Suspension mechanics: I. Inertial and non-Newtonian migration of neutrally buoyant rigid spheres in two-dimensional unidirectional flows; II. The effect of viscoelasticity on the creeping motion of a train of neutrally buoyant Newtonian drops through a circular tube

The lateral migration of neutrally buoyant rigid spheres in two-dimensional unidirectional flows was studied theoretically. The cases of both inertia-induced migration in a Newtonian fluid and normal stress-induced migration in a second-order fluid were considered. Analytical results for the lateral velocities were obtained, and the equilibrium positions and trajectories of the spheres compared favorably with the experimental data available in the literature. The effective viscosity was obtained for a dilute suspension of spheres which were simultaneously undergoing inertia-induced migration and translational Brownian motion in a plane Poiseuille flow. The migration of spheres suspended in a second-order fluid inside a screw extruder was also considered.

The creeping motion of neutrally buoyant concentrically located Newtonian drops through a circular tube was studied experimentally for drops which have an undeformed radius comparable to that of the tube. Both a Newtonian and a viscoelastic suspending fluid were used in order to determine the influence of viscoelasticity. The extra pressure drop due to the presence of the suspended drops, the shape and velocity of the drops, and the streamlines of the flow were obtained for various viscosity ratios, total flow rates, and drop sizes. The results were compared with existing theoretical and experimental data.

Flow of wet powder in a conical centrifugal filter-an analytical model

A one-dimensional analytical model is developed for the steady state, axisymmetric, slender flow of saturated powder in a rotating perforated cone. Both the powder and the fluid spin with the cone with negligible slip in the hoop direction. They migrate up the wall of the cone along a generator under centrifugal force, which also forces the fluid out of the cone through the powder layer and the porous wall. The flow thus evolves from an over-saturated paste at inlet into a nearly dry powder at outlet. The powder is treated as a Mohr-Coulomb granular solid of constant void fraction and permeability. The shear traction at the wall is assumed to be velocity and pressure dependent. The fluid is treated as Newtonian viscous. The model provides the position of the colour line (the transition from over- to under-saturation) and the flow velocity and thickness profiles over the cone. Surface tension effects are assumed negligible compared to the centrifugal acceleration. Two alternative conditions are considered for the flow structure at inlet: fully settled powder at inlet, and progressive settling of an initially homogeneous slurry. The position of the colour line is found to be similar for these two cases over a wide range of operating conditions. Dominant dimensionless groups are identified which control the position of the colour line in a continuous conical centrifuge. Experimental observations of centrifuges used in the sugar industry provide preliminary validation of the model. © 2011 Elsevier Ltd.

Instabilities in the oscillatory flow of a complex fluid.

The dynamics of a fluid in a vertical tube, subjected to an oscillatory pressure gradient, is studied experimentally for both a Newtonian and a viscoelastic shear-thinning fluid. Particle image velocimetry is used to determine the two-dimensional velocity fields in the vertical plane of the tube axis, in a range of driving amplitudes from 0.8 to 2.5 mm and of driving frequencies from 2.0 to 11.5 Hz. The Newtonian fluid exhibits a laminar flow regime, independent of the axial position, in the whole range of drivings. For the complex fluid, instead, the parallel shear flow regime exhibited at low amplitudes [Torralba, Phys. Rev. E 72, 016308 (2005)] becomes unstable at higher drivings against the formation of symmetric vortices, equally spaced along the tube. At even higher drivings the vortex structure itself becomes unstable, and complex nonsymmetric structures develop. Given that inertial effects remain negligible even at the hardest drivings (Re < 10(-1)), it is the complex rheology of the fluid that is responsible for the instabilities observed. The system studied represents an interesting example of the development of shear-induced instabilities in nonlinear complex fluids in purely parallel shear flow.

A comparison of the value of viscosity for several water models using Poiseuille flow in a nano-channel.

The viscosity-temperature relation is determined for the water models SPC/E, TIP4P, TIP4P/Ew, and TIP4P/2005 by considering Poiseuille flow inside a nano-channel using molecular dynamics. The viscosity is determined by fitting the resulting velocity profile (away from the walls) to the continuum solution for a Newtonian fluid and then compared to experimental values. The results show that the TIP4P/2005 model gives the best prediction of the viscosity for the complete range of temperatures for liquid water, and thus it is the preferred water model of these considered here for simulations where the magnitude of viscosity is crucial. On the other hand, with the TIP4P model, the viscosity is severely underpredicted, and overall the model performed worst, whereas the SPC/E and TIP4P/Ew models perform moderately.

