On Solutions of Some Non-Linear Differential Equations Arising in Newtonian and Non-Newtonian Fluids

Some steady as well as unsteady solutions of the equations of motion for an incompressible Newtonian and non-Newtonian (second-grade) fluids are obtained by applying different methods including the Lie symmetry group method. The flows considered are axially symmetric with the swirling motion, and the governing equations for second-grade fluid flow have been modeled. Expressions for streamlines, velocity and vorticity components are constructed explicitly in each case. Exact analytical solutions in second-grade fluid are obtained and compared with the corresponding viscous solutions.     

Power law fluid model for blood flow through a tapered artery with a stenosis

In the present paper, blood flow through a tapered artery with a stenosis is analyzed, assuming the flow is steady and blood is treated as non-Newtonian power law fluid model. Exact solution has been evaluated for velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different types of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest. Some special cases of the problem are also presented.     

微极流体在两个伸展平面之间的不稳定轴对称MHD流动

研究在两个径向伸展的平面之间,微极流体作随时间变化的磁流体动力学(MHD)流动.考虑了高浓度微元(n=0)和低浓度微元(n=0.5)两种情况.使用恰当的变换,将偏微分方程转换为常微分方程.用同伦分析法(HAM),对变换后的方程求解.给出不同参数下,角速度、表面摩擦因数和面应力偶系数的图形结果.     

Structure and dynamics of highly PEG-ylated sterically stabilized micelles in aqueous media

Molecular assemblies of highly PEG-ylated phospholipids are important in many biomedical applications. We have studied sterically stabilized micelles (SSMs) of self-assembled DSPE–PEG2000 in pure water and isotonic HEPES-buffered saline solution. The observed SSM sizes of 2–15 nm largely depend on the solvent and the lipid concentration used. The critical micelle concentration of DSPE–PEG2000 is 10 times higher in water than in buffer, and the viscosity of the dispersion dramatically increases with the lipid concentration. To explain the experimentally observed results, we performed atomistic molecular dynamics simulations of solvated SSMs. Our modeling revealed that the observed assemblies have very different aggregation numbers (N(agg) ≈ 90 in saline solution and N(agg) < 8 in water) because of very different screening of their charged PO4(–) groups. We also demonstrate that the micelle cores can inflate and their coronas can fluctuate strongly, thus allowing storage and delivery of molecules with different chemistries.     

Development of an efficient protein phosphatase-based colorimetric test for okadaic acid detection

Okadaic acid (OA), responsible for gastrointestinal problems, inhibits protein phosphatase 2A (PP2A). Therefore, the inhibition exerted by the toxin on PP2A could be used to detect the presence of OA in aqueous solution and in shellfish sample.In this work, two commercial PP2As (from ZEU Immunotec and Millipore) and one produced by molecular engineering (from GTP Technology) were tested. Enzymes were used in solution and also immobilized within a polymeric gel. In solution, best performances were obtained using PP2A purchased from ZEU Immunotec (Spain). OA was detected in aqueous solution in concentration as low as 0.0124 μg L⁻¹ using the enzyme from ZEU Immunotec whereas the detection limits were 0.47 μg L⁻¹ and 0.123 μg L⁻¹ with PP2As from Millipore and GTP Technology, respectively. Considering that the immobilization step contributes to stabilize the PP2A activity, enzymes were entrapped within a photopolymer and an agarose gel. These different polymeric matrices were optimized, tested and compared. Agarose gel seems to be a good alternative to the photopolymer largely used in our group. For instance, the IC₅₀ value obtained with the test based on PP2A from ZEU Immunotec immobilized within an agarose gel was 1.98 μg L⁻¹. This value was 1.8-fold lower than those obtained with the photopolymer test using the same enzyme. The proposed test is sensitive, fast and does not require expensive equipment. To evaluate the efficiency of the assay, PP inhibition tests based on PP2A from ZEU Immunotec in solution or immobilized within a gel were used for OA detection in contaminated shellfish.     

Poiseuille Flow of a Third Grade Fluid in a Porous Medium

Effects of porous medium have been investigated on the steady flow of a third grade fluid between two stationary porous plates. The continuity and momentum equations along with modified Darcy??s law are used for the development of mathematical problem. The governing nonlinear problem is solved by a homotopy analysis method. The dimensionless velocity and shear stresses at the plates are analyzed.     

Time-dependent three-dimensional flow and mass transfer of elastico-viscous fluid over unsteady stretching sheet

This article studies the three-dimensional boundary layer flow of an elasticoviscous fluid over a stretching surface. Velocity of the stretching sheet is assumed to be time-dependent. Effect of mass transfer with higher order chemical reaction is further considered. Computations are made by the homptopy analysis method (HAM). Convergence of the obtained series solutions is explicitly analyzed. Variations of embedding parameters on the velocity and concentration are graphically discussed. Numerical computations of surface mass transfer are reported. Comparison of the present results with the numerical solutions is also given.     

Perturbation analysis of a modified second grade fluid over a porous plate

A modified second grade non-Newtonian fluid model is considered. The model is a combination of power-law and second grade fluids in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The flow of this fluid is considered over a porous plate. Equations of motion in dimensionless form are derived. When the power-law effects are small compared to second grade effects, a regular perturbation problem arises which is solved. The validity criterion for the solution is derived. When second grade effects are small compared to power-law effects, or when both effects are small, the problem becomes a boundary layer problem for which the solutions are also obtained. Perturbation solutions are contrasted with the numerical solutions. For the regular perturbation problem of small power-law effects, an excellent match is observed between the solutions if the validity criterion is met. For the boundary layer solution of vanishing second grade effects however, the agreement with the numerical data is not good. When both effects are considered small, the boundary layer solution leads to the same solution given in the case of a regular perturbation problem.     

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...