Treating Inertia in Passive Microbead Rheology

The dynamic modulus G * of a viscoelastic medium is often measured by following the trajectory of a small bead subject to Brownian motion in a method called "passive microbead rheology." This equivalence between the positional autocorrelation function of the tracer bead and G * is assumed via the generalized Stokes-Einstein relation (GSER). However, inertia of both bead and medium are neglected in the GSER so that the analysis based on the GSER is not valid at high frequency where inertia is important. In this paper we show how to treat both contributions to inertia properly in one-bead passive microrheological analysis. A Maxwell fluid is studied as the simplest example of a viscoelastic fluid to resolve some apparent paradoxes of eliminating inertia. In the original GSER, the mean-square displacement (MSD) of the tracer bead does not satisfy the correct initial condition. If bead inertia is considered, the proper initial condition is realized, thereby indicating an importance of including inertia, but the MSD oscillates at a time regime smaller than the relaxation time of the fluid. This behavior is rather different from the original result of the GSER and what is observed. What is more, the discrepancy from the GSER result becomes worse with decreasing bead mass, and there is an anomalous gap between the MSD derived by naïvely taking the zero-mass limit in the equation of motion and the MSD for finite bead mass as indicated by McKinley et al. [J. Rheol. 53, 148

Accurate method for the Brownian dynamics simulation of spherical particles with hard-body interactions

In Brownian Dynamics simulations, the diffusive motion of the particles is simulated by adding random displacements, proportional to the square root of the chosen time step. When computing average quantities, these Brownian contributions usually average out, and the overall simulation error becomes proportional to the time step. A special situation arises if the particles undergo hard-body interactions that instantaneously change their properties, as in absorption or association processes, chemical reactions, etc. The common "naive simulation method" accounts for these interactions by checking for hard-body overlaps after every time step. Due to the simplification of the diffusive motion, a substantial part of the actual hard-body interactions is not detected by this method, resulting in an overall simulation error proportional to the square root of the time step. In this paper we take the hard-body interactions during the time step interval into account, using the relative positions of the particles at the beginning and at the end of the time step, as provided by the naive method, and the analytical solution for the diffusion of a point particle around an absorbing sphere. Ottinger used a similar approach for the one-dimensional case [Stochastic Processes in Polymeric Fluids (Springer, Berlin, 1996), p. 270]. We applied the "corrected simulation method" to the case of a simple, second-order chemical reaction. The results agree with recent theoretical predictions [K. Hyojoon and Joe S. Kook, Phys. Rev. E 61, 3426 (2000)]. The obtained simulation error is proportional to the time step, instead of its square root. The new method needs substantially less simulation time to obtain the same accuracy. Finally, we briefly discuss a straightforward way to extend the method for simulations of systems with additional (deterministic) forces. (C) 2002 American Institute of Physics

Proactive esophageal cooling protects against thermal insults during high-power short-duration radiofrequency cardiac ablation

