Effect of fibrils on curvature- and rotation-induced hydrodynamic stability

Flow of a suspension of water and nano-fibrillated cellulose (NFC) in a curved and rotating channel is studied experimentally and theoretically. The aim is to investigate how NFC affects the stability of the flow. This flow is subject to a centrifugal instability creating counter-rotating vortices in the flow direction. These rolls can be both stabilised and destabilised by system rotation, depending on direction and velocity of the rotation. Flow visualisation images with pure water and an NFC/water suspension are categorised, and stability maps are constructed. A linear stability analysis is performed, and the effect of fibrils is taken into account assuming straight fibrils and constant orientation distributions, i.e., without time-dependent flow-orientation coupling. The results show that NFC has a less stabilising effect on the primary flow instability than indicated from the increase in viscosity measured by a rotary viscometer, but more than predicted from the linear stability analysis. Several unknown parameters (the most prominent being fibril aspect ratio and the interaction parameter in the rotary diffusion) appear in the analysis.     

Stability of flow of a structurally viscous fluid in the boundary layer on a flat plate

The method of small perturbations has been used to study the hydrodynamical stability of flow of a structurally viscous fluid in the boundary layer on a flat plate.     

Fluid reaction on a vibrating disc in a viscous medium

This article studies the fluid reaction on a vibrating disc immersed in a viscous fluid. The fluid is considered incompressible and Newtonian. The disc which is of negligible thickness vibrates harmonically in the direction perpendicular to its surface with an amplitude much smaller than the radius of the disc, in such a way that the non-linear terms can be neglected. The flow is axisymmetric and the velocity tends to zero away from the disc. Different approaches to this problem are presented. The first method consists in solving numerically an integral equation obtained from the Navier–Stokes equation. The second method calculates in an analytic fashion the asymptotic series for the pressure differential across the plate for large values of the dimensionless parameter β, equal to the frequency times the radius squared divided by the kinematic viscosity. The limit when β tends to zero is also studied. The analytical expressions give more reliable results when approaching the limits β large and β small than the numerical solution.     

Nonlinear stability of a viscous axisymmetric jet

Summary The nonlinear temporal stability of a viscous axisymmetric jet is studied with respect to axisymmetric disturbances. The weakly nonlinear Stuart Watson perturbation expansion is used to study the self interaction of the fundamental in a neighborhood of the critical Reynolds number (R _c). The Landau constant is positive indicating there is a supercritical Hopf bifurcation. In order to extend these results pastRR _c, a severely truncated Fourier modal expansion using the Stuart Watson functions to represent ther dependence, exponentials inz and unknown amplitudes in time is substituted into the Navier-Stokes equation. A projection onto an appropriate subspace leads to a low dimensional (five) system of amplitude equations for the disturbance of the fundamental, harmonic and distortion to the mean flow.Numerical results show that the periodic solution is stable for 55.3<R<72.3. There is a secondary bifurcation atR=72.3 to a quasiperiodic solution with 2 incommensurate frequenciesf ₁ andf ₂. Each peak in the Fourier spectrum can be indexed according tof=f ₁+nf ₂ forn=0,±1,±2,... AsR increases pastR=78 there is a transition through another periodic regime and then finally a transition to intermittency for 100<R<1000. No chaotic solutions were observed in this low dimensional model.     

Force on a defect in non-linear elastic medium

A derivation is given for the force per unit surface of a defect (e.g. a dislocation) in a non-linear elastic medium. The derivation is based on a Lagrangian of the same form as in linear elasticity, introduced in [1]. Principle of energy conservation is deduced on the basis of a particular case of Noether's theorem. Some peculiar properties of the Lagrangian are discussed. In the particular case of a constant Burgers vector the force reduces to the Peach-Koehler force per unit dislocation line, known in the linear theory of elasticity.     

Modelling micromachines with elastic parts in a viscous environment

 Designing micromachines with elastic components has not been addressed by the research community. In this paper, the Boundary Element Method for Stokes flows is used to model a micromachine consisting of a “head” and an elastic “tail” immersing in viscous fluid. The general numerical implementation can be used for a wide range of micromachines with rotating and arbitrarily deforming tail. A particular periodic tail motion is suggested for illustrative purposes. To assist the forward motion, enlarging of the head during the second half cycle only is proposed. A physical model has been suggested that may be used for comparing its performance with that deduced from our calculations.     

