An innovative extensional viscometer for low-viscosity and low-elasticity liquids

A spinline-type extensional viscometer is described in which an innovative method of tensile stress measurement is employed. A limited amount of liquid flows through a vertical capillary at a constant flow rate under the influence of a constant pressure head. The drainage time decreases when the liquid stream leaving the capillary is stretched by the application of vacuum. These drainage times are measured in a manner similar to that used for intrinsic viscosity measurements. The measured difference in drainage times, with and without stretching, is trivially related to the extensional stress at the capillary exit, and this provides a very simple method of accurately determining fluid stretching forces having a magnitude as low as 10^-4 N; stresses at other axial locations in the stretched liquid jet are obtained by means of a force balance in the usual manner. The validity of the proposed technique is demonstrated by obtaining the expected results for a Newtonian oil having a shear viscosity of 56.2 mPa-s. Also presented are preliminary data on polyethylene oxide-in-water solutions having an even lower shear viscosity.     

The mechanical problems in tumor and tumor microenvironment

肿瘤微环境包括肿瘤细胞、间质细胞、细胞外基质等.其在肿瘤的生长和发展过程中起着关键作用.肿瘤的微环境与正常组织的微环境有着显著的不同.肿瘤中的压应力对微环境有着多方面的影响, 例如, 可调控血管与淋巴管的功能, 造成代谢异常和间质高压, 压缩间隙基质, 增大药物输运的困难, 促进间质细胞变异并诱导肿瘤细胞转移. 因此, 肿瘤中的力学因素引起了广泛关注.本文总结了肿瘤及其微环境力学问题的研究进展, 讨论了肿瘤微环境中应力产生、药物输运、肿瘤转移等问题, 介绍了肿瘤微环境正常化的策略及其对肿瘤治疗的意义.     

On the basic laws of anisotropic viscoelasticity

The main aim of this work is to develop a consistent formulation of the rheological behavior for different anisotropic polymer systems. The unified theory of anisotropic viscoelasticity is developed based on the symmetry principles. The Maxwell rheological equation is extended to nonsymmetric anisotropic liquids. Transitions from the most general anisotropy to particular cases of anisotropy are established. It appears that the coupled relaxation of symmetric and antisymmetric stresses is a natural phenomenon in nonsymmetric viscoelasticity. Within the concept of an internal state variable, a stress–order relation is derived for a fully nonlinear case. The order tensor dynamics is also considered. A simple method of deriving the equation of the internal rotational motion is developed for the general macroscopic anisotropy. This paper was presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece     

Sharp Estimates of Bounded Solutions to Some Second-order Forced Dissipative Equations

Résumé A l’aide d’inégalités différentielles, on établit une estimation proche de l’optimalité pour la norme dans de l’unique solution bornée de u′′ + cu′ + Au = f(t) lorsque A = A ^* ≥ λ I est un opérateur borné ou non sur un espace de Hilbert réel H, V = D(A ^1/2) et λ, c sont des constantes positives, tandis que . By using differential inequalities, a close-to-optimal bound of the unique bounded solution of u′′ + cu′ + Au = f(t) is obtained whenever A = A ^* ≥ λ I is a bounded or unbounded linear operator on a real Hilbert space H, V = D(A ^1/2) and λ, c are positive constants, while .

---

     

On a Serrin-Type Regularity Criterion for the Navier–Stokes Equations in Terms of the Pressure

We prove a Serrin-type regularity result for Leray–Hopf solutions to the Navier–Stokes equations, extending a recent result of Zhou [28].     

Axisymmetric free vibrations of infinite thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Flows in a lower half heated upper half cooled cylindrical model reactor loaded with porous media

This paper presents an experimental and numerical investigation on the natural convection flow in a cylindrical model hydrothermal reactor. The flow is visualized non-intrusively and simulated with a conjugate computational model. Results show that the flow structure consists of wall layers and core flows. In the lower half, the flows are steady due to the porous media. The three-dimensional unsteady upper core flow is driven by the streams originated from the wall layer collision. The thermal condition in the upper half core region is mainly determined by the total heat flow rate specified on the lower sidewall; while the variations of porous media parameters, in the normal range for hydrothermal crystal growth process, have minor effects.     

Stability and Synchronization of a Ring of Identical Cells with Delayed Coupling

We consider a ring of identical elements with time delayed, nearest neighbour coupling. The individual elements are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. The linear stability of the trivial solution is completely analyzed and illustrated in the parameter space of the coupling strength and the coupling delay. Conditions for global stability of the trivial solution are also given. The bifurcation and stability of nontrivial synchronous solutions from the trivial solution is analyzed using a centre manifold construction.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.     

Fluid dynamics of self-propelled microorganisms,from individuals to concentrated populations

Nearly close-packed populations of the swimming bacterium Bacillus subtilis form a collective phase, the “Zooming BioNematic” (ZBN). This state exhibits large-scale orientational coherence, analogous to the molecular alignment of nematic liquid crystals, coupled with remarkable spatial and temporal correlations of velocity and vorticity, as measured by both novel and standard applications of particle imaging velocimetry. The appearance of turbulent dynamics in a system which is nominally in the regime of Stokes flow can be understood by accounting for the local energy input by the swimmers, with a new dimensionless ratio analogous to the Reynolds number. The interaction between organisms and boundaries, and with one another, is modeled by application of the methods of regularized Stokeslets.     

Numerical investigation of transpiration and ablation cooling

To predict the integral performance of transpiration and ablation cooling during the reentry of hypersonic vehicles, an unsteady numerical model based on the assumption of thermal equilibrium is presented. The non-thermal equilibrium model and the thermal equilibrium model are coupled by the effective thermal properties of the porous matrix and the coolant. The calculation using the thermal equilibrium model shows the influence of the variation of the effective thermal properties on the numerical results by a comparison between constant and variable thermal properties. The comparison indicates that near the melting temperature of the porous matrix, the position of the moving boundary due to ablation is sensitive to the temperature, therefore, the variation of the thermal properties are considered in this paper. The process of ablation and transpiration cooling is simulated under different numerical conditions. The simulations demonstrate that the injection rate of coolant mass flow and initial temperature of cooling are important parameters for the control of the ablation process.