High-frequency effective viscosity of a dilute suspension of particles in Poiseuille flow between parallel walls

2016 ◽  
Vol 800 ◽  
pp. 111-139
Author(s):  
François Feuillebois ◽  
Maria L. Ekiel-Jeżewska ◽  
Eligiusz Wajnryb ◽  
Antoine Sellier ◽  
Jerzy Bławzdziewicz
Keyword(s):  
Aspect Ratio ◽  
Intrinsic Viscosity ◽  
Poiseuille Flow ◽  
High Frequency ◽  
Effective Viscosity ◽  
Volume Fraction ◽  
Positive Contribution ◽  
Important Conclusion ◽  
Dilute Suspension ◽  
Quadrupole Term

It is shown that the formal expression for the effective viscosity of a dilute suspension of arbitrary-shaped particles in Poiseuille flow contains a novel quadrupole term, besides the expected stresslet. This term becomes important for a very confined geometry. For a high-frequency flow field (in the sense used in Feuillebois et al. (J. Fluid Mech., vol. 764, 2015, pp. 133–147), the suspension rheology is Newtonian at first order in volume fraction. The effective viscosity is calculated for suspensions of $N$-bead rods and of prolate spheroids with the same length, volume and aspect ratio (up to 6), entrained by the Poiseuille flow between two infinite parallel flat hard walls. The numerical computations, based on solving the Stokes equations, indicate that the quadrupole term gives a significant positive contribution to the intrinsic viscosity $[{\it\mu}]$ if the distance between the walls is less than ten times the particle width, or less. It is found that the intrinsic viscosity in bounded Poiseuille flow is generally smaller than the corresponding value in unbounded flow, except for extremely narrow gaps when it becomes larger because of lubrication effects. The intrinsic viscosity is at a minimum for a gap between walls of the order of 1.5–2 particle width. For spheroids, the intrinsic viscosity is generally smaller than for chains of beads with the same aspect ratio, but when normalized by its value in the bulk, the results are qualitatively the same. Therefore, a rigid chain of beads can serve as a simple model of an orthotropic particle with a more complicated shape. The important conclusion is that the intrinsic viscosity in shear flow is larger than in the Poiseuille flow between two walls, and the difference is significant even for relatively wide channels, e.g. three times wider than the particle length. For such confined geometries, the hydrodynamic interactions with the walls are significant and should be taken into account.

High-frequency viscosity of a dilute suspension of elongated particles in a linear shear flow between two walls

2014 ◽  
Vol 764 ◽  
pp. 133-147 ◽  
Author(s):  
François Feuillebois ◽  
Maria L. Ekiel-Jeżewska ◽  
Eligiusz Wajnryb ◽  
Antoine Sellier ◽  
Jerzy Bławzdziewicz
Keyword(s):  
Aspect Ratio ◽  
Shear Flow ◽  
Intrinsic Viscosity ◽  
Effective Viscosity ◽  
Geometric Constraints ◽  
Particle Orientation ◽  
Hydrodynamic Coupling ◽  
Linear Shear ◽  
Dilute Suspension ◽  
Particle Length

AbstractA general expression for the effective viscosity of a dilute suspension of arbitrary-shaped particles in linear shear flow between two parallel walls is derived in terms of the induced stresslets on particles. This formula is applied to $N$-bead rods and to prolate spheroids with the same length, aspect ratio and volume. The effective viscosity of non-Brownian particles in a periodic shear flow is considered here. The oscillating frequency is high enough for the particle orientation and centre-of-mass distribution to be practically frozen, yet small enough for the flow to be quasi-steady. It is known that for spheres, the intrinsic viscosity $[{\it\mu}]$ increases monotonically when the distance $H$ between the walls is decreased. The dependence is more complex for both types of elongated particles. Three regimes are theoretically predicted here: (i) a ‘weakly confined’ regime (for $H>l$, where $l$ is the particle length), where $[{\it\mu}]$ is slightly larger for smaller $H$; (ii) a ‘semi-confined’ regime, when $H$ becomes smaller than $l$, where $[{\it\mu}]$ rapidly decreases since the geometric constraints eliminate particle orientations corresponding to the largest stresslets; (iii) a ‘strongly confined’ regime when $H$ becomes smaller than 2–3 particle widths $d$, where $[{\it\mu}]$ rapidly increases owing to the strong hydrodynamic coupling with the walls. In addition, for sufficiently slender particles (with aspect ratio larger than 5–6) there is a domain of narrow gaps for which the intrinsic viscosity is smaller than that in unbounded fluid.

