Mixed-mode self-oscillations, stochastic excitability, and coherence resonance in flows of highly concentrated suspensio
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ORIGINAL PAPER
Mixed-mode self-oscillations, stochastic excitability, and coherence resonance in flows of highly concentrated suspensions Irina Bashkirtseva · Lev Ryashko
Received: 5 March 2020 / Accepted: 13 October 2020 © Springer Nature B.V. 2020
Abstract Complex mixed-mode oscillatory regimes in flows of concentrated suspensions are studied on the base of the nonlinear dynamical model. A mechanism of the generation of such regimes is associated with the N-shaped flow curve which reflects the dependence of the shear rate on the shear stress. In the zone of the unstable equilibria, amplitude and frequency characteristics of mixed-mode self-sustained oscillations are investigated. A transformation of quasi-harmonic oscillations to non-harmonic ones under increase of the stiffness of the flow curve is discussed. In the zone of the stable equilibria, a phenomenon of stochastic excitement of spike oscillations is studied by the analytical stochastic sensitivity method along with direct numerical simulations. For these mixed-mode stochastic oscillations, a parametric analysis of statistics of interspike intervals is carried out and a phenomenon of coherence resonance is discussed. Keywords Mixed-mode oscillations · Concentrated suspensions · Excitability · Stochastic sensitivity · Coherence resonance
I. Bashkirtseva · L. Ryashko (B) Ural Federal University, Lenina, 51, Yekaterinburg, Russia 620000 e-mail: [email protected] I. Bashkirtseva e-mail: [email protected]
1 Introduction Complex fluids, such as particulate suspensions, surfactant solutions, and polymer solutions play an important role in many industrial, geotechnical, and biological processes. The nonlinear dynamic behavior of such fluids is the subject of intensive study by physicists and engineers [14,19,30]. Unexpected and often counterintuitive transitions from steady states to complex oscillatory regimes in hard-particle suspensions have been observed in many experiments [2,9,16,18]. It was found that such transformations of dynamics are commonly associated with the phenomenon of shear thickening, namely the increase of viscosity with the increase of shear rate [10,21,24,32]. The phenomenon of shear thickening was connected with a specific nonlinear N-shape of the flow curve [6,20] and attributed to hysteresis [11,26]. In the parametric zone between extrema of N-shaped flow curve, the flow is unstable [25]. Such instability is a prime reason of appearance of self-sustained oscillations. To explain such nonlinear oscillations observed in experiments, in the paper [6], a mathematical model taking into account N-shape of the rheological curve has been proposed. The aim of the present paper is to study a variability of mixed-mode oscillations in framework of this model, including those caused by random perturbations. In Sect. 2, we give a short description of the idealized rheophysical model of the suspension flow in a planar gap between two parallel planes lower of
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which is fixed while a constant shear stre
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