Application of parameter differentiation for flow of a third grade fluid past an infinite porous plate

This article investigates the analytic solution for the flow of a third grade fluid past an infinite porous plate. The method of parameter differentiation is used to linearized the governing flow equation. The solution of the obtained linear equation is developed by differential transform method in combination with the method of superposition. The obtained results are compared with existing results in the literature and an excellent agreement is found. This shows that the parameter differentiation is a powerful technique for solving nonlinear problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Finite element and sensitivity analysis of thermally induced flow instabilities

This paper presents a finite element algorithm for the simulation of thermo‐hydrodynamic instabilities causing manufacturing defects in injection molding of plastic and metal powder. Mold‐filling parameters determine the flow pattern during filling, which in turn influences the quality of the final part. Insufficiently, well‐controlled operating conditions may generate inhomogeneities, empty spaces or unusable parts. An understanding of the flow behavior will enable manufacturers to reduce or even eliminate defects and improve their competitiveness. This work presents a rigorous study using numerical simulation and sensitivity analysis. The problem is modeled by the Navier–Stokes equations, the energy equation and a generalized Newtonian viscosity model. The solution algorithm is applied to a simple flow in a symmetrical gate geometry. This problem exhibits both symmetrical and non‐symmetrical solutions depending on the values taken by flow parameters. Under particular combinations of operating conditions, the flow was stable and symmetric, while some other combinations leading to large thermally induced viscosity gradients produce unstable and asymmetric flow. Based on the numerical results, a stability chart of the flow was established, identifying the boundaries between regions of stable and unstable flow in terms of the Graetz number (ratio of thermal conduction time to the convection time scale) and B, a dimensionless ratio indicating the sensitivity of viscosity to temperature changes. Sensitivities with respect to flow parameters are then computed using the continuous sensitivity equations method. We demonstrate that sensitivities are able to detect the transition between the stable and unstable flow regimes and correctly indicate how parameters should change in order to increase the stability of the flow. Copyright © 2009 John Wiley & Sons, Ltd.     

Pressure-driven flow of a rate-type fluid with stress threshold in an infinite channel

In this paper we extend some of our previous works on continua with stress threshold. In particular here we propose a mathematical model for a continuum which behaves as a non-linear upper convected Maxwell fluid if the stress is above a certain threshold and as a Oldroyd-B type fluid if the stress is below such a threshold. We derive the constitutive equations for each phase exploiting the theory of natural configurations (introduced by Rajagopal and co-workers) and the criterion of the maximization of the rate of dissipation. We state the mathematical problem for a one-dimensional flow driven by a constant pressure gradient and study two peculiar cases in which the velocity of the inner part of the fluid is spatially homogeneous.     

A parametrisation of the direct correlation function for the square-shoulder fluid

We introduce a parametrisation of the direct correlation function for the square-shoulder fluid and demonstrate that this parametrisation is in quantitative agreement with the numerical solution of the Ornstein–Zernike equation within the Percus–Yevick approximation. Moreover, the radial distribution function obtained from the parametrisation reproduces quantitatively Monte Carlo simulation data. Our results show that the parametrisation is accurate over a large regime of densities for different interaction ranges and potential strengths.     

Monte Carlo simulations of star-branched polyelectrolyte micelles

The concentration profiles of monomers and counterions in star-branched polyelectrolyte micelles are calculated through Monte Carlo simulations, using the freely jointed chain model. We have investigated the onset of different regimes corresponding to the spherical and Manning condensation of counterions as a function of the strength of the Coulomb coupling. The Monte Carlo results are in fair agreement with the predictions of Self-Consistent-Field analytical models. We have simulated a real system of diblock copolymer micelles of (sodium-polystyrene-sulfonate)(NaPSS)-(polyethylene-propylene)(PEP) with f = 54 hydrophilic branches of N = 251 monomers at room temperature in salt-free solution. The calculated form factor compares nicely with our neutron scattering data. Received 18 July 2002 and Received in final form 11 October 2002 RID="a" ID="a"e-mail: roger@drecam.saclay.cea.fr     

