Analytical Solution of a Walters’ Liquid B Flow Over a Linear Stretching Sheet in a Porous Medium

This chapter represents the analytical solution of two-dimensional linear stretching sheet problem involving a non-Newtonian liquid and suction by (a) invoking the boundary layer approximation and (b) using this result to solve the stretching sheet problem without using boundary layer approximation. The basic boundary layer equations for momentum, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The results reveal a new analytical procedure for solving the boundary layer equations arising in a linear stretching sheet problem involving a non-Newtonian liquid (Walters’ liquid B). The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem.

Simulation of plant cell shrinkage during drying : A SPH–DEM approach

Plant based dried food products are popular commodities in global market where much research is focused to improve the products and processing techniques. In this regard, numerical modelling is highly applicable and in this work, a coupled meshfree particle-based two-dimensional (2-D) model was developed to simulate micro-scale deformations of plant cells during drying. Smoothed Particle Hydrodynamics (SPH) was used to model the viscous cell protoplasm (cell fluid) by approximating it to an incompressible Newtonian fluid. The visco-elastic characteristic of the cell wall was approximated to a Neo-Hookean solid material augmented with a viscous term and modelled with a Discrete Element Method (DEM). Compared to a previous work [H. C. P. Karunasena, W. Senadeera, Y. T. Gu and R. J. Brown, Appl. Math. Model., 2014], this study proposes three model improvements: linearly decreasing positive cell turgor pressure during drying, cell wall contraction forces and cell wall drying. The improvements made the model more comparable with experimental findings on dried cell morphology and geometric properties such as cell area, diameter, perimeter, roundness, elongation and compactness. This single cell model could be used as a building block for advanced tissue models which are highly applicable for product and process optimizations in Food Engineering.

A coupled SPH-DEM model for micro-scale structural deformations of plant cells during drying

A single plant cell was modeled with smoothed particle hydrodynamics (SPH) and a discrete element method (DEM) to study the basic micromechanics that govern the cellular structural deformations during drying. This two-dimensional particle-based model consists of two components: a cell fluid model and a cell wall model. The cell fluid was approximated to a highly viscous Newtonian fluid and modeled with SPH. The cell wall was treated as a stiff semi-permeable solid membrane with visco-elastic properties and modeled as a neo-Hookean solid material using a DEM. Compared to existing meshfree particle-based plant cell models, we have specifically introduced cell wall–fluid attraction forces and cell wall bending stiffness effects to address the critical shrinkage characteristics of the plant cells during drying. Also, a moisture domain-based novel approach was used to simulate drying mechanisms within the particle scheme. The model performance was found to be mainly influenced by the particle resolution, initial gap between the outermost fluid particles and wall particles and number of particles in the SPH influence domain. A higher order smoothing kernel was used with adaptive smoothing length to improve the stability and accuracy of the model. Cell deformations at different states of cell dryness were qualitatively and quantitatively compared with microscopic experimental findings on apple cells and a fairly good agreement was observed with some exceptions. The wall–fluid attraction forces and cell wall bending stiffness were found to be significantly improving the model predictions. A detailed sensitivity analysis was also done to further investigate the influence of wall–fluid attraction forces, cell wall bending stiffness, cell wall stiffness and the particle resolution. This novel meshfree based modeling approach is highly applicable for cellular level deformation studies of plant food materials during drying, which characterize large deformations.

Microcontinuum approach to the pulsatile flow in tubes with and without longitudinal vibration

A fully developed pulsatile flow in a circular rigid tube is analysed by a microcontinuum approach. Solutions for radial variation of axial velocity and cell rotational velocity across the tube are obtained using the momentum integral method. Simplified forms of the solutions are presented for the relevant physiological data. Marked deviations in the results are observed when compared to a Newtonian fluid model. It is interesting to see that there is sufficient reduction in the mass flow rate, phase lag and friction due to the micropolar character of the fluid.

Heat transfer to power-law fluids in thermal entrance region with viscous dissipation for constant heat flux conditions

An analytical solution of the heat transfer problem with viscous dissipation for non-Newtonian fluids with power-law model in the thermal entrance region of a circular pipe and two parallel plates under constant heat flux conditions is obtained using eigenvalue approach by suitably replacing one of the boundary conditions by total energy balance equation. Analytical expressions for the wall and the bulk temperatures and the local Nusselt number are presented. The results are in close agreement with those obtained by implicit finite-difference scheme. It is found that the role of viscous dissipation on heat transfer is completely different for heating and cooling conditions at the wall. The results for the case of cooling at the wall are of interest in the design of the oil pipe line.

