Ashwin Vaidya

ORIENTATION OF SYMMETRIC BODIES FALLING IN A SECOND-ORDER LIQUID AT NONZERO REYNOLDS NUMBER

We study the steady translational fall of a homogeneous body of revolution around an axis a, with fore-and-aft symmetry, in a second-order liquid at nonzero Reynolds (Re) and Weissenberg (We) numbers. We show that, at first order in these parameters, only two orientations are allowed, namely, those with a either parallel or perpendicular to the direction of the gravity g. In both cases the translational velocity is parallel to g. The stability of the orientations can be described in terms of a critical value Ec for the elasticity number E = We/Re, where Ec depends only on the geometric properties of the body, such as size or shape, and on the quantity (Ψ1 + Ψ2)/Ψ1, where Ψ1 and Ψ2 are the first and second normal stress coefficients. These results are then applied to the case when the body is a prolate spheroid. Our analysis shows, in particular, that there is no tilt-angle phenomenon at first order in Re and We.

Analytical solutions to Stokes-type flows of inhomogeneous fluids

Abstract In this paper, we study the unsteady motion of an inhomogeneous incompressible viscous fluid, where the viscosity varies spatially according to various models. We study the Stokes-type flow for these types of fluids where in the first case the flow between two parallel plates is examined with one of the plates oscillating and in the second case when the flow is caused by a pulsatile pressure gradient. A general argument establishes the existence of oscillatory solutions to our problem. Exact solutions are obtained in terms of some special functions and comparisons are made with the cases of constant viscosity and the slow flow regimes.

A modified Stokes-Einstein equation for Aβ aggregation

BackgroundIn all amyloid diseases, protein aggregates have been implicated fully or partly, in the etiology of the disease. Due to their significance in human pathologies, there have been unprecedented efforts towards physiochemical understanding of aggregation and amyloid formation over the last two decades. An important relation from which hydrodynamic radii of the aggregate is routinely measured is the classic Stokes-Einstein equation. Here, we report a modification in the classical Stokes-Einstein equation using a mixture theory approach, in order to accommodate the changes in viscosity of the solvent due to the changes in solute size and shape, to implement a more realistic model for Aβ aggregation involved in Alzheimer’s disease. Specifically, we have focused on validating this model in protofibrill lateral association reactions along the aggregation pathway, which has been experimentally well characterized.ResultsThe modified Stokes-Einstein equation incorporates an effective viscosity for the mixture consisting of the macromolecules and solvent where the lateral association reaction occurs. This effective viscosity is modeled as a function of the volume fractions of the different species of molecules. The novelty of our model is that in addition to the volume fractions, it incorporates previously published reports on the dimensions of the protofibrils and their aggregates to formulate a more appropriate shape rather than mere spheres. The net result is that the diffusion coefficient which is inversely proportional to the viscosity of the system is now dependent on the concentration of the different molecules as well as their proper shapes. Comparison with experiments for variations in diffusion coefficients over time reveals very similar trends.ConclusionsWe argue that the standard Stokes-Einstein’s equation is insufficient to understand the temporal variations in diffusion when trying to understand the aggregation behavior of Aβ 42 proteins. Our modifications also involve inclusion of improved shape factors of molecules and more appropriate viscosities. The modification we are reporting is not only useful in Aβ aggregation but also will be important for accurate measurements in all protein aggregation systems.

Steady fall of bodies of arbitrary shape in a second-order fluid at zero reynolds number

We study the slow motion of rigid bodies of arbitrary shape sedimenting in a quiescent viscoelastic liquid under the action of gravity. The liquid is modeled by the second-order fluid equations. We show existence of steady state solutions for small Weissenberg numbers. The case of pure translational motions is analyzed for specific geometric symmetries of the body and this allows us to show that the sedimentation behavior can be dramatically different between Newtonian and viscoelastic liquids.

Vortex Induced Oscillations of Cylinders at Low and Intermediate Reynolds Numbers

We study the orientational behavior of a hinged cylinder suspended in a water tunnel in the presence of an incompressible flow with Reynolds number (Re), based on particle dimensions, ranging between 100 and 6000 and non-dimensional inertia of the body(I *) in the range 0.1–0.6. The cylinder displays four unique features, which include: steady orientation, random oscillations, periodic oscillations and autorotation.We illustrate these features displayed by the cylinder using a phase diagram which captures the observed phenomena as a function of Re and I *. We identify critical Re and I * to distinguish the different behaviors of the cylinders. We used the hydrogen bubble flow visualization technique to show vortex shedding structure in the cylinder’s wake which results in these oscillations.

