Dissipative structures in shear-thickening complex fluids

Turcio, M.; Chávez, A. E.; López-Aguilar, J. Esteban; Vargas, René O.; Capella, Antonio; Manero, Ο.

doi:10.1063/1.5051768

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…Such a connection might benefit both fields as more involved scenarios are investigated, e.g. coupling to additional degrees of freedom: For models of complex fluids, additional spatial dimensions [135] or coupling to internal structure of the fluid [136,137] can lead to a variety of intricate spatiotemporal patterns; for mass-conserving reaction-diffusion systems, additional components or additional conserved species can equally lead to a broad range of phenomena [28,79,138]. Studying such systems in a phase-space geometric framework offers an exciting new perspective for future research.…”

Section: Topological Equivalence With Shear Banding In Complex Fluidsmentioning

confidence: 99%

Phase-space geometry of mass-conserving reaction-diffusion dynamics

Brauns,

Halatek,

Frey

2018

Preprint

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Experimental studies of protein pattern formation (both in vivo and in vitro) have stimulated new interest in the dynamics of reaction-diffusion systems. However, a comprehensive theoretical understanding of the dynamics of such highly nonlinear, spatially extended systems is still missing. In contrast, for dynamical systems described by ordinary differential equations, major insights can be gained from the geometric analysis of their phase-space structure, and this approach has proven invaluable in shaping our intuition about nonlinear dynamics. Here we show how such an analysis can be generalized to mass-conserving reaction-diffusion (McRD) systems, which are the generic case for intracellular protein pattern-forming systems.We present a comprehensive theory for two-component McRD systems, which serve as paradigmatic minimal systems that encapsulate the core principles and concepts of our framework. The key insight is that shifting local equilibria -controlled by the local mass density -give rise to concentration gradients that drive diffusive redistribution of total density. Thereby local chemical equilibria serve as a 'supporting framework' (referred to as scaffold here) for patterns during their entire dynamics.We show that the reactive nullcline (line of chemical equilibria) and the flux-balance subspace, where the diffusive fluxes are balanced, are the geometric objects that facilitate a full characterization of the reaction-diffusion dynamics in the phase plane of the reaction kinetics. (i) We demonstrate that the lateral instability underlying pattern formation in reaction-diffusion systems ('Turing instability') is a mass-redistribution instability (MRI). The mechanism underlying the emergence of MRIs is a feedback loop between shifting local equilibria and mass redistribution due to gradients induced by the shifting equilibria (mass redistribution cascade). The onset of an MRI is characterized by a simple geometric criterion based on the slope of the reactive nullcline. Whether the onset of MRI is sub-or supercritical is determined by the local curvature of the nullcline. (ii) Beyond the weakly nonlinear analysis, we find that the characteristics and bifurcations of stationary patterns can be graphically determined by a flux-balance construction on the reactive nullcline (akin to the 'common tangent construction' employed to find binodal and spinodal lines for phase separation at thermal equilibrium). (iii) By dissecting the patterns into spatial regions that exhibit characteristic signatures, we provide a complete quantitative characterization of all pattern types in two-component reaction-diffusion systems with mass conservation. Remarkably, our approach unambiguously reveals that excitability is inextricably linked to regional lateral instabilities and can be easily read off the nullcline shape.Taken together, these results demonstrate that phase-space geometry provides the essential elements of a comprehensive theory of pattern formation far beyond the linear regime -the effects of nonlinearities o...

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Section: Topological Equivalence With Shear Banding In Complex Fluidsmentioning

confidence: 99%

Phase-space geometry of mass-conserving reaction-diffusion dynamics

Brauns,

Halatek,

Frey

2018

Preprint

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“…In the last few years, the established view that shear thickening is caused by hydroclusters has been rejected due to recent simulations suggesting that contact forces dominate both in discontinuous and continuous shear thickening (Seto et al, 2013;Mari et al, 2014;Lin et al, 2015). The formation of multiple bands due to a discontinuity in the viscosity is other proposed mechanism in the last years (Vázquez-Quesada et al, 2017;Turcio et al, 2018). According to the complicated mechanism of shear thickening fluids, models which can predict different rheological phenomena are being studied (Manero et al, 2007;Garcia-Rojas et al, 2009).…”

Section: Introductionmentioning

confidence: 99%

New analysis and correlation between steady and oscillatory tests in fumed silica-based shear thickening fluids

Moron

Boada

et al. 2019

Rheol Acta

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In recent years, the non-Newtonian behavior of shear thickening fluids (STFs) has motivated a sharp increase in the number of studies related to their use for engineering applications. For this reason, rheological characterization of STFs is crucial in order to develop and design new devices based on these novel smart fluids. Typically, different experiments have been carried out for the rheological characterization of STFs to prove their shear/strain thickening behavior. In order to find an empirical relationship between steady and oscillatory experiments, the modified Cox-Merz rule has been recently used to correlate the results with enormous controversy between authors due to the disparity in the correlations achieved. In this paper, we present an improvement in the correlation between the results obtained in steady and oscillatory tests in STFs using fumed silica-concentrated suspensions. The proposed method with the use of strain sweep oscillatory tests has improved the correlation in all STF regimes (pre-transition, transition, and post-transition) in comparison with the results obtained using the modified Cox-Merz rule, which uses oscillatory frequency sweep tests. This improvement has been experimentally validated using concentrated colloidal suspensions with different concentrations of fumed silica (from 12.5 wt % to 25 wt %).

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