Viscous Flow

Ockendon, H.; Ockendon, J. R.

doi:10.1017/cbo9781139174206

Cited by 150 publications

(95 citation statements)

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“…No slip boundary conditions are applied at the surface of the sphere and plane and we assume the squeeze flow rates to be slow enough so that we may neglect inertia of the fluid and we further assume that a quasi-steady state exists at each time step as the sphere approaches the wall (see also Shuler and Advani 18 who considered a similar scenario for the flow between two plates). During the initial stages of penetration the impact Reynolds number, Re = ρ R 0 V 0 /μ 0 , based on 19 ) and this quantity is indeed small at this initial stage and becomes smaller as the sphere penetrates the film. Thus inertial effects are neglected in this work.…”

Section: Theory a Model Formulationmentioning

confidence: 92%

Squeeze flow of a Carreau fluid during sphere impact

2012

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Articles you may be interested inWe present results from a combined numerical and experimental investigation into the squeeze flow induced when a solid sphere impacts onto a thin, ultra-viscous film of non-Newtonian fluid. We examine both the sphere motion through the liquid as well as the fluid flow field in the region directly beneath the sphere during approach to a solid plate. In the experiments we use silicone oil as the model fluid, which is welldescribed by the Carreau model. We use high-speed imaging and particle tracking to achieve flow visualisation within the film itself and derive the corresponding velocity fields. We show that the radial velocity either diverges as the gap between the sphere and the wall diminishes (Z tip → 0) or that it reaches a maximum value and then decays rapidly to zero as the sphere comes to rest at a non-zero distance (Z tip = Z min ) away from the wall. The horizontal shear rate is calculated and is responsible for significant viscosity reduction during the approach of the sphere. Our model of this flow, based on lubrication theory, is solved numerically and compared to experimental trials. We show that our model is able to correctly describe the physical features of the flow observed in the experiments. C 2012 American Institute of Physics. [http://dx

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Section: Theory a Model Formulationmentioning

confidence: 92%

Squeeze flow of a Carreau fluid during sphere impact

2012

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“…The flow rate through a given pore (i, j) in layer k at timet,q (i,j) k (t), is given by Poiseuille's law [16],…”

Section: Mathematical Modelmentioning

confidence: 99%

Designing asymmetric multilayered membrane filters with improved performance

Griffiths¹,

Kumar

Stewart

2016

Journal of Membrane Science

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Asymmetric multilayered filters, comprising a series of membranes with varying pore sizes stacked on top of one another, allow filtration to be tailored in a variety of novel ways. We develop a network model that systematically captures the complex filtration behaviour in such multilayer filters. The model allows us to understand the response of the system when challenged with a particular feed composition, characterized through the particle size and adhesivity to the membrane. We show how the model enables comprehensive and time-efficient sweeps in parameter space to be conducted that determine the optimal mulilayered filter configuration for a given filtration challenge, classified by the number of membrane layers, the change in pore size between each layer (filter taper angle), and the level of transpore interconnectivity between each layer. The model allows us to isolate and analyse the effect of each of the specific filter characteristics and identify the practical merits and disadvantages. In particular, we predict that the optimal arrangement for maximizing throughput through the filter is to have pore radius gradually decreasing with depth a slight level of pore interconnectivity, with the precise set-up a function of the particle size, adhesivity and number of filter layers. The results of the analysis are used to draw conclusions on the design of membrane filters for optimal filter performance.

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“…Ockendon and Ockendon, 1995) to neglect inertia and radial pressure gradients. This relies on the reduced Reynolds number Re c being small, a condition we verify in Appendix B.…”

Section: Flow In the Fibre Corementioning

confidence: 99%

Mathematical modelling of fibre-enhanced perfusion inside a tissue-engineering bioreactor

Whittaker

Booth

Dyson

et al. 2009

Journal of Theoretical Biology

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We develop a simple mathematical model for forced flow of culture medium through a porous scaffold in a tissue engineering bioreactor. Porous-walled hollow fibres penetrate the scaffold and act as additional sources of culture medium. The model, based on Darcy's law, is used to examine the nutrient and shear stress distributions throughout the scaffold. We consider several configurations of fibres and inlet and outlet pipes. Compared with a numerical solution of the full Navier-Stokes equations within the complex scaffold geometry, the modelling approach is cheap, and does not require knowledge of the detailed microstructure of the particular scaffold being used. The potential of this approach is demonstrated through quantification of the effect the additional flow from the fibres has on the nutrient and shear-stress distribution.

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Viscous Flow

Cited by 150 publications

References 0 publications

Squeeze flow of a Carreau fluid during sphere impact

Squeeze flow of a Carreau fluid during sphere impact

Designing asymmetric multilayered membrane filters with improved performance

Mathematical modelling of fibre-enhanced perfusion inside a tissue-engineering bioreactor

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