400 research outputs found
Mobility of Power-law and Carreau Fluids through Fibrous Media
The flow of generalized Newtonian fluids with a rate-dependent viscosity
through fibrous media is studied with a focus on developing relationships for
evaluating the effective fluid mobility. Three different methods have been used
here: i) a numerical solution of the Cauchy momentum equation with the Carreau
or power-law constitutive equations for pressure-driven flow in a fiber bed
consisting of a periodic array of cylindrical fibers, ii) an analytical
solution for a unit cell model representing the flow characteristics of a
periodic fibrous medium, and iii) a scaling analysis of characteristic bulk
parameters such as the effective shear rate, the effective viscosity,
geometrical parameters of the system, and the fluid rheology. Our scaling
analysis yields simple expressions for evaluating the transverse mobility
functions for each model, which can be used for a wide range of medium porosity
and fluid rheological parameters. While the dimensionless mobility is, in
general, a function of the Carreau number and the medium porosity, our results
show that for porosities less than , the dimensionless
mobility becomes independent of the Carreau number and the mobility function
exhibits power-law characteristics as a result of high shear rates at the pore
scale. We derive a suitable criterion for determining the flow regime and the
transition from a constant viscosity Newtonian response to a power-law regime
in terms of a new Carreau number rescaled with a dimensionless function which
incorporates the medium porosity and the arrangement of fibers
Visco-Elasto-Capillary Thinning and Break-Up of Complex Fluids
Submitted to Annual Rheology Reviews, 2005.The progressive break-up of an initially stable fluid column or thread into a
number of smaller droplets is an important dynamical process that impacts many
commercial operations from spraying and atomization of fertilizers and pesticides, to
paint application, roll-coating of adhesives and food processing operations such as
container- and bottle-filling. The progressive thinning of a fluid filament is driven by
capillarity and resisted by inertia, viscosity and additional stresses resulting from the
extensional deformation of the fluid microstructure within the thread. In many
processes of interest the fluid undergoing break-up is non-Newtonian and may contain
dissolved polymer, suspended particles, surfactants or other microstructural
constituents. In such cases the transient extensional viscosity of the fluid plays an
important role in controlling the dynamics of break-up. The intimate connection
between the degree of strain-hardening that develops during free extensional flow and
the dynamical evolution in the profile of a thin fluid thread is also manifested in
heuristic concepts such as âspinnabilityâ, âtackinessâ and âstringinessâ. In this review
we survey recent experimental and theoretical developments in the field of capillarydriven
thinning and break-up with a special focus on how quantitative measurements
of the thinning and rupture processes can be used to quantify the material properties of
the fluid. As a result of the absence of external forcing the dynamics of the necking
process are often self-similar and observations of this âself-thinningâ can be used to
extract qualitative, and even quantitative, measures of the transient extensional
viscosity of a complex fluid.NASA, NSF, Schlumberger Foundatio
Dimensionless Groups For Understanding Free Surface Flows of Complex Fluids
Submitted to Bulletin of the Society of Rheology, May 2005No abstrac
Coupled dynamics of flow, microstructure, and conductivity in sheared suspensions
We propose a model for the evolution of the conductivity tensor for a flowing
suspension of electrically conductive particles. We use discrete particle
numerical simulations together with a continuum physical framework to construct
an evolution law for the suspension microsutructure during flow. This model is
then coupled with a relationship between the microstructure and the electrical
conductivity tensor. The parameters of the joint model are fit experimentally
using rheo- electrical conductivity measurements of carbon black suspensions
under flow over a range of shear rates. The model is applied to the case of
steady shearing as well as time-varying conductivity of unsteady flow
experiments. We find that the model prediction agrees closely with the measured
experimental data in all cases.Comment: 5 pages, 4 figure
Wolfgang von Ohnesorge
This manuscript got started when one of us (G.H.M.) presented a lecture at the Institute of Mathematics and its Applications at the University of Minnesota. The presentation included a photograph of Rayleigh and made frequent mention of the Ohnesorge number. When the other of us (M.R.) enquired about a picture of Ohnesorge, we found out that none were readily available on the web. Indeed, little about Ohnesorge is available from easily accessible public sources. A good part of the reason is certainly that, unlike other ânumbermenâ of fluid mechanics, Ohnesorge did not pursue an academic career. The purpose of this article is to fill the gap and shed some light on the life of Wolfgang von Ohnesorge. We shall discuss the highlights of his biography, his scientific contributions, their physical significance, and their impact today
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