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

Bouchendouka, Abdellah; Fellah, Zine El Abiddine; Larbi, Zakaria; Ongwen, Nicholas O.; Ogam, Erick; Fellah, M.; Dépollier, Claude

doi:10.3390/fractalfract6100582

Cited by 7 publications

(4 citation statements)

References 49 publications

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“…A very important aspect to point out is that the velocity distribution ( 28), the fluid discharge (35), and the friction factor (43) are new expressions that contain fractal dimensions, which are theoretically based. These new expressions are very interesting because they can prove useful in the prediction of the behavior of complex fluids that are in contact with a surface that present an irregular pattern.…”

Section: Resultsmentioning

confidence: 99%

“…A study was recently carried out on the flow of a self-similar, non-Newtonian fluid through a cylindrical pipe. The results showed the effect of the self-similar structure on the rheological behavior of the non-Newtonian fluid [43]. Another study [44] looked at the impact of surface roughness on the flow of a viscous non-Newtonian fluid, using surface fractal dimensions to model the roughness.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Resultsmentioning

confidence: 99%

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

Self Cite

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“…This advancement in generalizing differential vector operators to non-integer dimensions supports the use of continuous models for fractal media in NIDS [13,14]. The NIDS calculus developed from this allows for the description of both isotropic and anisotropic fractal media, and has been instrumental in advancing the study of fractal hydrodynamics [15,16,17,18,19], fractal electrodynamics, the elasticity of fractal materials, and acoustics of fractal porous media [20,21,22]. This study aims to apply the NIDS operators referenced in prior research to model ultrasonic wave propagation through a fractal porous medium.…”

Section: Introductionmentioning

confidence: 83%

Non-Integer Dimensional Analysis of Ultrasonic Wave Propagation in Fractal Porous Media

Bouchendouka,

Fellah,

Ogam

et al. 2024

J. Phys.: Conf. Ser.

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This paper explores the acoustics of porous media characterized by fractal, or self-similar, structures. Employing a fractal approach, we use differential operators in non-integer dimensional spaces to address the fundamental equations of acoustics in such media. The primary aim is to examine the transmission of ultrasonic waves within a fractal porous medium. Our findings reveal that the fractal dimension significantly influences wave transmission. In fractal porous materials, waves travel along more complex and intricate paths, resulting in increased tortuosity and attenuation. We introduce the concept of an effective path length leff , which is dependent on the fractal dimension Dx , to describe the actual trajectory of wave propagation. Additionally, we define an effective tortuosity αDx , directly proportional to l e f f 2 , to quantify the additional tortuosity brought about by the fractal structure. The insights gained from this study are crucial, as they enhance our understanding of wave behavior in self-similar porous media, which are prevalent in various natural settings and have multiple practical applications, including sound insulation and the design of acoustic materials. Furthermore, understanding the impact of fractal dimensions on wave behavior is vital for developing more efficient acoustic solutions. This research also sets the stage for further theoretical and experimental work on applying fractal geometry to analyze wave propagation in porous structures.

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“…Chan et al [19] proposed that the Weierstrass-Mandelbrot function can be used to adopt self-affine roughness almost at full scale. By studying the flow characteristics of non-Newtonian fluids through cylindrical pipes with self-similar wall roughness characteristics, Bouchendouka et al [20] proposed the influence of self-similar structures on the rheological behavior of non-Newtonian fluids. Correspondingly, there is another similar work, which describes the roughness of pipe walls by fractal dimension, and analyzes the influence of roughness on the flow characteristics of non-Newtonian fluids [21].…”

Section: Introductionmentioning

confidence: 99%

A Simplified Lattice Boltzmann Boundary Conditions for Gas Transport in Self-Affine Microchannels with an Inherent Roughness of in a Tight Reservoir

Wang

Liu

et al. 2023

Fractal Fract

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A simplified method of determining lattice Boltzmann boundary conditions based on self-affine microchannels with an inherent roughness in a tight reservoir is presented in this paper to address nonlinear efficiency problems in fluid simulation. This approach effectively combines the influence of rough surfaces in the simulation of the flow field, the description of L-fractal theory applied to rough surfaces, and a generalized lattice Boltzmann method with equivalent composite slip boundary conditions for inherent roughness. The numerical simulations of gas slippage in a two-dimensional plate model and rough surfaces to induce gas vortex reflux flow are also successfully carried out, and the results are in good agreement with the simulation results, which establishes the reliability and flexibility of the proposed simplified method of rough surfaces. The effects of relative average height and fractal dimensions of the rough surfaces under exact boundary conditions and equivalent coarsened ones are investigated from three perspectives, namely those of the average lattice velocity, the lattice velocity at average height position at the outlet, and the coefficient of variation for lattice velocity at average height position. It was found that the roughness effect on gas flow behavior was more obvious when it was associated with the enhanced rarefaction effect. In addition, the area of gas seepage was reduced, and the gas flow resistance was increased. When the fractal dimension of the wall was about 1.20, it has the greatest impact on the fluid flow law. In addition, excessive roughness of the wall surface tends to lead to vortex backflow of the gas in the region adjacent to the wall, which greatly reduces its flow velocity. For gas flow in the nanoscale seepage space, wall roughness hindered gas migration rate by 84.7%. For pores larger than 200 nm, the effects of wall roughness on gas flow are generally negligible.

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

Cited by 7 publications

References 49 publications

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

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

Non-Integer Dimensional Analysis of Ultrasonic Wave Propagation in Fractal Porous Media

A Simplified Lattice Boltzmann Boundary Conditions for Gas Transport in Self-Affine Microchannels with an Inherent Roughness of in a Tight Reservoir

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