Generalized Viscoplastic Modeling of Debris Flow

Various concepts have been proposed or used in the development of rheological models for debris flow. The earliest model developed by Bagnold was based on the concept of the “dispersive” pressure generated by grain collisions. Bagnold’s concept appears to be theoretically sound, but his empirical model has been found to be inconsistent with most theoretical models developed from non-Newtonian fluid mechanics. Although the generality of Bagnold’s model is still at issue, debris-flow modelers in Japan have generally accepted Takahashi’s formulas derived from Bagnold’s model. Some efforts have recently been made by theoreticians in non-Newtonian fluid mechanics to modify or improve Bagnold’s concept or model. A viable rheological model should consist both of a rate-independent part and a rate-dependent part. A generalized viscoplastic fluid (GVF) model that has both parts as well as two major rheological properties (i.e., the normal stress effect and soil yield criterion) is shown to be sufficiently accurate, yet practical, for general use in debris-flow modeling. In fact, Bagnold’s model is found to be only a particular case of the GVF model. Analytical solutions for (steady) uniform debris flows in wide channels are obtained from the GVF model based on Bagnold’s simplified assumption of constant grain concentration.

Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid

Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

HEATING IN VASCULAR TISSUE AND FLOW-THROUGH TISSUE PHANTOMS INDUCED BY FOCUSED ULTRASOUND

High intensity focused ultrasound (HIFU) can be used to control bleeding, both from individual blood vessels as well as from gross damage to the capillary bed. This process, called acoustic hemostasis, is being studied in the hope that such a method would ultimately provide a lifesaving treatment during the so-called "golden hour", a brief grace period after a severe trauma in which prompt therapy can save the life of an injured person. Thermal effects play a major role in occlusion of small vessels and also appear to contribute to the sealing of punctures in major blood vessels. However, aggressive ultrasound-induced tissue heating can also impact healthy tissue and can lead to deleterious mechanical bioeffects. Moreover, the presence of vascularity can limit one’s ability to elevate the temperature of blood vessel walls owing to convective heat transport. In an effort to better understand the heating process in tissues with vascular structure we have developed a numerical simulation that couples models for ultrasound propagation, acoustic streaming, ultrasound heating and blood cooling in Newtonian viscous media. The 3-D simulation allows for the study of complicated biological structures and insonation geometries. We have also undertaken a series of in vitro experiments, in non-uniform flow-through tissue phantoms, designed to provide a ground truth verification of the model predictions. The calculated and measured results were compared over a range of values for insonation pressure, insonation time, and flow rate; we show good agreement between predictions and measurements. We then conducted a series of simulations that address two limiting problems of interest: hemostasis in small and large vessels. We employed realistic human tissue properties and considered more complex geometries. Results show that the heating pattern in and around a blood vessel is different for different vessel sizes, flow rates and for varying beam orientations relative to the flow axis. Complete occlusion and wall- puncture sealing are both possible depending on the exposure conditions. These results concur with prior clinical observations and may prove useful for planning of a more effective procedure in HIFU treatments.

Viscoelastic flow through a planar contraction using a semi-Lagrangian finite volume method

A semi-Lagrangian finite volume scheme for solving viscoelastic flow problems is presented. A staggered grid arrangement is used in which the dependent variables are located at different mesh points in the computational domain. The convection terms in the momentum and constitutive equations are treated using a semi-Lagrangian approach in which particles on a regular grid are traced backwards over a single time-step. The method is applied to the 4 : 1 planar contraction problem for an Oldroyd B fluid for both creeping and inertial flow conditions. The development of vortex behaviour with increasing values of We is analyzed.

A semi-Lagrangian finite volume method for Newtonian contraction flows

A new finite volume method for solving the incompressible Navier--Stokes equations is presented. The main features of this method are the location of the velocity components and pressure on different staggered grids and a semi-Lagrangian method for the treatment of convection. An interpolation procedure based on area-weighting is used for the convection part of the computation. The method is applied to flow through a constricted channel, and results are obtained for Reynolds numbers, based on half the flow rate, up to 1000. The behavior of the vortex in the salient corner is investigated qualitatively and quantitatively, and excellent agreement is found with the numerical results of Dennis and Smith [Proc. Roy. Soc. London A, 372 (1980), pp. 393-414] and the asymptotic theory of Smith [J. Fluid Mech., 90 (1979), pp. 725-754].

