Coronavirus peplomer interaction.

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 or may not be spherical, 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.

Peplomer bulb shape and coronavirus rotational diffusivity.

Recently, the rotational diffusivity of the coronavirus particle in suspension was calculated, from first principles, using general rigid bead-rod theory [M. A. Kanso, Phys. Fluids 32, 113101 (2020)]. We did so by beading the capsid and then also by replacing each of its bulbous spikes with a single bead. However, each coronavirus spike is a glycoprotein trimer, and each spike bulb is triangular. In this work, we replace each bulbous coronavirus spike with a bead triplet, where each bead of the triplet is charged identically. This paper, thus, explores the role of bulb triangularity on the rotational diffusivity, an effect not previously considered. We thus use energy minimization for the spreading of triangular bulbs over the spherical capsid. The latter both translates and twists the coronavirus spikes relative to one another, and we then next arrive at the rotational diffusivity of the coronavirus particle in suspension, from first principles. We learn that the triangularity of the coronavirus spike bulb decreases its rotational diffusivity. For a typical peplomer population of 74, bulb triangularity decreases the rotational diffusivity by 39 % .

Coronavirus rotational diffusivity.

Just 11 weeks after the confirmation of first infection, one team had already discovered and published [D. Wrapp et al., "Cryo-EM structure of the 2019-nCoV spike in the prefusion conformation," Science 367(6483), 1260-1263 (2020)] in exquisite detail about the new coronavirus, along with how it differs from previous viruses. We call the virus particle causing the COVID-19 disease SARS-CoV-2, a spherical capsid covered with spikes termed peplomers. Since the virus is not motile, it relies on its own random thermal motion, specifically the rotational component of this thermal motion, to align its peplomers with targets. The governing transport property for the virus to attack successfully is thus the rotational diffusivity. Too little rotational diffusivity and too few alignments are produced to properly infect. Too much, and the alignment intervals will be too short to properly infect, and the peplomer is wasted. In this paper, we calculate the rotational diffusivity along with the complex viscosity of four classes of virus particles of ascending geometric complexity: tobacco mosaic, gemini, adeno, and corona. The gemini and adeno viruses share icosahedral bead arrangements, and for the corona virus, we use polyhedral solutions to the Thomson problem to arrange its peplomers. We employ general rigid bead-rod theory to calculate complex viscosities and rotational diffusivities, from first principles, of the virus suspensions. We find that our ab initio calculations agree with the observed complex viscosity of the tobacco mosaic virus suspension. From our analysis of the gemini virus suspension, we learn that the fine detail of the virus structure governs its rotational diffusivity. We find the characteristic time for the adenovirus from general rigid bead-rod theory. Finally, from our analysis of the coronavirus suspension, we learn that its rotational diffusivity descends monotonically with its number of peplomers.

Degradation in cone-plate rheometry.

We analyze quantitatively the oxidative degradation of a sample in a cone-plate rheometer, as oxygen diffuses inward, radially, from the free boundary. We examine rheometer error mitigation by means of nitrogen blanketing, and also, of cone-plate partitioning. We arrive at exact analytical expressions for the oxygen concentration, and thus, for the degradation rate. We then integrate this rate over time to get the amount of oxygen reacted as a function of radial position and time in the degrading sample. To illustrate the usefulness of our analytical expressions, we provide two worked examples investigating the effect of nitrogen blanketing and cone-plate partitioning. We find that, though nitrogen blanketing always produces less degradation, its benefits are limited for short times. Additionally, cone-plate partitioning provides a simpler solution and allows samples to be run for longer times without degradation compromising measurement, even in samples initially saturated with oxygen. We close by considering the effect of antioxidants.

Polymer Fluid Dynamics: Continuum and Molecular Approaches.

To solve problems in polymer fluid dynamics, one needs the equations of continuity, motion, and energy. The last two equations contain the stress tensor and the heat-flux vector for the material. There are two ways to formulate the stress tensor: (a) One can write a continuum expression for the stress tensor in terms of kinematic tensors, or (b) one can select a molecular model that represents the polymer molecule and then develop an expression for the stress tensor from kinetic theory. The advantage of the kinetic theory approach is that one gets information about the relation between the molecular structure of the polymers and the rheological properties. We restrict the discussion primarily to the simplest stress tensor expressions or constitutive equations containing from two to four adjustable parameters, although we do indicate how these formulations may be extended to give more complicated expressions. We also explore how these simplest expressions are recovered as special cases of a more general framework, the Oldroyd 8-constant model. Studying the simplest models allows us to discover which types of empiricisms or molecular models seem to be worth investigating further. We also explore equivalences between continuum and molecular approaches. We restrict the discussion to several types of simple flows, such as shearing flows and extensional flows, which are of greatest importance in industrial operations. Furthermore, if these simple flows cannot be well described by continuum or molecular models, then it is not necessary to lavish time and energy to apply them to more complex flow problems.