[EN] Background Proactive cooling with a novel cooling device has been shown to reduce endoscopically identified thermal injury during radiofrequency (RF) ablation for the treatment of atrial fibrillation using medium power settings. We aimed to evaluate the effects of proactive cooling during high-power short-duration (HPSD) ablation. Methods A computer model accounting for the left atrium (1.5 mm thickness) and esophagus including the active cooling device was created. We used the Arrhenius equation to estimate the esophageal thermal damage during 50 W/ 10 s and 90 W/ 4 s RF ablations. Results With proactive esophageal cooling in place, temperatures in the esophageal tissue were significantly reduced from control conditions without cooling, and the resulting percentage of damage to the esophageal wall was reduced around 50%, restricting damage to the epi-esophageal region and consequently sparing the remainder of the esophageal tissue, including the mucosal surface. Lesions in the atrial wall remained transmural despite cooling, and maximum width barely changed (<0.8 mm). Conclusions Proactive esophageal cooling significantly reduces temperatures and the resulting fraction of damage in the esophagus during HPSD ablation. These findings offer a mechanistic rationale explaining the high degree of safety encountered to date using proactive esophageal cooling, and further underscore the fact that temperature monitoring is inadequate to avoid thermal damage to the esophagus.Research reported in this publication was supported by the National Heart, Lung, And Blood Institute of the National Institutes of Health under Award Number R44HL158375 (the content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health) and by the Spanish Ministerio de Ciencia, Innovacion y Universidades/Agencia Estatal de Investigacion (MCIN/AEI/10.13039/501100011033 under grant RTI2018-094357-B-C21).Mercado Montoya, M.; Gomez Bustamante, T.; Berjano, E.; Mickelsen, SR.; Daniels, JD.; Hernández Arango, P.; Schieber, J.... (2022). Proactive esophageal cooling protects against thermal insults during high-power short-duration radiofrequency cardiac ablation. International Journal of Hyperthermia. 39(1):1202-1212. https://doi.org/10.1080/02656736.2022.21218601202121239

Predictions of anisotropic thermal transport in non-linear-non-isothermal polymeric flows

Trabajo presentado en: 90th Annual Meeting of The Society of Rheology, 14 a 18 de ocubre de 2018, HoustonOver the last decades, significant efforts have been dedicated to include more complete rheological constitutive models into finite elements methods to simulate the complex flows in polymer manufacturing. However, while a remarkable portion of these processes are intrinsically non-isothermal, the study and implementation of non-isothermal flows has been very limited. The degree of complexity of such calculations is considerably increased by: 1) the addition to the problem of the energy equation; 2) a strong coupling to the momentum balance due to a highly temperature-dependent rheological behavior and 3) the strong influence that deformation-induced molecular orientation has on the thermo-physical properties of polymeric materials. Experimental evidence has shown that thermal conductivity becomes anisotropic in polymers subjected to deformation. Furthermore, a linear relationship between the thermal conductivity and stress tensors has been found to be universal (i.e. independent of polymer chemistry) and to extend beyond the finite extensibility limit. We make use of molecular simulation techniques to gain insights into the transport mechanisms behind these surprising results. On a more practical level, our work combines the thermal conductivity/stress response with two recent constitutive equations proposed for linear (Rolie Poly) and branched (eXtended Pom-Pom) polymers to venture predictions for the anisotropy in thermal conductivity in a number of interesting flows. These two constitutive models provide accurate descriptions of the available non-linear rheology and thermal transport data. Remarkably, our approach allows implementation of anisotropy in thermal conductivity into finite elements simulations without adding any adjusting parameters to those of the viscoelastic model. Our work represents a first step towards a molecular-to-continuum methodology for the simulation of industrially relevant non-isothermal flows to predict flow characteristics and the material final properties after processingMolecular to Continuum Investigation of Anisotropic Thermal Transport in Polymers “MCIATTP” Project # 750985Horizon 2020, “MCIATTP” Project # 75098

Fluctuating Entanglements in Single-Chain Mean-Field Models

We consider four criteria of acceptability for single-chain mean-field entangled polymer models: consistency with a multi-chain level of description, consistency with nonequilibrium thermodynamics, consistency with the stress-optic rule, and self-consistency between Green–Kubo predictions and linear viscoelastic predictions for infinitesimally driven systems. Each of these topics has been considered independently elsewhere. However, we are aware of no molecular entanglement model that satisfies all four criteria simultaneously. Here we show that an idea from Ronca and Allegra, generalized to arbitrary flows, can be implemented in a slip-link model to create a model that does satisfy all four criteria. Aside from the direct benefits of agreement, the result modifies the relation between the initial relaxation modulus G(0) and the entanglement molecular weight Me. If this implementation is correct, current estimates for Me would require modification that brings their values more in line with estimates based on topological analysis of molecular dynamics simulations

Towards a unified theory for entangled polymers : linear, branched and crosslinked

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