scholarly journals Flow Velocity and Effective Viscosity of a Fluid Containing Rigid Cylindrical Inclusions

2005 ◽  
Vol 60 (6) ◽  
pp. 401-407 ◽  
Author(s):  
Siegfried Hess
Keyword(s):  
Effective Viscosity ◽  
Volume Fraction ◽  
Dimensional Problem ◽  
Flow Properties ◽  
Cylindrical Inclusions ◽  
Dilute Suspension ◽  
Oriented Parallel ◽  
Relative Change ◽  
Special Case

The determination of the flow properties of a fluid containing a cylindrical inclusion with its long axis oriented parallel to the vorticity direction is a 2-dimensional problem which is treated as a special case in a calculation of the corresponding D-dimensional problem. The velocity and pressure are obtained from the solution of the equations of hydrodynamics where D-dimensional multipole potential tensors are used. The effective viscosity of a dilute suspension is evaluted via the entropy production, as suggested by Einstein, and via an effective stress tensor. The relative change of the viscosity is proportional to the volume fraction. For D = 2 the proportionality factor Z is found to be 2 and 3 when the inclusion rotates with an angular velocity equal to the vorticity and when the inclusion does not rotate, repectively. The corresponding results for D=3 are the well known number Z = 2.5 and Z = 4.

Stability of plane Poiseuille flow of a dilute suspension of slender fibres

1978 ◽  
Vol 87 (2) ◽  
pp. 321-333 ◽  
Author(s):  
Fritz H. Bark ◽  
Hernán Tinoco
Keyword(s):  
Poiseuille Flow ◽  
Critical Reynolds Number ◽  
Volume Fraction ◽  
Plane Poiseuille Flow ◽  
Mean Flow ◽  
Initial Value ◽  
Large Wave ◽  
Inclination Angles ◽  
Dilute Suspension ◽  
The Mean

The linear hydrodynamic stability problem for plane Poiseuille flow of a dilute suspension of rigid fibres is solved numerically. The constitutive equation given by Batchelor (1970a, b, 1971) is used to model the rheological properties of the suspension. The resulting eigenvalue problem is shown to be singular. The appropriate contour in the complex plane is determined by considering an initial-value problem. It is shown that, for a fixed, but not too large, inclination of the wave front to the mean flow, the fibres cause the critical Reynolds number to increase monotonically with the product of the volume fraction of the fibres and the square of their aspect ratio. The stabilizing influence of the fibres seems to vanish for large wave inclination angles.

scholarly journals Jet Impingement Heat Transfer of Confined Single and Double Jets with Non-Newtonian Power Law Nanofluid under the Inclined Magnetic Field Effects for a Partly Curved Heated Wall

2021 ◽  
Vol 13 (9) ◽  
pp. 5086
Author(s):  
Fatih Selimefendigil ◽  
Hakan F. Oztop ◽  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Particle Size ◽  
Aspect Ratio ◽  
Power Law ◽  
Volume Fraction ◽  
Inclined Magnetic Field ◽  
Magnetic Field Effects ◽  
Power Law Nanofluid ◽  
Power Law Index

Single and double impinging jets heat transfer of non-Newtonian power law nanofluid on a partly curved surface under the inclined magnetic field effects is analyzed with finite element method. The numerical work is performed for various values of Reynolds number (Re, between 100 and 300), Hartmann number (Ha, between 0 and 10), magnetic field inclination (γ, between 0 and 90), curved wall aspect ratio (AR, between 01. and 1.2), power law index (n, between 0.8 and 1.2), nanoparticle volume fraction (ϕ, between 0 and 0.04) and particle size in nm (dp, between 20 and 80). The amount of rise in average Nusselt (Nu) number with Re number depends upon the power law index while the discrepancy between the Newtonian fluid case becomes higher with higher values of power law indices. As compared to case with n = 1, discrepancy in the average Nu number are obtained as −38% and 71.5% for cases with n = 0.8 and n = 1.2. The magnetic field strength and inclination can be used to control the size and number or vortices. As magnetic field is imposed at the higher strength, the average Nu reduces by about 26.6% and 7.5% for single and double jets with n greater than 1 while it increases by about 4.78% and 12.58% with n less than 1. The inclination of magnetic field also plays an important role on the amount of enhancement in the average Nu number for different n values. The aspect ratio of the curved wall affects the flow field slightly while the average Nu variation becomes 5%. Average Nu number increases with higher solid particle volume fraction and with smaller particle size. At the highest particle size, it is increased by about 14%. There is 7% variation in the average Nu number when cases with lowest and highest particle size are compared. Finally, convective heat transfer performance modeling with four inputs and one output is successfully obtained by using Adaptive Neuro-Fuzzy Interface System (ANFIS) which provides fast and accurate prediction results.

