated with Jeffery rotation and the steady-state orbit distribution. Particle stresses associated with the increased tilt during the interaction were found to be comparable to the stresses induced directly by particle contact forces and the hydrodynamic velocity disturbances of other particles. The hydrodynamic diffusivity coefficients in the gradient and vorticity directions were also obtained and were found to be two orders of magnitude larger than the corresponding values in fiber suspensions at the same particle concentrations. Rotary Brownian dynamics simulations of isolated Brownian rings were used to understand the shear rate dependence of suspension rheology. The orbit distribution observed in the regime of weak Brownian motion, P e ≫ ϕ T − 3, was surprisingly similar to that obtained from pairwise interaction calculations of non-Brownian rings. Here, the Peclet number P e is the ratio of the shear rate and the rotary diffusivity of the particle and ϕ T is the effective inverse-aspect ratio of the particle (approximately equal to 2 π times the inverse of its non-dimensional Jeffery time period). Thus, the rheology results obtained from pairwise interactions should retain accuracy even for weakly Brownian rings ( n ≪ 1 and ϕ T − 3 ≪ P e ). 

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2. Extensional rheology of a dilute particle-laden viscoelastic solution

   https://doi.org/10.1103/PhysRevFluids.4.091301  

   Jain, Anika; Einarsson, Jonas; Shaqfeh, Eric S. (September 2019, Physical Review Fluids)
3. Stress in a dilute suspension of spheres in a dilute polymer solution subject to simple shear flow at finite Deborah numbers

   https://doi.org/10.1103/PhysRevFluids.1.013301  

   Koch, Donald L.; Lee, Eric F.; Mustafa, Ibrahim (May 2016, Physical Review Fluids)
4. Velocity fluctuations in a dilute suspension of viscous vortex rings

   https://doi.org/10.1103/PhysRevFluids.4.044501  

   Morrell, Thomas A.; Spagnolie, Saverio E.; Thiffeault, Jean-Luc (April 2019, Physical Review Fluids)
5. Dilute solution structure of bottlebrush polymers

   https://doi.org/10.1039/c9sm00033j  

   Dutta, Sarit; Wade, Matthew A.; Walsh, Dylan J.; Guironnet, Damien; Rogers, Simon A.; Sing, Charles E. (April 2019, Soft Matter)

   Bottlebrush polymers are a class of macromolecules that have recently found use in a wide variety of materials, ranging from lubricating brushes and nanostructured coatings to elastomeric gels that exhibit structural colors. These polymers are characterized by dense branches extending from a central backbone and thus have properties distinct from linear polymers. It remains a challenge to specifically understand conformational properties of these molecules, due to the wide range of architectural parameters that can be present in a system, and thus there is a need to accurately characterize and model these molecules. In this paper, we use a combination of viscometry, light scattering, and computer simulations to gain insight into the conformational properties of dilute solution bottlebrush polymers. We focus on a series of model bottlebrushes consisting of a poly(norbornene) (PNB) backbone with poly(lactic acid) (PLA) side chains. We demonstrate that intrinsic viscosity and hydrodynamic radius are experimental observations sensitive to molecular architecture, exhibiting distinct differences with different choices of branches and backbone lengths. Informed by the atomistic structure of this PNB–PLA system, we rationalize a coarse-grained simulation model that we evaluate using a combination of Brownian dynamics and Monte Carlo simulations. We show that this exhibits quantitative matching to experimental results, enabling us to characterize the overall shape of the bottlebrush via a number of metrics that can be extended to more general bottlebrush architectures. 

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