Fourier decomposition of polymer orientation in large-amplitude oscillatory shear flow.

In our previous work, we explored the dynamics of a dilute suspension of rigid dumbbells as a model for polymeric liquids in large-amplitude oscillatory shear flow, a flow experiment that has gained a significant following in recent years. We chose rigid dumbbells since these are the simplest molecular model to give higher harmonics in the components of the stress response. We derived the expression for the dumbbell orientation distribution, and then we used this function to calculate the shear stress response, and normal stress difference responses in large-amplitude oscillatory shear flow. In this paper, we deepen our understanding of the polymer motion underlying large-amplitude oscillatory shear flow by decomposing the orientation distribution function into its first five Fourier components (the zeroth, first, second, third, and fourth harmonics). We use three-dimensional images to explore each harmonic of the polymer motion. Our analysis includes the three most important cases: (i) nonlinear steady shear flow (where the Deborah number [Formula: see text] is zero and the Weissenberg number [Formula: see text] is above unity), (ii) nonlinear viscoelasticity (where both [Formula: see text] and [Formula: see text] exceed unity), and (iii) linear viscoelasticity (where [Formula: see text] exceeds unity and where [Formula: see text] approaches zero). We learn that the polymer orientation distribution is spherical in the linear viscoelastic regime, and otherwise tilted and peanut-shaped. We find that the peanut-shaping is mainly caused by the zeroth harmonic, and the tilting, by the second. The first, third, and fourth harmonics of the orientation distribution make only slight contributions to the overall polymer motion.

A new dual-plate slipometer for measuring slip between molten polymers and extrusion die materials.

In this work, we study the slip behaviors common to plastics die extrusion metals or platings using a new instrument called a dual-plate slipometer. By dual-plate, we mean that whereas the stationary plate incorporates a local shear stress transducer, the moving plate does not. The stationary plate and transducer are made of one stainless steel, but the moving plate is made from, or plated with, different extrusion die materials under study. This new instrument allows slip velocity to be measured without having to build a new shear stress transducer from each extrusion metal or plating under study. We explore the effect of extrusion die composition and die metal surface morphology on the slip properties of polyolefins using a sliding plate rheometer. In this work, we studied the slip behaviors of polyolefins on four common plastics die extrusion metals or platings, without having to build a new shear stress transducer from each. Specifically, our new method replaces the moving plate; with each of the four die metals or platings under study without changing the stainless steel material of the shear stress transducer and its stationary plate. Our experiments include high-density polyethylene, low-density polyethylene, and polypropylene (PP) on four different die metals or platings. We use steady simple shear to obtain shear stress versus nominal shear rate for different gaps, from which we can then deduce the slip velocity using the Mooney analysis. We then fit four slip models to our experimental measurements, and we find the Hatzikiriakos hyperbolic sine model to be accurate, even for the measured inflections in the slip velocity as a function of shear stress curves. Our analysis includes detailed characterization of the die metal plating surfaces, including measurements of the composition of the sliding plates by energy dispersive spectroscopy, surface energy by contact angle goniometry, and surface roughness by both white light interference and stylus profilometries. We use our slip measurements to evaluate the Allal-Vergnes equation for the critical shear stress for slip [A. Allal and B. Vergnes, "Effect of die surface on the onset of stick-slip transition in the flow of molten linear polymers," J. Non-Newtonian Fluid Mech. 167-168, 46-49 (2012)]. We conclude our analysis by dedimensionalizing slip, and we then use these dimensionless groups to analyze slip. This paper provides a set of reference data for extrusion die designers for polyolefins.

Dilute rigid dumbbell suspensions in large-amplitude oscillatory shear flow: shear stress response.

We examine the simplest relevant molecular model for large-amplitude shear (LAOS) flow of a polymeric liquid: the suspension of rigid dumbbells in a Newtonian solvent. We find explicit analytical expressions for the shear rate amplitude and frequency dependences of the first and third harmonics of the alternating shear stress response. We include a detailed comparison of these predictions with the corresponding results for the simplest relevant continuum model: the corotational Maxwell model. We find that the responses of both models are qualitatively similar. The rigid dumbbell model relies entirely on the dumbbell orientation to explain the viscoelastic response of the polymeric liquid, including the higher harmonics in large-amplitude oscillatory shear flow. Our analysis employs the general method of Bird and Armstrong ["Time-dependent flows of dilute solutions of rodlike macromolecules," J. Chem. Phys. 56, 3680 (1972)] for analyzing the behavior of the rigid dumbbell model in any unsteady shear flow. We derive the first three terms of the deviation of the orientational distribution function from the equilibrium state. Then, after getting the "paren functions," we use these for evaluating the shear stress for LAOS flow. We find the shapes of the shear stress versus shear rate loops predicted to be reasonable.