Surface chemistry, dispersion behavior, and slip casting of Ti 3AlC2 suspensions

The surface chemistry and dispersion properties of aqueous Ti 3AlC2 suspension were studied in terms of hydrolysis, adsorption, electrokinetic, and rheological measurements. The Ti 3AlC2 particle had complex surface hydroxyl groups, such as ≡Ti-OH,=Al-OH, and -OTi-(OH)2, etc. The surface charging of the Ti3AlC2 particle and the ion environment of suspensions were governed by these surface groups, which thus strongly influenced the stability of Ti3AlC2 suspensions. PAA dispersant was added into the Ti3AlC2 suspension to depress the hydrolysis of the surface groups by the adsorption protection mechanism and to increase the stability of the suspension by the steric effect. Ti3AlC2 suspensions with 2.0 dwb% PAA had an excellent stability at pH=∼5 and presented the characteristics of Newtonian fluid. Based on the well-dispersed suspension, dense Ti3AlC2 materials were obtained by slip casting and after pressureless sintering. This work provides a feasible forming method for the engineering applications of MAX-phase ceramics, wherein complex shapes, large dimensions, or controlled microstructures are needed.

Sodium-alginate-based proton-exchange membranes as electrolytes for DMFCs

Novel mixed-matrix membranes prepared by blending sodium alginate (NaAlg) with polyvinyl alcohol (PVA) and certain heteropolyacids (HPAs), such as phosphomolybdic acid (PMoA), phosphotungstic acid (PWA) and silicotungstic acid (SWA), followed by ex-situ cross-linking with glutaraldehyde (GA) to achieve the desired mechanical and chemical stability, are reported for use as electrolytes in direct methanol fuel cells (DMFCs). NaAlg-PVA-HPA mixed matrices possess a polymeric network with micro-domains that restrict methanol cross-over. The mixed-matrix membranes are characterised for their mechanical and thermal properties. Methanol cross-over rates across NaAlg-PVA and NaAlg-PVA-HPA mixed-matrix membranes are studied by measuring the mass balance of methanol using a density meter. The DMFC using NaAlg-PVA-SWA exhibits a peak power-density of 68 mW cm(-2) at a load current-density of 225 mA cm(-2), while operating at 343 K. The rheological properties of NaAlg and NaAlg-PVA-SWA viscous solutions are studied and their behaviour validated by a non-Newtonian power-law.

Low reynolds number flow of a dilute suspension in slowly varying tubes

We have discussed here the flow of a dilute suspension of rigid particles in Newtonian fluid in slowly varying tubes characterized by a small parameter ε. Solutions are presented in the form of asymptotic expansions in powers of ε. The effect of the suspension on the fluid is described by two parameters β and γ which depend on the volume fraction of the particles which we assume to be small. It is found that the presence of the particles accelerate the process of eddy formation near the constriction and shifts the point of separation.

The collective dynamics of self-propelled particles

We propose a method for the dynamic simulation of a collection of self-propelled particles in a viscous Newtonian fluid. We restrict attention to particles whose size and velocity are small enough that the fluid motion is in the creeping flow regime. We propose a simple model for a self-propelled particle, and extended the Stokesian Dynamics method to conduct dynamic simulations of a collection of such particles. In our description, each particle is treated as a sphere with an orientation vector p, whose locomotion is driven by the action of a force dipole Sp of constant magnitude S0 at a point slightly displaced from its centre. To simplify the calculation, we place the dipole at the centre of the particle, and introduce a virtual propulsion force Fp to effect propulsion. The magnitude F0 of this force is proportional to S0. The directions of Sp and Fp are determined by p. In isolation, a self-propelled particle moves at a constant velocity u0 p, with the speed u0 determined by S0. When it coexists with many such particles, its hydrodynamic interaction with the other particles alters its velocity and, more importantly, its orientation. As a result, the motion of the particle is chaotic. Our simulations are not restricted to low particle concentration, as we implement the full hydrodynamic interactions between the particles, but we restrict the motion of particles to two dimensions to reduce computation. We have studied the statistical properties of a suspension of self-propelled particles for a range of the particle concentration, quantified by the area fraction φa. We find several interesting features in the microstructure and statistics. We find that particles tend to swim in clusters wherein they are in close proximity. Consequently, incorporating the finite size of the particles and the near-field hydrodynamic interactions is of the essence. There is a continuous process of breakage and formation of the clusters. We find that the distributions of particle velocity at low and high φa are qualitatively different; it is close to the normal distribution at high φa, in agreement with experimental measurements. The motion of the particles is diffusive at long time, and the self-diffusivity decreases with increasing φa. The pair correlation function shows a large anisotropic build-up near contact, which decays rapidly with separation. There is also an anisotropic orientation correlation near contact, which decays more slowly with separation. Movies are available with the online version of the paper.

A coupled VOF-IBM-enthalpy approach for modeling motion and growth of equiaxed dendrites in a solidifying melt

A coupled methodology for simulating the simultaneous growth and motion of equiaxed dendrites in solidifying melts is presented. The model uses the volume-averaging principles and combines the features of the enthalpy method for modeling growth, immersed boundary method for handling the rigid solid-liquid interfaces, and the volume of fluid method for tracking the advection of the dendrite. The algorithm also performs explicit-implicit coupling between the techniques used. A two-dimensional framework with incompressible and Newtonian fluid is considered. Validation with available literature is performed and dendrite growth in the presence of rotational and buoyancy driven flow fields is studied. It is seen that the flow fields significantly alter the position and morphology of the dendrites. (C) 2012 Elsevier Inc. All rights reserved.