scholarly journals Modelling the Molecular Permeation through Mixed-Matrix Membranes Incorporating Tubular Fillers

Membranes ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 58
Author(s):  
Ali Zamani ◽  
F. Handan Tezel ◽  
Jules Thibault
Keyword(s):  
Aspect Ratio ◽  
Relative Permeability ◽  
Polymer Matrix ◽  
Volume Fraction ◽  
Mixed Matrix Membranes ◽  
Analytical Prediction ◽  
Mixed Matrix ◽  
Permeability Ratio ◽  
Filler Volume Fraction ◽  
Matrix Membranes

Membrane-based processes are considered a promising separation method for many chemical and environmental applications such as pervaporation and gas separation. Numerous polymeric membranes have been used for these processes due to their good transport properties, ease of fabrication, and relatively low fabrication cost per unit membrane area. However, these types of membranes are suffering from the trade-off between permeability and selectivity. Mixed-matrix membranes, comprising a filler phase embedded into a polymer matrix, have emerged in an attempt to partly overcome some of the limitations of conventional polymer and inorganic membranes. Among them, membranes incorporating tubular fillers are new nanomaterials having the potential to transcend Robeson’s upper bound. Aligning nanotubes in the host polymer matrix in the permeation direction could lead to a significant improvement in membrane permeability. However, although much effort has been devoted to experimentally evaluating nanotube mixed-matrix membranes, their modelling is mostly based on early theories for mass transport in composite membranes. In this study, the effective permeability of mixed-matrix membranes with tubular fillers was estimated from the steady-state concentration profile within the membrane, calculated by solving the Fick diffusion equation numerically. Using this approach, the effects of various structural parameters, including the tubular filler volume fraction, orientation, length-to-diameter aspect ratio, and permeability ratio were assessed. Enhanced relative permeability was obtained with vertically aligned nanotubes. The relative permeability increased with the filler-polymer permeability ratio, filler volume fraction, and the length-to-diameter aspect ratio. For water-butanol separation, mixed-matrix membranes using polydimethylsiloxane with nanotubes did not lead to performance enhancement in terms of permeability and selectivity. The results were then compared with analytical prediction models such as the Maxwell, Hamilton-Crosser and Kang-Jones-Nair (KJN) models. Overall, this work presents a useful tool for understanding and designing mixed-matrix membranes with tubular fillers.

scholarly journals A Micro-mechanical Investigation of Empirical Models for the Effective Properties of Aligned Short-Fibre Composites

1995 ◽  
Vol 4 (1) ◽  
pp. 096369359500400
Author(s):  
T.D. Papathanasiou
Keyword(s):  
Aspect Ratio ◽  
Volume Fraction ◽  
Tensile Modulus ◽  
Fibre Volume ◽  
Short Fibre ◽  
Computational Results ◽  
Volume Fractions ◽  
Fibre Composites ◽  
Effective Tensile Modulus ◽  
Fibre Aspect Ratio

The predictions of the Halpin equation concerning the effect of fibre volume fraction and fibre aspect ratio on the effective tensile modulus of uniaxially aligned short-fibre composites are compared with computational experiments on three-dimensional, multiparticle composite samples. The method of boundary elements is used to model the mechanical behaviour of composite specimens consisting of up to 40 discrete aligned fibres randomly dispersed in an elastic matrix. Statistical averages of computational results relating the effective tensile modulus to the aspect ratio and volume fraction of the fibres are found to agree very well with the predictions of the Halpin equation for fibre aspect ratio up to 10 and fibre volume fractions up to 20%. Computational results seem to indicate that the predictions of the Halpin equation fall bellow those of micro-mechanical models at higher volume fractions.

