Abstract
The paper proposes a mathematical framework for the use of fractional-order impedance models to capture fluid mechanics properties in frequency-domain experimental datasets. An overview of non-Newtonian (NN) fluid classification is given as to motivate the use of fractional-order models as natural solutions to capture fluid dynamics. Four classes of fluids are tested: oil, sugar, detergent and liquid soap. Three nonlinear identification methods are used to fit the model: nonlinear least squares, genetic algorithms and particle swarm optimization. The model identification results obtained from experimental datasets suggest the proposed model is useful to characterize various degree of viscoelasticity in NN fluids. The advantage of the proposed model is that it is compact, while capturing the fluid properties and can be identified in real-time for further use in prediction or control applications.This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.
Highlights
Most properties of non-Newtonian (NN) fluids overlap with that of viscoelastic materials, such as polymers, lung tissue, gel-like substances, rubber, etc. [1,2]
Creep and shear stress do not follow classical Newton’s Law of Viscosity and has been proven to be well characterized by combinations of power-law and exponential functions [3,4]. These are non-rational expressions of combined nonlinear effects in material creep and strain which have been well characterized by the nonlinear Mittag–Leffler function [5,6,7]. They represent a generalization from integer-order differential equations to fractional-order differential equations
A great advantage of fractional-order impedance models (FOIMs) expressed in Laplace and their equivalent frequency-domain forms is their capability to capture in a compact form complex nonlinear properties and have these identified in a real-time context
Summary
Most properties of non-Newtonian (NN) fluids overlap with that of viscoelastic materials, such as polymers, lung tissue, gel-like substances, rubber, etc. [1,2]. The memory property of such fluids was captured with variations of the fractional order in time [22] Such in-depth theoretical analysis is a solid basis and motivation for using the FOIMs. The term FOIM was coined some decades ago in an application of modelling respiratory tissue properties such as tissue compliance as a function of anatomical and structural changes in respiratory disorders [15]. A great advantage of FOIMs expressed in Laplace and their equivalent frequency-domain forms is their capability to capture in a compact form complex nonlinear properties and have these identified in a real-time context This was previously shown in modelling memory effects in blood [5] and in designing a closed-loop control of suspended objects in a blood-like varying context of viscoelastic fluid properties [26]. The main outcome of this work is summarized in the conclusion
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