Rotating electroosmotic flow of an Eyring fluid

A perturbation analysis is presented in this paper for the electroosmotic (EO) flow of an Eyring fluid through a wide rectangular microchannel that rotates about an axis perpendicular to its own. Mildly shear-thinning rheology is assumed such that at the leading order the problem reduces to that of Newtonian EO flow in a rotating channel, while the shear thinning effect shows up in a higher-order problem. Using the relaxation time as the small ordering parameter, analytical solutions are deduced for the leading- as well as first-order problems in terms of the dimensionless Debye and rotation parameters. The velocity profiles of the Ekman-electric double layer (EDL) layer, which is the boundary layer that arises when the Ekman layer and the EDL are comparably thin, are also deduced for an Eyring fluid. It is shown that the present perturbation model can yield results that are close to the exact solutions even when the ordering parameter is as large as order unity. By this order of the relaxation time parameter, the enhancing effect on the rotating EO flow due to shear-thinning Eyring rheology can be significant.

On the time development of dispersion in electroosmotic flow througha rectangular channel

This is an analytical study on the time develop- ment of hydrodynamic dispersion of an inert species in elec- troosmotic flow through a rectangular channel. The objec- tive is to determine how the channel side walls may affect the dispersion coefficient at different instants of time. To this end, the generalized dispersion model, which is valid for short and long times, is employed in the present study. An- alytical expressions are derived for the convection and dis- persion coefficients as functions of time, the aspect ratio of the channel, and the Debye-Htickel parameter representing the thickness of the electric double layer. For transport in a channel of large aspect ratio, the dispersion may undergo several stages of transience. The initial, fast time develop- ment is controlled by molecular diffusion across the narrow channel height, while the later, slower time development is governed by diffusion across the wider channel breadth. For a sufficiently large aspect ratio, there can be an interlude between these two periods during which the coefficient is nearly steady, signifying the resemblance of the transport to that in a parallel-plate channel. Given a sufficiently long time, the dispersion coefficient will reach a fully-developed steady value that may be several times higher than that with- out the side wall effects. The time scales for these periods of transience are identified in this paper.

Effect of a Submerged Porous Plate on the Hydroelastic Response of a Very Large Floating Structure

Scattering of oblique flexural-gravity waves by a submerged porous plate in a finite water depth is investigated under the assumptions of linearized surface waves and small-amplitude structural response. The study is carried out using eigenfunction expansions and the corresponding orthogonal mode-coupling relations associated with flexural-gravity waves in uniform water depth. The characteristics of the roots of the complex dispersion relation are examined using the principle of counting argument and contour plot. Characteristics of the flexural-gravity waves are studied by assuming both the floating elastic plate and the submerged porous plate are infinitely extended in horizontal directions. The effectiveness of the submerged porous structure on the reflection, transmission, and dissipation coefficients is analyzed for various wave and structural parameters.

Propagating characteristics of waves on a thin layer of mud

The propagating characteristics of the water and muddy waves are one of the concerns of theoretical studies because of the following facts:(1)With the development of the economy in the estuaries,local residents and government paid increasing attention to the ecological environment of the estuarine beaches The propagating characteristics of the water and muddy waves are closely related to the ecological environment,the concern of the government and the residents.(2)The propagating characteristics of the mud are the bottleneck of the study of the coastal and beach dynamics because of the complicated constitutive relation of the mud.The different constitutive models may lead to different explanations of its mechanism.Hence,the proper selection of the model is one of the keys to reveal the true kinematic properties of the mud in the estuaries.This paper first establishes a power law model of the constitutive relation of the mud.Based on this model,a gravity wave theory is proposed.According to the mechanism of the mud wave transportation,the coupled mud-water wave field can be divided into two layers.The upper layer is described as the viscous Newtonian fluid,whereas the lower high-concentration mud layer is described as the power law fluid.Next,the equations of the proposed model are discretized and the calculations are made by using the difference method.Then,the propagating characteristics are discussed,and the dispersion relations of the water and mud waves are analyzed in detail.

推移质运动过程的非线性动力学特性

天然沙质海岸及河床上存在着不同形式的床面形态,其运动变化受床面附近推移质泥沙的运动特性所决定.从床面层内推移质集体运动出发,探讨了推移质运动过程的非线性动力学特性,发现泥沙起动、推移质平衡输沙以及床面形态由平整到沙纹及沙垄等不同发展阶段,受推移质运动过程的非线性动力特征所决定,它们分别对应于推移运动过程中的不同非线性状态.通过与法国夏都水利实验室床面形态试验比较,进一步证明:“床面形态从平整到沙垄的演化与否”由推移质泥沙运动过程的突变特性所决定,“突变分界线”是平整床面与沙纹及沙垄床面的分界曲线.

Nonlinear dynamical characteristics of bed load motion

Bed forms of various kinds that evolve naturally on the bottom of sandy coasts and rivers are a result of the kinematics of bed load transport. Based on the group motion of particles in the bed load within the bottom layer, a study on the nonlinear dy- namics of bed load transport is presented in this paper. It is found that some development stages, such as the initiation, the equilibrium sediment transport, and the transition from a smooth bed to sand dunes, can be accounted for by different states in the nonlinear sys- tem of the bed load transport. It is verified by comparison with experimental data reported by Laboratoire Nationae D’Hydraulique, Chatou, France, that the evolution from a smooth bed to sand dunes is determined by mutation in the bed load transport. This paper pre- sents results that may offer theoretical explanations to the experimental observations. It is also an attempt to apply the state-of-the-art nonlinear science to the classical sediment transport mechanics.