A non-Newtonian computational fluid dynamics study of the stencil printing process

This paper describes the application of computational fluid dynamics (CFD) to simulate the macroscopic bulk motion of solder paste ahead of a moving squeegee blade in the stencil printing process during the manufacture of electronic components. The successful outcome of the stencil printing process is dependent on the interaction of numerous process parameters. A better understanding of these parameters is required to determine their relation to print quality and improve guidelines for process optimization. Various modelling techniques have arisen to analyse the flow behaviour of solder paste, including macroscopic studies of the whole mass of paste as well as microstructural analyses of the motion of individual solder particles suspended in the carrier fluid. This work builds on the knowledge gained to date from earlier analytical models and CFD investigations by considering the important non-Newtonian rheological properties of solder pastes which have been neglected in previous macroscopic studies. Pressure and velocity distributions are obtained from both Newtonian and non-Newtonian CFD simulations and evaluated against each other as well as existing established analytical models. Significant differences between the results are observed, which demonstrate the importance of modelling non-Newtonian properties for realistic representation of the flow behaviour of solder paste.

A cell-centred finite volume method for modelling viscoelastic flow

An unstructured cell-centred finite volume method for modelling viscoelastic flow is presented. The method is applied to the flow through a planar channel and the 4:1 planar contraction for creeping flow of an Oldroyd-B fluid. The results are presented for a range of Weissenberg numbers. In the case of the planar channel results are compared with analytical solutions. For the 4:1 planar contraction benchmark problem the convection terms in the constitutive equations are approximated using both first and second order differencing schemes to compare the techniques and the effect of mesh refinement on the solution is investigated. This is the first time that a fully unstructured, cell-centredfinitevolume technique has been used to model the Oldroyd-B fluid for the test cases presented in this paper.

Friction losses of Newtonian and non-Newtonian fluids flowing in laminar regime in a helical coil

This study aimed to carry out experimental work to determine, for Newtonian and non-Newtonian fluids, the friction factor (fc) with simultaneous heat transfer, at constant wall temperature as boundary condition, in fully developed laminar flow inside a vertical helical coil. The Newtonian fluids studied were aqueous solutions of glycerol, 25%, 36%, 43%, 59% and 78% (w/w). The non-Newtonian fluids were aqueous solutions of carboxymethylcellulose (CMC), a polymer, with concentrations of 0.2%, 0.3%, 0.4% and 0.6% (w/w) and aqueous solutions of xanthan gum (XG), another polymer, with concentrations of 0.1% and 0.2% (w/w). According to the rheological study done, the polymer solutions had shear-thinning behavior and different values of viscoelasticity. The helical coil used has an internal diameter, curvature ratio, length and pitch, respectively: 0.00483 m, 0.0263, 5.0 m and 11.34 mm. It was concluded that the friction factors, with simultaneous heat transfer, for Newtonian fluids can be calculated using expressions from literature for isothermal flows. The friction factors for CMC and XG solutions are similar to those for Newtonian fluids when the Dean number, based in a generalized Reynolds number, is less than 80. For Dean numbers higher than 80, the friction factors of the CMC solutions are lower those of the XG solutions and of the Newtonian fluids. In this range the friction factors decrease with the increase of the viscometric component of the solution and increase for increasing elastic component. The change of behavior at Dean number 80, for Newtonian and non-Newtonian fluids, is in accordance with the study of Ali [4]. There is a change of behavior at Dean number 80, for Newtonian and non-Newtonian fluids, which is in according to previous studies. The data also showed that the use of the bulk temperature or of the film temperature to calculate the physical properties of the fluid has a residual effect in the friction factor values.

Heat transfer coefficients from Newtonian and non-Newtonian fluids flowing in laminar regime in a helical coil

This study aimed to carry out experimental work to obtain, for Newtonian and non-Newtonian fluids, heat transfer coefficients, at constant wall temperature as boundary condition, in fully developed laminar flow inside a helical coil. The Newtonian fluids studied were aqueous solutions of glycerol, 25%, 36%, 43%, 59% and 78% (w/w) and the non-Newtonian fluids aqueous solutions of carboxymethylcellulose (CMC), a polymer, with concentrations 0.1%, 0.2%, 0.3%, 0.4% and 0.6% (w/w) and aqueous solutions of xanthan gum (XG), another polymer, with concentrations 0.1% and 0.2% (w/w). According to the rheological study performed, the polymer solutions had shear thinning behavior and different values of elasticity. The helical coil used has internal diameter, curvature ratio, length and pitch, respectively: 0.004575 m, 0.0263, 5.0 m and 11.34 mm. The Nusselt numbers for the CMC solutions are, on average, slightly higher than those for Newtonian fluids, for identical Prandtl and generalized Dean numbers. As outcome, the viscous component of the shear thinning polymer tends to potentiate the mixing effect of the Dean cells. The Nusselt numbers of the XG solutions are significant lower than those of the Newtonian solutions, for identical Prandtl and generalized Dean numbers. Therefore, the elastic component of the polymer tends to diminish the mixing effect of the Dean cells. A global correlation, for Nusselt number as a function of Péclet, generalized Dean and Weissenberg numbers for all Newtonian and non-Newtonian solutions studied, is presented.