Viscosity for fractal suspensions: dependence on fractal dimensionality

Shiyan, A. A.

doi:10.1016/0375-9601(96)00479-3

Cited by 5 publications

(3 citation statements)

References 1 publication

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“…However, the same value enables good agreement with data at other frequencies and good agreement with the frequency dependence at a given concentration. Fractal dimensions of steady state suspensions have been determined empirically by measuring PH and thermal di!usion [24,25]. It would be extremely di$cult to employ these techniques on the falling and #owing suspensions considered here because of their transitory nature.…”

Section: Of D!dmentioning

confidence: 99%

Particle Irregularity and Aggregation Effects in Airborne Suspensions at Audio- And Low Ultrasonic Frequencies

Wang

Attenborough

Woodhead

2000

Journal of Sound and Vibration

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Section: Of D!dmentioning

confidence: 99%

Particle Irregularity and Aggregation Effects in Airborne Suspensions at Audio- And Low Ultrasonic Frequencies

Wang

Attenborough

Woodhead

2000

Journal of Sound and Vibration

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“…Fluids and rough surfaces which are the scope of our study also exhibit a self-similar "fractal" structure. Examples of self-similar "fractal" fluids include fractal emulsions in which a fluid is fractally dispersed in another fluid [16], fractal solutions, with a fractal distribution of a solute dissolved in a nonfractal solvent [17], fractal suspensions in which a solid is fractally distributed in a fluid [18]. Several researchers have developed models for examining fractal fluids in noninteger dimensional spaces (NIDS), including Ostoja-Starzewski [19][20][21][22], Balankin [23][24][25], and Tarasov [26,27].…”

Section: Introductionmentioning

confidence: 99%

A Generalization of Poiseuille’s Law for the Flow of a Self-Similar (Fractal) Fluid through a Tube Having a Fractal Rough Surface

et al. 2023

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In this paper, a generalization of Poiseuille’s law for a self-similar fluid flow through a tube having a rough surface is proposed. The originality of this work is to consider, simultaneously, the self-similarity structure of the fluid and the roughness of the tube surface. This study can have a wide range of applications, for example, for fractal fluid dynamics in hydrology. The roughness of the tube surface presents a fractal structure that can be described by the surface fractal noninteger dimensions. Complex fluids that are invariant to changes in scale (self-similar) are modeled as a continuous medium in noninteger dimensional spaces. In this work, the analytical solution of the Navier–Stokes equations for the case of a self-similar fluid flow through a rough “fractal” tube is presented. New expressions of the velocity profiles, the fluid discharge, and the friction factor are determined analytically and plotted numerically. These expressions contain fractal dimensions describing the effects of the fractal aspect of the fluid and of that of the tube surface. This approach reveals some very important results. For the velocity profile to represent a physical solution, the fractal dimension of the fluid ranges between 0.5 and 1. This study also qualitatively demonstrates that self-similar fluids have shear thickening-like behavior. The fractal (self-similarity) nature of the fluid and the roughness of the surface both have a huge impact on the dynamics of the flow. The fractal dimension of the fluid affects the amplitude and the shape of the velocity profile, which loses its parabolic shape for some values of the fluid fractal dimension. By contrast, the roughness of the surface affects only the amplitude of the velocity profile. Nevertheless, both the fluid’s fractal dimension and the surface roughness have a major influence on the behavior of the fluid, and should not be neglected.

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“…The mass of a self-similar fluid obeys the power law M ∝ R D , where M is the mass of a spherical region of the fluid with radius R, and D is the fractal mass dimension. Fractal fluids include solutions containing a fractal distribution of a solute dissolved in a nonfractal solvent [16], emulsions in which one phase is fractally dispersed in the other [17], suspensions in which solid particles are fractally distributed in a liquid [18,19] and classical fluids confined in a fractal configuration space [20]. To explain fractal fluids, there exist four basic ways [21,22]: (a) using the methods of "Analysis on fractals" [23][24][25]; (b) using fractional-differential continuum models [26][27][28][29][30] and also [31][32][33]; (c) applying fractional-integral continuum models [34,35]; and (d) using the theory of integration and differentiation for a noninteger dimensional space [36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Flow of a Self-Similar Non-Newtonian Fluid Using Fractal Dimensions

et al. 2022

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In this paper, the study of the fully developed flow of a self-similar (fractal) power-law fluid is presented. The rheological way of behaving of the fluid is modeled utilizing the Ostwald–de Waele relationship (covering shear-thinning, Newtonian and shear-thickening fluids). A self-similar (fractal) fluid is depicted as a continuum in a noninteger dimensional space. Involving vector calculus for the instance of a noninteger dimensional space, we determine an analytical solution of the Cauchy equation for the instance of a non-Newtonian self-similar fluid flow in a cylindrical pipe. The plot of the velocity profile obtained shows that the rheological behavior of a non-Newtonian power-law fluid is essentially impacted by its self-similar structure. A self-similar shear thinning fluid and a self-similar Newtonian fluid take on a shear-thickening way of behaving, and a self-similar shear-thickening fluid becomes more shear thickening. This approach has many useful applications in industry, for the investigation of blood flow and fractal fluid hydrology.

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Viscosity for fractal suspensions: dependence on fractal dimensionality

Cited by 5 publications

References 1 publication

Particle Irregularity and Aggregation Effects in Airborne Suspensions at Audio- And Low Ultrasonic Frequencies

Particle Irregularity and Aggregation Effects in Airborne Suspensions at Audio- And Low Ultrasonic Frequencies

A Generalization of Poiseuille’s Law for the Flow of a Self-Similar (Fractal) Fluid through a Tube Having a Fractal Rough Surface

Flow of a Self-Similar Non-Newtonian Fluid Using Fractal Dimensions

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