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 $\varepsilon\simeq0.65$, 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 âspinnability’, âtackiness’ and âstringiness’. 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-thinning’ 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

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 “numbermen” 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

High-flux magnetorheology at elevated temperatures

Commercial applications of magnetorheological (MR) fluids often require operation at elevated temperatures as a result of surrounding environmental conditions or intense localized viscous heating. Previous experimental investigations of thermal effects on MR fluids have reported significant reductions in the magnetorheological stress with increasing temperature, exceeding the predictions made by considering the thermal variations in the individual physical properties of the fluid and solid constituents of a typical MR fluid. In the low-flux regime, designers of MR fluid actuators can alleviate this thermal reduction in stress by increasing the applied magnetic field strength. However, this is not possible in the high-flux regime because of magnetic saturation, and it becomes necessary to explore and understand the intrinsic limitations of the fluid at elevated temperature. We describe a new magnetorheological fixture, which was designed as an accessory to a commercial torsional shear rheometer, capable of applying magnetic flux densities up to 1 T and controlling the sample temperature up to 150°C. During the design of the instrument, close attention was given to the uniformity of the magnetic field applied to the sample by using numerical simulations. Incorporation of a custom-built magnetic flux sensor which matches the environmental capabilities of the fixture enables in situ measurement of the local magnetic field at each temperature. The numerical results are also validated by spatially resolved measurements of the local magnetic field. Finally, we explore the ability of a shift factor between fluid magnetization and yield strength to describe the measured variation in the MR fluid response at elevated temperatures

Modeling the shear and extensional rheology of saliva and mucin hydrogels using a sticky gel network model

There is increasing interest in using rheological measurements of saliva and other bodily secretions such as cervical and respiratory mucus as non-invasive diagnostics for pathology and disease. However, there is only limited literature available on the shear and extensional rheology of saliva, and nearly no consideration of its temporal stability in the face of biological degradation. Indeed, capillary breakup extensional rheometry (CaBER) data of saliva samples at various ages shows that both the time to breakup and relaxation time of these highly elastic but low viscosity aqueous solutions decrease as a function of age. The viscoelastic properties of saliva can primarily be attributed to the presence of large glycoproteins (MUC5B mucins) in solution. It is well known that these ‘MUCmers’ physically associate and interact with each other and their surroundings via ion-mediated crosslinking and hydrogen bonding interactions to form a weak hydrogel or ‘pre-gel’. This motivates the development of a Sticky Network model for mucin-containing solutions, building on earlier work of Tripathi et al for synthetic HEUR associative polymer systems. The mucin macromolecules are modeled as a semi-dilute and semi-flexible network of physically-associated finitely extensible elastic segments with a stretch-dependent ‘stickiness’ energy parameter that must be overcome in order for the chains to be able to reversibly dissociate from the rest of the network under imposed deformation. We show that this model is able to accurately capture capillary thinning and filament rupture behaviour of saliva using biologically-derived parameters, and can systematically account for temporal changes in the rheology through a progressive decrease in the molecular weight of the MUC5B chains. To probe the role of the different association mechanisms in the network we construct a series of model mucopolysaccharide hydrogels using purified MUC2 and MUC5 mucins in aqueous solution, We characterize the linear and nonlinear rheology of these physically-associated networks and show that their linear viscoelastic properties are characterized by broad power-law relaxation characteristics. To demonstrate the very wide range of time-scales and length-scales that characterize the different network interactions present in these hydrogels we use a series of additives (low-molecular weight surfactants, salt and reducing agents such as acetylcysteine) to respectively disrupt the hydrophobic, ionic and disulphide interactions between the MUCmers that form the hydrogel network

Microfluidic rheometry

The development and growth of microfluidics has stimulated interest in the behaviour of complex liquids in micro-scale geometries and provided a rich platform for rheometric investigations of non-Newtonian phenomena at small scales. Microfluidic techniques present the rheologist with new opportunities for material property measurement and this review discusses the use of microfluidic devices to measure bulk rheology in both shear and extensional flows. Capillary, stagnation and contraction flows are presented in this context and developments, limitations and future perspectives are examined

A comprehensive constitutive law for waxy crude oil: a thixotropic yield stress fluid

Guided by a series of discriminating rheometric tests, we develop a new constitutive model that can quantitatively predict the key rheological features of waxy crude oils. We first develop a series of model crude oils, which are characterized by a complex thixotropic and yielding behavior that strongly depends on the shear history of the sample. We then outline the development of an appropriate preparation protocol for carrying out rheological measurements, to ensure consistent and reproducible initial conditions. We use RheoPIV measurements of the local kinematics within the fluid under imposed deformations in order to validate the selection of a particular protocol. Velocimetric measurements are also used to document the presence of material instabilities within the model crude oil under conditions of imposed steady shearing. These instabilities are a result of the underlying non-monotonic steady flow curve of the material. Three distinct deformation histories are then used to probe the material's constitutive response. These deformations are steady shear, transient response to startup of steady shear with different aging times, and large amplitude oscillatory shear (LAOS). The material response to these three different flows is used to motivate the development of an appropriate constitutive model. This model (termed the IKH model) is based on a framework adopted from plasticity theory and implements an additive strain decomposition into characteristic reversible (elastic) and irreversible (plastic) contributions, coupled with the physical processes of isotropic and kinematic hardening. Comparisons of experimental to simulated response for all three flows show good quantitative agreement, validating the chosen approach for developing constitutive models for this class of materials.Chevron Corporatio

The Extensional Rheology of Non-Newtonian Materials

The evolution of the transient extensional stresses in dilute and semi-dilute viscoelastic polymer solutions are measured with a filament stretching rheometer of a design similar to that first introduced by Sridhar, et al. The solutions are polystyrene-based (PS) Boger fluids that are stretched at constant strain rates ranging from 0.6 less than or equal to epsilon(0) less than or equal to 4s(exp -1) and to Hencky strains of epsilon greater than 4. The test fluids all strain harden and Trouton ratios exceeding 1000 are obtained at high strains. The experimental data strain hardens at lower strain levels than predicted by bead-spring FENE models. In addition to measuring the transient tensile stress growth, we also monitor the decay of the tensile viscoelastic stress difference in the fluid column following cessation of uniaxial elongation as a function of the total imposed Hencky strain and the strain rate. The extensional stresses initially decay very rapidly upon cessation of uniaxial elongation followed by a slower viscoelastic relaxation, and deviate significantly from FENE relaxation predictions. The relaxation at long times t is greater than or equal to 5 s, is compromised by gravitational draining leading to non-uniform filament profiles. For the most elastic fluids, partial decohension of the fluid filament from the endplates of the rheometer is observed in tests conducted at high strain rates. This elastic instability is initiated near the rigid endplate fixtures of the device and it results in the progressive breakup of the fluid column into individual threads or 'fibrils' with a regular azimuthal spacing. These fibrils elongate and bifurcate as the fluid sample is elongated further. Flow visualization experiments using a modified stretching device show that the instability develops as a consequence of an axisymmetry-breaking meniscus instability in the nonhomogeneous region of highly deformed fluid near the rigid endplate