Effect of fluid viscosity on wave propagation in a cylindrical bore in micropolar elastic medium

Wave propagation in a cylindrical bore filled with viscous liquid and situated in a micropolar elastic medium of infinite extent is studied. Frequency equation for surface wave propagation near the surface of the cylindrical bore is obtained and the effect of viscosity and micropolarity on dispersion curves is observed. The earlier problems of Biot and of Banerji and Sengupta have been reduced as a special case of our problem.     

VPF粘性介质粘弹性本构关系研究

为研究粘性介质的力学性能对板材变形的影响,通过剪切蠕变-回复和松弛试验分析了甲基乙烯基粘性介质的流变性能.实验结果表明粘性介质可以简化为线性粘弹性材料.建立了粘性介质的积分型粘弹性本构方程,并结合剪切蠕变-回复过程的有限元分析确定了方程中的材料参数.利用该本构方程对粘性介质压力胀形过程进行了有限元分析,模拟结果与试验结果对比表明,所建立的本构方程可以较好的预测板材的变形过程.     

The unsteady hydrodynamic force during the collision of two spheres in a viscous fluid

The time-dependent Stokes equations were solved in the vicinity of two spheres colliding in a viscous fluid with viscosity ν to determine the rate of change of the hydrodynamic forces during large accelerations associated with Hertzian mechanical contact of small duration \({\tau_{\rm c}}\). It was assumed that the gap clearance remains finite during contact and is approximately equal to the height σ of surface micro-asperities. The initial condition corresponds to the steady-state axisymmetric solution of Cooley and O’Neill (Mathematika 16:37–49, 1969), and the initial value problem for the time-dependent Stokes streamfunction was solved using Laplace transform methods. Assuming that σ is small compared to the sphere radius a, we used singular perturbation expansions and tangent-sphere coordinates to obtain an asymptotic solution for the viscous flow in the gap and around the moving sphere. The solution provides the dependence of the resistance, added mass and history forces on σ, the sphere velocity and acceleration, and the ratio of the sphere diameters. We found that the relative importance of viscous and mechanical forces during contact depends on a new Stokes number \({St_{\rm c}=\sigma^2/\nu \tau_{\rm c}}\). Integration of Newton’s equation for the motion of the sphere during mechanical contact showed that there is a critical \({St_{\rm c}=O(\sigma/a)}\) for which there is no rebound at the end of contact.     

Effect of the temperature on the hydrodynamic efficiency and stability of polyethylene oxide and polyacryl amide

The article describes a comparative study of the effect of the temperature on the hydrodynamic efficiency and stability of polyethylene oxide (PEO) and polyacryl amide (PAA).Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 4, pp. 558–565, October, 1984.     

Some experiments on the elastic stability of some highly elastic bodies

Uniaxial compression experiments on solid circular bars, rectangular bars, and thick-walled circular tubes made of rubber materials are described, and the data are compared with known theoretical results derived for neo-Hookean materials. It is found in all cases that the general nature of certain global analytical estimates are in good qualitative agreement with existence of a transition slenderness ratio that separates buckling characteristic of long bars from axisymmetrie bulging characteristic of short bars. The data agrees qualitatively also with other more precise analytical results for circular and rectangular bars, but only as regards Euler type buckling. Specific analytical results for axisymmetrie deformation of circular tubes are found to be without experimental foundation.     

Resistance to the free steady-state motion of a sphere in a viscous medium

An approximate method is proposed for calculating the drag and velocity of spherical particles in a viscous medium.     

The motion of a particle in a nonuniform moving viscous medium

The motion of particles is examined in a nonuniform moving viscous medium in the regions Re < 1 and 1 < Re 300. Solutions are presented for the differential equations which make it possible to calculate the trajectories of particle motion in a nonuniform moving viscous medium.     

Flow stability of a film of viscous liquid on the surface of a rotating disk

The stability of a steady axisymmetric flow of a film is studied using the assumption of local plane parallelity. We present the results of numerical calculation.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 52, No. 6, pp. 936–940, June, 1987.