Spray characterization of straight vegetable oils at high injection pressures

We present results of high pressure spray characterization of Straight Vegetable Oils (SVOs) which are potential diesel fuel substitutes. SVO sprays are visualized at high injection pressures (up to 1600 bar) to study their atomization characteristics. Spray structure studies are reported for the first time for Jatropha and Pongamia vegetable oils, under atmospheric conditions. Jatropha and Pongamia SVO sprays are found to be poorly atomized and intact liquid cores are observed even at an injection pressure of 1600 bar. Non-Newtonian behavior of Jatropha and Pongamia oil is shown to be the reason for observed spray structure. (C) 2012 Elsevier Ltd. All rights reserved.

Total internal reflection Raman spectroscopy of poly(alpha-olefin) oils in a lubricated contact

The rheology of a poly(alpha-olefin) base oil (PAO) in a sliding point contact has been investigated by total internal reflection (TIR) Raman spectroscopy. TIR Raman has the sensitivity to analyse nanometer-thick lubricant films in a tribological contact. The Raman signal generated from the sliding contact was used to determine the lubricant film thickness. The experimentally obtained film thicknesses were compared with theoretical calculations and a transition from Newtonian to non-Newtonian behaviour was observed at high shear rates. The Raman spectra showed no significant changes in the conformation of the PAO chains under the applied conditions of pressure and shear, but the polarisation dependence of the spectra revealed a preferred orientation of the hydrocarbon side chains in the shear-thinned region. Monolayers formed by a boundary lubricant, arachidic acid, dissolved in the PAO could be detected on the surfaces in the elastohydrodynamic regime.

Rheological Behavior of Al-7Si-0.3Mg Alloy at Mushy State

In recent years, semisolid manufacturing has emerged as an attractive option for near net shape forming of components with aluminum alloys. In this class of processes, the key to success lies mainly in the understanding of rheological behavior of the semi-solid slurry in the temperature range between liquidus and solidus. The present study focuses on the non-Newtonian flow behavior of the pseudo plastic slurry of Al-7Si-0.3Mg alloy for a wide shear range using a high-temperature Searle-type rheometer. The rheological behavior of the slurry is studied with respect to relevant process variables and microstructural features such as shear rate, shear duration, temperature history, primary particle size, shape, and their distribution. The experiments performed are isothermal tests, continuous cooling tests, shear jump tests, and shear time tests. The continuous cooling experiments are aimed toward studying the viscosity and shear stress evolution within the slurry matrix with increasing solid fraction at a constant shear rate. Three different cooling rates are considered and their effect on flow behavior of the slurry was studied under iso-shear condition. Descending shear jump experiments are performed to understand the viscous instability of the slurry.

Design and Validation of On-chip Planar Mixer Based on Advection and Viscoelastic Effects

Mixing at low Reynolds number is usually due to diffusion and requires longer channel lengths for complete mixing. In order to reduce the mixing lengths, advective flow can be induced by varying the channel geometry. Additionally, in non-newtonian fluids, appropriate modifications to channel geometry can be used to aid the mixing process by capitalizing on their viscoelastic nature. Here we have exploited the advection and viscoelastic effects to implement a planar passive micro-mixer. Microfluidic devices incorporating different blend of mixing geometries were conceived. The optimum design was chosen based on the results of the numerical simulations performed in COMSOL. The chosen design had sudden expansion and contraction along with teeth patterns along the channel walls to improve mixing. Mixing of two different dyes was performed to validate the mixing efficiency. Particle dispersion experiments were also carried out. The results indicated effective mixing. In addition, the same design was also found to be compatible with electrical power free pumping mechanism like suction. The proposed design was then used to carry out on-chip chemical cell lysis with human whole blood samples to establish its use with non-newtonian fluids. Complete lysis of the erythrocytes was observed leaving behind the white blood cells at the outlet.

Designing Of Partial Similarity Models And Evaluation Method In Polymer Flooding Experiment

Based on the scaling criteria of polymer flooding reservoir obtained in our previous work in which the gravity and capillary forces, compressibility, non-Newtonian behavior, absorption, dispersion, and diffusion are considered, eight partial similarity models are designed. A new numerical approach of sensitivity analysis is suggested to quantify the dominance degree of relaxed dimensionless parameters for partial similarity model. The sensitivity factor quantifying the dominance degree of relaxed dimensionless parameter is defined. By solving the dimensionless governing equations including all dimensionless parameters, the sensitivity factor of each relaxed dimensionless parameter is calculated for each partial similarity model; thus, the dominance degree of the relaxed one is quantitatively determined. Based on the sensitivity analysis, the effect coefficient of partial similarity model is defined as the summation of product of sensitivity factor of relaxed dimensionless parameter and its relative relaxation quantity. The effect coefficient is used as a criterion to evaluate each partial similarity model. Then the partial similarity model with the smallest effect coefficient can be singled out to approximate to the prototype. Results show that the precision of partial similarity model is not only determined by the number of satisfied dimensionless parameters but also the relative relaxation quantity of the relaxed ones.