Electro-osmotic flow of a viscoelastic fluid in a channel : Applications to physiological fluid mechanics

The paper presents a comprehensive theoretical study on the electro-osmotic flow of a viscoelastic fluid past a channel having stretching walls. An attempt has been made to investigate the effect of rheological and electro-osmotic parameters on the kinematics of the fluid. Results presented here pertain to the case where the channel height is much greater than the thickness of electrical double layer comprising the Stern and diffuse layers. The study reveals that an increase in electro-osmotic parameter leads to an increase in the axial velocity throughout the channel for a fluid having viscoelastic coefficient equal to that of blood. This aspect provides a source of novel insight into the process of designing bio-sensing and micro-fluidic devices.     

Exact and explicit solutions of Euler-Painlevé equations through generalized Cole-Hopf transformations

More general Euler-Painlevé equations are exactly linearized using generalized Cole-Hopf transform and are shown to admit exact solutions in terms of Kummer functions. The asymptotic behaviours of Euler-Painlevé equations are also derived.     

Oscillatory and asymptotic behaviour of fourth order nonlinear difference equations

This paper considers a class of fourth order nonlinear difference equations Δ²(r _n Δ²(y _n ) + Δ²(r _n ,f(n,n _n )=0,n ∈N(n ₀) wheref(n, y) may be classified as superlinear, sublinear, strongly superlinear and strongly sublinear. In superlinear and sublinear cases, necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions with special asymptotic properties. In strongly superlinear and strongly sublinear cases, sufficient conditions are given for all solutions to be oscillatory. Partially Supported by the National Science Foundation of China     

Time shifted aliasing error upper bounds for truncated sampling cardinal series

Time shifted aliasing error upper bound extremals for the sampling reconstruction procedure are fully characterized. Sharp upper bounds are found on the aliasing error of truncated cardinal series and the corresponding extremals are described for entire functions from certain specific Lp, p>1, classes. Analogous results are obtained in multidimensional regular sampling. Truncation error analysis is provided in all cases considered. Moreover, sharpness of bounding inequalities, convergence rates and various sufficient conditions are discussed.     

A model of weak viscoelastic nematodynamics

The paper develops a continuum theory of weak viscoelastic nematodynamics of Maxwell type. It can describe the molecular elasticity effects in mono-domain flows of liquid crystalline polymers as well as the viscoelastic effects in suspensions of uniaxially symmetric particles in polymer fluids. Along with viscoelastic and nematic kinematics, the theory employs a general form of weakly elastic thermodynamic potential and the Leslie–Ericksen–Parodi type constitutive equations for viscous nematic liquids, while ignoring inertia effects and the Frank (orientation) elasticity in liquid crystal polymers. In general case, even the simplest Maxwell model has many basic parameters. Nevertheless, recently discovered algebraic properties of nematic operations reveal a general structure of the theory and present it in a simple form. It is shown that the evolution equation for director is also viscoelastic. An example of magnetization exemplifies the action of non-symmetric stresses. When the magnetic field is absent, the theory is reduced to the symmetric, fluid mechanical case with relaxation properties for both the stress and director. Our recent analyses of elastic and viscous soft deformation modes are also extended to the viscoelastic case. The occurrence of possible soft modes minimizes both the free energy and dissipation, and also significantly decreases the number of material parameters. In symmetric linear case, the theory is explicitly presented in terms of anisotropic linear memory functionals. Several analytical results demonstrate a rich behavior predicted by the developed model for steady and unsteady flows in simple shearing and simple elongation.     

Viscoelastic properties of phosphoric and oxalic acid-based chitosan hydrogels

In a previous work, we have shown that chitosan true physical gelation occurs in some organic and inorganic acids (Hamdine et al. 2004). Two systems presenting similar gelation mechanisms were characterized furthermore in order to investigate the sol–gel transition: the chitosan–phosphoric acid and the chitosan–oxalic acid systems. By performing rheological measurements in the framework of linear viscoelasticity, we have investigated the effect of time, temperature, and polymer concentration on the gelation evolution. For both acid-based systems, gelation occurred above a critical polymer concentration around 5% w/v (g/100 ml) of chitosan. Isothermal time sweep experiments showed that the gelation occurs in three stages: (i) incubation; (ii) rapid increase of G′; and (iii) a last stage where G′ slowly reached its equilibrium value due to slow molecular diffusion. At the gel point, G′ and G′′ scaled with ω ⁿ , with n=0.55 for both acid-based systems and a fractal dimension d _f of 1.9. Cooling–heating cycles revealed that the gels showed thermoreversibility after one sequence, but became permanent during subsequent cycles.This revised version was published online in October 2005 with corrections to the author's name.     

Predictive values instead of normal ranges: less data, more information

Diagnostic strategies can have various goals at two levels: to facilitate the diagnostic process on the cognitive level, and to serve considerations on the level of the doctor–patient relationship. Requests for laboratory tests could be intended to exclude a disease or to affirm the presence of disease. Thirdly, tactical motives to smoothen the negotiations between doctor and patient probably seem to be important as well. These three intentions differ in prior probability, should lead to different sets of tests, and to different interpretations. Even the cut-off points should differ. This leads to three different decision strategies, both at requesting, as at interpreting the results. Following this line of thought, post-test probabilities are more suitable than normal ranges. Excluding strategy: this is the most prevalent. However, the disadvantage of an excluding strategy (prior 1–5%) is a false-positive result. A positive test result should lead to follow-up by wait and see or by repeated testing. More extensive testing usually is not a very sensible strategy. In practice, physicians simply ignore slightly abnormal values. Mentally they put the cut-off points for normality more broader. The number of tests is small. Confirmative strategy: the disadvantage of a confirmative intention (prior 10–30%) is a false-negative result. Follow-up without testing, repeated testing, or even accepting marginal normal results as abnormal is a proper strategy. The number of tests is moderate to high. Tactical strategy: the tactical intention strategy to reassure the patient – or avoid referrals – could lead to ignoring all slightly positive test results by choosing a higher cut-off point. Actually, considering the usual insignificant diagnostic gain when testing for tactical reasons, all test results are clinically insignificant, unsuspected outliers excluded. Here, a very limited set of tests should be chosen. The laboratory test is the currency in mutual trading medical expectations and relationship considerations between doctor and patient. The number of tests is minimal. If the physician chooses a strategy, a limited range of prior probability is chosen. Then a possibly computerized algorithm produces a “Value (posterior probability)” as test result, replacing “Value (normal ranges)”. Thus one number less on the lab form, yielding more significant information.Presented at the 10th Conference Quality in the Spotlight, March 2005, Antwerp, Belgium     

A new decoupled finite element algorithm for viscoelastic flow. Part 2: Convergence properties of the algorithm

We present the results of some numerical experiments which were carried out in order to investigate the general characteristics of the algorithm described in Part I of this paper.