Towards finite-dimensional gelation

We consider the gelation of particles which are permanently connected by random crosslinks, drawn from an ensemble of finite-dimensional continuum percolation. To average over the randomness, we apply the replica trick, and interpret the replicated and crosslink-averaged model as an effective molecular fluid. A Mayer-cluster expansion for moments of the local static density fluctuations is set up. The simplest non-trivial contribution to this series leads back to mean-field theory. The central quantity of mean-field theory is the distribution of localization lengths, which we compute for all connectivities. The highly crosslinked gel is characterized by a one-to-one correspondence of connectivity and localization length. Taking into account higher contributions in the Mayer-cluster expansion, systematic corrections to mean-field can be included. The sol-gel transition shifts to a higher number of crosslinks per particle, as more compact structures are favored. The critical behavior of the model remains unchanged as long as finite truncations of the cluster expansion are considered. To complete the picture, we also discuss various geometrical properties of the crosslink network, e.g. connectivity correlations, and relate the studied crosslink ensemble to a wider class of ensembles, including the Deam-Edwards distribution. Received on 24 April 2002 Published online 14 October 2002 RID="a" ID="a"deceased RID="b" ID="b"e-mail: weigt@theorie.physik.uni-goettingen.de     

A superdense star model as charged analogue of Schwarzschild’s interior solution

A charged analogue of Schwarzschilds interior solution has been derived by considering the non-gravitational energy density to be constant along with a special choice of electric intensity. The charged fluid sphere so obtained is seen to be more general than that of P.S. Florides and joins smoothly with the Reissner-Nordström metric at the pressure-free interface. Also the new charged fluid sphere is capable of representing a superdense star with surface density of 2×10¹⁴ g cm^–3 which can occupy maximum mass 1.502408 times the solar mass. In the process of deriving the solution, the authors have also come across A. L. Mehras gaseous charged fluid model which is found to be unphysical as it has negative pressure at least at the center of the model.This revised version was published online in April 2005. The publishing date was inserted.     

Unsteady hydromagnetic rotating flow of a conducting second grade fluid

The purpose of this work is to investigate the hydromagnetic oscillatory flow of a fluid bounded by a porous plate, when the entire system rotates about an axis normal to the plate. The fluid is assumed to be non-Newtonian (second grade), incompressible and electrically conducting. The magnetic field is applied transversely to the direction of the flow. Such a flow model has great significance not only of its theoretical interest, but also for applications to geophysics and engineering. The resulting initial value problem has been solved analytically for steady and unsteady cases. The analysis of the obtained results showed that the flow field is appreciably influenced by the material parameter of the second grade fluid, the applied magnetic field, the imposed frequency, rotation and suction and blowing parameters. It is observed in a second grade fluid that a steady asymptotic hydromagnetic solution exists for blowing and resonance which is different from the hydrodynamic situation.     

Heck coupling reaction of iodobenzene and styrene using supercritical water in the absence of a catalyst

Heck coupling reaction of iodobenzene and styrene proceeds rapidly and selectively in supercritical water even without any catalyst in the presence of base. Both the choice of base and the reaction conditions had a significant effect on the conversion and the selectivity of the coupling products. The addition of a relatively mild base such as potassium acetate facilitated the cross-coupling reaction, while the hydrolysis of phenyl halide was favored in the presence of a strong base. The conversion and the yields of coupling products increased with increasing temperature, reaching a maximum at 650 K near the critical temperature of water, and then decreased as the temperature was further increased. Water density had a significant influence on the reaction rate, showing nearly 30% augmentation with a slight increase in density from 0.45 to 0.56 g cm(-3), but had less effect on the product selectivity. Two possibilities of the role of water responsible for the noncatalytic Heck coupling reaction in supercritical water, that is, ion and water-catalyzed mechanisms have been considered.     

Large time behavior to the system of incompressible non-Newtonian fluids in R

In this paper, the authors study the large time behavior for the weak solutions to a class system of the incompressible non-Newtonian fluids in R². It is proved that the weak solutions decay in L² norm at (1+t)^−1/2 and the estimate for the decay rate is sharp in the sense that it coincides with the decay rate of a solution to the heat equation.