General rigid bead-rod theory with hydrodynamic interaction for polymer viscoelasticity

By virtue of their lack of motility, viruses rely entirely on their own temperature (Brownian motion) to position themselves properly for cell attachment. Spiked viruses use one or more spikes (called peplomers) to attach. The coronavirus uses adjacent peplomer pairs. These peplomers, identically charged, repel one another over the surface of their convex capsids to form beautiful polyhedra. We identify the edges of these polyhedra with the most important peplomer hydrodynamic interactions. These convex capsids may be spherical or not, and their peplomer population declines with infection time. These peplomers are short, equidimensional, and bulbous, with triangular bulbs. In this short paper, we explore the interactions between nearby peplomer bulbs. By interactions, we mean the hydrodynamic interferences between the velocity profiles caused by the drag of the suspending fluid when the virus rotates. We find that these peplomer hydrodynamic interactions raise rotational diffusivity of the virus, and thus affect its ability to infect.

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“…II of Refs. 8 and 14 , and specifically, we neglect “other” terms in Eqs. (29)–(30) and (18)–(19), respectively.…”

Section: Methodsmentioning

confidence: 99%

Coronavirus peplomer interaction

Pak¹,

Chakraborty

Kanso

et al. 2022

Physics of Fluids

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Complex viscosity of poly[n]catenanes including olympiadanes

et al. 2022

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Chains of mechanically interlocking or intersecting organic rings, called poly[[Formula: see text]]catenanes, afford interesting opportunities to study the role of orientation in suspensions. We call poly[[Formula: see text]]catenanes olympiadanes. In this work, we use general rigid bead-rod theory to arrive at general expressions, from first principles, for the complex viscosity of poly[[Formula: see text]]catenane suspensions. General rigid bead-rod theory relies entirely on suspension orientation to explain the elasticity of the liquid. We obtain analytical expressions for the complex viscosity of poly[n]catenanes for both [Formula: see text] even and odd, for both mechanically interlocking and intersecting rings, and for identically sized rings. We restrict our analysis to evenly spaced poly[n]catenanes of orthogonal adjacency. We find that the parts of the complex viscosity for intersecting and interlocking rings, when made dimensionless with the polymer contribution to the zero-shear viscosity, match. We find good agreement with the available complex viscosity measurements for molten intersecting polystyrene poly[1,3]catenanes, but not so for poly[2]catenanes. We next calculate space filling equilibrium structures of these poly[[Formula: see text]]catenanes, only to discover that each polystyrene ring looks more like a bead. We find that, for these polystyrene poly[[Formula: see text]]catenanes and for good agreement with the available complex viscosity measurements, the shish-kebab theory suffices.

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Hydrodynamic interaction and complex viscosity of multi-bead rods

Kanso

Pak²,

Kim³

et al. 2022

Physics of Fluids

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One good way to explain the elasticity of a polymeric liquid is to just consider the orientation distribution of the macromolecules. When exploring how macromolecular architecture affects the elasticity of a polymeric liquid, we find the general rigid bead–rod theory to be both versatile and accurate. This theory sculpts macromolecules using beads and rods. Whereas beads represent points of Stokes flow resistances, the rods represent rigid separations. In this way, how the shape of the macromolecule affects its rheological behavior in suspension is determined. Until recently, general rigid bead–rod theory has neglected interferences of the Stokes flow velocity profiles between nearby beads. We call these hydrodynamic interactions, and we here employ our new method for exploring how these interactions affect the complex viscosity of suspensions of multi-bead rods. These multi-bead rods are also called shish-kebabs. We use the center-to-center distance between adjacent beads as the characteristic length. We proceed analytically, beginning with a geometric expression for the shish-kebab bead positions. Our analytical solution for the complex viscosity presents as one for [Formula: see text], one for [Formula: see text], and another for the rigid dumbbell, [Formula: see text]. We find that for shish-kebabs, hydrodynamic interactions (i) increase zero-shear viscosity, (ii) increase zero-shear first normal stress coefficient, (iii) decrease the real part of the dimensionless complex viscosity, and (iv) increase minus the dimensionless imaginary part. We find that the combination of (iii) and (iv) explains crossovers of the parts of the complex viscosity. We further find that for a monodisperse polystyrene solution, the general rigid bead–rod theory with hydrodynamic interaction, for both parts of the complex viscosity, provides stunning improvement over without.

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General rigid bead-rod theory with hydrodynamic interaction for polymer viscoelasticity

Cited by 13 publications

References 24 publications

Coronavirus peplomer interaction

Coronavirus peplomer interaction

Complex viscosity of poly[n]catenanes including olympiadanes

Hydrodynamic interaction and complex viscosity of multi-bead rods

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