A Novel Gap Narrowing Process for Creating High Aspect Ratio Transduction Gaps for MEM HF Resonators

2008 ◽  
Vol 1139 ◽  
Author(s):  
Steve Stoffels ◽  
George Bryce ◽  
Rita Van Hoof ◽  
Bert Du Bois ◽  
Robert Mertens ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Silicon Germanium ◽  
High Frequency ◽  
Air Gaps ◽  
Processing Step ◽  
Process Methodology ◽  
Thick Layers ◽  
Validation Experiments ◽  
Structural Layer

AbstractIn this work a novel technique to create nanometer sized air gaps for high frequency (HF) mechanical resonators will be presented. The technique is based on the narrowing of initially wide gaps with a conformal “narrowing” layer. The novelty of this technique is that it enables the creation of narrow high-aspect ratio gaps (e.g. 100nm gaps in 10μm thick layers) without the need for complex lithography or high aspect ratio etching. Furthermore, the electrodes and the resonator itself can be patterned in a single processing step. The process methodology will be explained and validation experiments in a silicon-germanium (SiGe) based technology will be shown. This technology uses low temperature (∼450°C) poly silicon-germanium (SiGe) as the structural layer, which can be processed above CMOS, and therefore allows the fabrication of MEM devices above CMOS.

FABRICATION OF ARRAY MICROSTRUCTURES USING SERIAL AND PARALLEL LOCALIZED ELECTRODEPOSITION

2009 ◽  
Vol 08 (03) ◽  
pp. 323-332 ◽  
Author(s):  
RA'A SAID ◽  
NIDAL ALSHWAWREH ◽  
YOUSEF HAIK
Keyword(s):  
Tissue Engineering ◽  
Aspect Ratio ◽  
Antenna Arrays ◽  
High Aspect Ratio ◽  
High Frequency ◽  
Neural Recording ◽  
Single Step ◽  
Fabrication Technique ◽  
Ultra High Frequency

To add to the development efforts in enhancing the capabilities of localized electrodeposition (LED) fabrication technique, this paper presents serial and parallel deposition algorithms to fabricate array microstructures. Such arrays can be implemented as microsensors in neural recording applications or as antenna arrays in ultra high frequency applications. Also, magnetic tip microarrays for tissue engineering can be realized. In the case of serial fabrication, an array of high aspect ratio microstructures is realized using the conventional single-tip microelectrode while implementing a multistep fabrication algorithm. In this algorithm, the fabricated microstructure elements within the array are realized one at a time. In the parallel deposition algorithm, the array is realized using a multitip array microelectrode while implementing a single step fabrication algorithm. In this algorithm, the microstructure elements within the array are fabricated simultaneously. The proposed algorithms are compared through a demonstration of fabricated array microstructures.

Nanoparticles-Laden Gas Film in Aerostatic Thrust Bearing

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Zhiru Yang ◽  
Dongfeng Diao ◽  
Xue Fan ◽  
Hongyan Fan
Keyword(s):  
Effective Viscosity ◽  
Flow Model ◽  
Thrust Bearing ◽  
Volume Fraction ◽  
Load Capacity ◽  
Sio2 Nanoparticles ◽  
Enhancement Effect ◽  
The Novel ◽  
Two Phase ◽  
Air Film

Nanoparticles-laden gas film (NLGF) was formed by adding SiO2 nanoparticles with volume fraction in the range of 0.014–0.330% and size of 30 nm into the air gas film in a thrust bearing. An effective viscosity of the gas-solid two phase lubrication media was introduced. The pressure distribution in NLGF and the load capacity of the thrust bearing were calculated by using the gas-solid two phase flow model with the effective viscosity under the film thicknesses range of 15–60 μm condition. The results showed that the NLGF can increase the load capacity when the film thickness is larger than 30 μm. The mechanism of the enhancement effect of load capacity was attributed to the increase of the effective viscosity of the NLGF from the pure air film, and the novel lubrication media of the NLGF can be expected for the bearing industry application.

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