Gradient and vorticity banding

“Banded structures” of macroscopic dimensions can be induced by simple shear flow in many different types of soft matter systems. Depending on whether these bands extend along the gradient or vorticity direction, the banding transition is referred to as “gradient banding” or “vorticity banding,” respectively. The main features of gradient banding can be understood on the basis of a relatively simple constitutive equation. This minimal model for gradient banding will be discussed in some detail, and its predictions are shown to explain many of the experimentally observed features. The minimal model assumes a decrease of the shear stress of the homogeneously sheared system with increasing shear rate within a certain shear-rate interval. The possible microscopic origin of the severe shear-thinning behaviour that is necessary for the resulting nonmonotonic flow curves is discussed for a few particular systems. Deviations between experimental observations and predictions by the minimal model are due to obvious simplifications within the scope of the minimal model. The most serious simplifications are the neglect of concentration dependence of the shear stress (or on other degrees of freedom) and of the elastic contributions to the stress, normal stresses, and the possibility of shear-induced phase transitions. The consequences of coupling of stress and concentration will be analyzed in some detail. In contrast to predictions of the minimal model, when coupling to concentration is important, a flow instability can occur that does not require strong shear thinning. Gradient banding is sometimes also observed in glassy- and gel-like systems, as well as in shear-thickening systems. Possible mechanisms that could be at the origin of gradient-band formation in such systems are discussed. Gradient banding can also occur in strongly entangled polymeric systems. Banding in these systems is discussed on the basis of computer simulations. Vorticity banding is less well understood and less extensively investigated experimentally as compared to gradient banding. Possible scenarios that are at the origin of vorticity banding will be discussed. Among other systems, the observed vorticity-banding transition in rod-like colloids is discussed in some detail. It is argued, on the basis of experimental observations for these colloidal systems, that the vorticity-banding instability for such colloidal suspensions is probably related to an elastic instability, reminiscent of the Weissenberg effect in polymeric systems. This mechanism might explain vorticity banding in discontinuously shear-thickening systems and could be at work in other vorticity-banding systems as well. This overview does not include time-dependent phenomena like oscillations and chaotic behaviour.     

Hall effects on the magnetohydrodynamic shear flow past an infinite porous flat plate subjected to uniform suction or blowing

An analysis is made of Hall effects on the steady shear flow of a viscous incompressible electrically conducting fluid past an infinite porous plate in the presence of a uniform transverse magnetic field. It is shown that for suction at the plate, steady shear flow solution exists only when S²<Q, where S and Q are the suction and magnetic parameters, respectively. The primary flow velocity decreases with increase in Hall parameter m. But the cross-flow velocity first increases and then decreases with increase in m. Similar results are obtained for variation of the induced magnetic field with m. It is further found that for blowing at the plate, steady shear flow solution exists only when , where S₁ is the blowing parameter.     

Estimation of vertical wind velocity using doppler radar data with vorticity constraints

The vorticity equation and the mass continuity equation are used as constraints to aid in calculation of the vertical component of a wind field from horizontal wind components. Typically the horizontal wind components result from estimations obtained from radar data. Using a Hilbert space minimization formulation, we characterize the estimated vertical velocity as a solution of an elliptic boundary value problem whose coefficients are functions of the horizontal wind components. Differentiable dependence of the vertical component of the wind field with respect to the horizontal fields is established. Finite dimensional approximating problems are obtained. A numerical study is presented using a sample problem based on the Beltrami flow to compare accuracy of the estimated vertical wind component with the exact. Also, sensitivity to perturbations in horizontal wind components are observed.     

玉米和类玉米杂交后代异染色质纽的遗传稳定性分析

利用玉米的近缘亲属摩擦禾的基因组DNA。对玉米自交系330、二倍体多年生类玉米及其远缘杂交孤雌生殖后代异源种质纯系540的染色体进行比较基因组原位杂交，发现上述3个供试种染色体上的异染色质纽因杂交信号极强而能被清楚地显示．与亲代相比，540中出现异染色质纽数目减少的现象．并讨论了造成这种现象的可能原因．     

Three dimensional non-isentropic subsonic Euler flows in rectangular nozzles

In this paper, we study the existence and uniqueness of three dimensional non-isentropic subsonic Euler flows in rectangular nozzles. This work is an extension of Chen and Xie’s work on isentropic subsonic Euler flows. If, besides small normal component of vorticity, Bernoulli’s function and entropy function with small variations are given on the entrance, the existence and uniqueness of non-isentropic subsonic Euler flows are established.     

Approximations of steady periodic water waves in flows with constant vorticity

We provide high-order approximations to periodic travelling wave profiles and to the velocity field and the pressure beneath the waves, in flows with constant vorticity over a flat bed.     

Performance of a 12-sensor vorticity probe in the near field of a rectangular turbulent jet

The design and operational characteristics of a 12-sensor hot wire probe for three-dimensional velocity–vorticity measurements in turbulent flow fields is described and discussed. The performance of the probe is investigated in comparison with X-sensor probe measurements in the near field of a rectangular turbulent jet with aspect ratio 6. Measurements have been conducted at Reynolds number Re _D = 21,000 at nozzle distances of x/D = 1, 3, 6 and 11, where D is the width of the nozzle. The results obtained with the 12-sensor probe compare well to the results of the X-sensor probe. Distributions of mean and fluctuating velocity–vorticity fields are presented and discussed. Among the results the most prominent is the experimental confirmation of the high levels of fluctuating vorticity in the shear layers.     

Potential flow of viscous fluids: Historical notes

In this essay I will attempt to identify the main events in the history of thought about irrotational flow of viscous fluids. I am of the opinion that when considering irrotational solutions of the Navier–Stokes equations it is never necessary and typically not useful to put the viscosity to zero. This observation runs counter to the idea frequently expressed that potential flow is a topic which is useful only for inviscid fluids; many people think that the notion of a viscous potential flow is an oxymoron. Incorrect statements like “… irrotational flow implies inviscid flow but not the other way around” can be found in popular textbooks.     

Conditions for similitude and the effect of finite Debye length in electroosmotic flows

Under certain conditions, the velocity field is similar to the electric field for electroosmotic flow (EOF) inside a channel. There was a disagreement between investigators on the necessity of the infinitesimal-Reynolds-number condition for the similarity when the Helmholtz-Smoluchowski relation is applied throughout the boundaries. What is puzzling is a recent numerical result that showed, contrary to the conventional belief, an evident Reynolds number dependence of the EOF. We show here that the notion that the infinitesimal-Reynolds-number condition is required originates from the misunderstanding that the EOF is the Stokes flow. We point out that the EOF becomes the potential flow when the Helmholtz-Smoluchowski relation is applied at the boundaries. We carry out a numerical simulation to investigate the effect of finiteness of the Debye length and the vorticity layer inherently existing at the channel wall. We show that the Reynolds number dependence of the previous numerical simulation resulted from the finiteness of the Debye length and subsequent convective transport of vorticity toward the bulk flow. We discuss in detail how the convection of vorticity occurs and what factors are involved in the transport process, after carrying out the simulation for different Reynolds numbers, Debye lengths, corner radii, and geometries.