Non-equilibrium pattern selection in particle sedimentation

Abstract In this paper, we explain some well known experimental observations in fluid solid interaction from a thermodynamic perspective. In particular we use the extremum of the rate of entropy production to establish the stability of specific patterns observed in single and multiparticle sedimentation in an infinite fluid and the sedimentation of spheres in the presence of walls. While these phenomena have been explained numerically, there is no known rigorous theoretical argument to establish the stability of the observed configurations. We provide a very convincing theoretical basis using entropy based arguments that are considered by several scientists as the underlying theme of nature, life and evolution. In the absence of many rigorous examples for the entropy production principle, our paper advances this argument and lends it much credibility. In addition to looking at the rate of entropy production, we also put forth a very plausible heuristic argument based on the thermal gradients in the systems being studied, which could be the underlying causal principle for many known patterns in nature.

A note on the orientation of symmetric rigid bodies sedimenting in a power-law fluid

We study the terminal orientation of symmetric bodies translating in a quiescent liquid modeled by the power-law fluid. We are able to show by invoking the symmetries of the sedimenting body and the Stokes flow field that at small Reynolds numbers, the competition of inertial and shear-thinning (or shear-thickening) contributions to the torque does not cause the tilt angle that is observed in experiments performed on viscoelastic liquids with shear-thinning properties.

Stability analysis of 4-species Aβ aggregation model: A novel approach to obtaining physically meaningful rate constants

Protein misfolding and concomitant aggregation towards amyloid formation is the underlying biochemical commonality among a wide range of human pathologies. Amyloid formation involves the conversion of proteins from their native monomeric states (intrinsically disordered or globular) to well-organized, fibrillar aggregates in a nucleation-dependent manner. Understanding the mechanism of aggregation is important not only to gain better insight into amyloid pathology but also to simulate and predict molecular pathways. One of the main impediments in doing so is the stochastic nature of interactions that impedes thorough experimental characterization and the development of meaningful insights. In this study, we have utilized a well-known intermediate state along the amyloid-β peptide aggregation pathway called protofibrils as a model system to investigate the molecular mechanisms by which they form fibrils using stability and perturbation analysis. Investigation of protofibril aggregation mechanism limits both the number of species to be modeled (monomers, and protofibrils), as well as the reactions to two (elongation by monomer addition, and protofibril-protofibril lateral association). Our new model is a reduced order four species model grounded in mass action kinetics. Our prior study required 3200 reactions, which makes determining the reaction parameters prohibitively difficult. Using this model, along with a linear perturbation argument, we rigorously determine stable ranges of rate constants for the reactions and ensure they are physically meaningful. This was accomplished by finding the ranges in which the perturbations dieout in a five-parameter sweep, which includes the monomer and protofibril equilibrium concentrations and three of the rate constants. The results presented are a proof-of-concept method in determining meaningful rate constants that can be used as a bonafide way for determining accurate rate constants for other models involving complex biological reactions such as amyloid aggregation.

MaxEP and Stable Configurations in Fluid–Solid Interactions

We review the experimental and theoretical literature on the steady terminal orientation of a body as it settles in a viscous fluid. The terminal orientation of a rigid body is a classic example of a system out of equilibrium. While the dynamical equations are effective in deriving the equilibrium states, they are far too complex and intractable as of yet to resolve questions about the nature of stability of the solutions. The maximum entropy production principle is therefore invoked, as a selection principle, to understand the stable, steady state patterns. Some on-going work and inherent complexities of fluid solid systems are also discussed.

Fostering Creativity Through Personalized Education

Abstract This article focuses on the philosophy of creativity and its enhancement through an undergraduate research experience. In this paper we offer suggestions for infusing the undergraduate mathematics and science curriculum with research experiences as a way of fostering creativity in our students. We refer to the term research broadly, offering suggestions to accommodate students from various backgrounds and with different goals. We posit that creativity is a necessary component of scientific thinking, producing students that are motivated, passionate, skilled, adaptable, and responsible. Research experiences at the undergraduate level instill a deep sense of personalized education and learning that can make the entire university experience extremely pleasurable and of lasting value.