Hydromagnetic rotating flow of a fourth‐order fluid past a porous plate

The rotating flow in the presence of a magnetic field is a problem belonging to hydromagnetics and deserves to be more widely studied than it has been to date. In the non‐linear regime the literature is scarce. We develop the governing equations for the unsteady hydromagnetic rotating flow of a fourth‐order fluid past a porous plate. The steady flow is governed by a boundary value problem in which the order of differential equations is more than the number of available boundary conditions. It is shown that by augmenting the boundary conditions based on asymptotic structures at infinity it is possible to obtain numerical solutions of the nonlinear hydromagnetic equations. Effects of uniform suction or blowing past the porous plate, exerted magnetic field and rotation on the flow phenomena, especially on the boundary layer structure near the plate, are numerically analysed and discussed. The flow behaviours of the Newtonian fluid and second‐, third‐ and fourth‐order non‐Newtonian fluids are compared for the special flow problem, respectively. Copyright © 2004 John Wiley & Sons, Ltd.     

Interaction mechanisms of U(VI) and graphene oxide from the perspective of particle size distribution

Graphene oxide (GO) is an ideal adsorbent due to excellent physicochemical properties. Humic acid (HA) is ubiquitous in aquatic and soil environment, which can affect the migration of metal ions. In this study, we investigated the sorption mechanisms of U(VI) onto GO surfaces in the presence of HA. pH dependent and ionic strength independent sorption process were observed and the concentration of HA is positively proportional to U(VI) sorption capacities. Results also suggest that a pre-mixing HA + U(VI) gave better results than a pre-mixing of GO + HA, which can be explained by the size distribution of different GO systems.

     

Effect of variable viscosity on the peristaltic transport of a Newtonian fluid in an asymmetric channel

The effect of variable viscosity on the peristaltic flow of a Newtonian fluid in an asymmetric channel has been discussed. Asymmetry in the flow is induced due to travelling waves of different phase and amplitude which propagate along the channel walls. A long wavelength approximation is used in the flow analysis. Closed form analytic solutions for velocity components and longitudinal pressure gradient are obtained. The study also shows that, in addition to the effect of mean flow parameter, the wave amplitude also effect the peristaltic flow. This effect is noticeable in the pressure rise and frictional forces per wavelength through numerical integration.     

Homotopy Solutions for a Generalized Second-Grade Fluid Past a Porous Plate

The flow of a second-grade fluid past a porous plate subject to either suction or blowing at the plate has been studied. A modified model of second-grade fluid that has shear-dependent viscosity and can predict the normal stress difference is used. The differential equations governing the flow are solved using homotopy analysis method (HAM). Expressions for the velocity have been constructed and discussed with the help of graphs. Analysis of the obtained results showed that the flow is appreciably influenced by the material and normal stress coefficient. Several results of interest are deduced as the particular cases of the presented analysis.     

Complexation of radionuclide <Superscript>152+154</Superscript>Eu(III) with alumina-bound fulvic acid studied by batch and time-resolved laser fluorescence spectroscopy

To contribute to the understanding of Eu(III) interaction preperties on hydrous alumina particles in the absence and presence of fulvic acid (FA), the complexation properties of Eu(III) with hydrous alumina, FA and FA-alumina hybrids are studied by batch and time-resolved laser fluorescence spectroscopy (TRLFS) techniques. The continuous increase in the fluorescence lifetime of Eu-alumina and Eu-FA with increasing pH indicates that the complexation is accompanied by decreasing number of hydration water in the first coordination sphere of Eu(III). Eu(III) is adsorbed onto alumina particles as outer-sphere surface complexes of ≡(Al?O)?Eu· (OH)· 7H₂O and ≡(Al?O)?Eu· 6H₂O at low pH values, and as inner-sphere surface complexes as ≡(Al?O)₂?Eu⁺· 4H₂O at high pH. In FA solution, Eu(III) forms complexes with FA as (COO)₂Eu⁺(H₂O) _x and the hydration water number in the first coordination sphere decreases with pH increasing. The formation of ≡COO?Eu?(O?Al≡)· 4H₂O is observed on FA-alumina hybrids, suggesting the formation of strong inner-sphere surface complexes in the presence of FA. The surface complexes are also characterized by their emission spectra [the ratio of emission intensities of ⁵ D ₀→⁷ F ₁ (λ=594 nm) and ⁵ D ₀→⁷ F ₂ (λ=619 nm) transitions] and their fluorescence lifetime. The findings is important to understand the contribution of FA in the complexation properties of Eu(III) on FA-alumina hybrids that the clarification of the environmental behavior of humic substances is necessary to understand fully the behavior of Eu(III), or its analogue trivalent lanthanide and actinide ions in natural environment.     

Interaction of radionuclides with natural and manmade materials using XAFS technique

The X-ray absorption fine structure (XAFS) technology has exhibited a very unique application in the study of sorption mechanism, chemical species and microstructures of radionuclides at the natural solid-water interfaces. In this review, the interaction mechanism of radionuclides with clay minerals and nanomaterials under different environmental conditions are summarized from the XAFS spectroscopy analysis. The coordination number and the bond distances of radionuclides, the oxidation-reduction reactions, the influence of humic substances and microorganisms on the species and structures of radionuclides at molecule level are reviewed and compared. This review is helpful to understand the interactions of radionuclides with oxides, natural clay minerals and nanomaterials, which is also crucial to evaluate the physicochemical behaviors of radionuclides in the natural environment.     

Dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Lévy jumps

In this paper, the dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Lévy jumps is considered. Besides a standard geometric Brownian motion, another two driving processes are taken into account: a stationary Poisson point process and a continuous time finite-state Markov chain. Firstly, we establish sufficient conditions for persistence in the mean of the disease. Then we obtain sufficient conditions for extinction of the disease. In addition, we also establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.     

Dynamical behavior of a stochastic Nicholson’s blowflies model with distributed delay and degenerate diffusion

Nonlinear Dynamics - The mathematical model with time delay is often more practical because it is subject to current and past state. What remains unclear are the details, such as how time delay and...     

Stationary distribution and extinction for a food chain chemostat model with random perturbation

In this paper, we study the dynamical behavior of a stochastic food chain chemostat model, in which the white noise is proportional to the variables. Firstly, we prove the existence and uniqueness of the global positive solution. Then by constructing suitable Lyapunov functions, we show the system has a unique ergodic stationary distribution. Furthermore, the extinction of microorganisms is discussed in two cases. In one case, both the prey and the predator species are extinct, and in the other case, the prey species is surviving and the predator species is extinct. Finally, numerical experiments are performed for supporting the theoretical results.     

Gliding motion of bacteria on power‐law slime

The present investigation deals with an undulating surface model for the motility of bacteria gliding on a layer of non‐Newtonian slime. The slime being the viscoelastic material is considered as a power‐law fluid. A hydrodynamical model of motility involving an undulating cell surface which transmits stresses through a layer of exuded slime to the substratum is examined. The non‐linear differential equation resulting from the balance of momentum and mass is solved numerically by a finite difference method with an iteration technique. The manner in which the various exponent values of the power‐law flow affect the structure of the boundary layer is delineated. A comparison is made of the power‐law fluid with the Newtonian fluid. For the power‐law fluid with respect to different power‐law exponent values, shear‐thinning and shear‐thickening effects can be observed, respectively. Copyright © 2004 John Wiley & Sons, Ltd.