NUMERICAL SIMULATION OF FLOW OF HIGHLY VISCOELASTIC FLOW IN THREE－DIMENSIONAL VARYING THICK SLIT CHANNEL

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Peristaltic motion of a third-order fluid in a planar channel

In order to determine the characteristics of the peristaltic transport of shear thinning non-Newtonian materials, the motion of a third-order fluid in a planar channel having walls that are transversely displaced by an infinite, harmonic traveling wave of large wavelength and negligibly small Reynolds number was analyzed using a perturbation expansion in terms of a variant of the Deborah number. Within the range of validity of this analysis, we found the pumping rate of a shear-thinning fluid is less than that for a Newtonian fluid having a shear viscosity the same as the lower-limiting viscosity of the nonNewtonian material. Also, the space of variables for which trapping of a bolus of fluid occurs is reduced for the shear-thinning fluid investigated here.     

Mixed Convection in a Horizontal Channel with Local Heating from Below

Mixed convection induced in the entrance region of a horizontal plane channel by a bottom heat source of finite dimensions is considered. The calculations were performed for the Prandtl number Pr = 1, Grashof numbers ranging from 4 · 10³ to 3.2 · 10⁴, and Reynolds numbers varying from 0 to 10. The dimensions of the heat source and its location were also varied. The results were obtained from a numerical solution of the 2D unsteady Navier-Stokes equations in the Boussinesq approximation, written in vorticity – stream function – temperature variables. The solution was found by the Galerkin finite element method.     

A method for calculating rheological and morphological properties of constant-volume polymer blend models in inhomogeneous shear fields

We show how to formulate two-point boundary-value problems in order to compute fully-developed laminar channel and tube flow profiles for viscoelastic fluid models. The formulation is applied to Couette and pressure-driven flows separately, or a combination of both. The application of this methodology is illustrated analytically for the Upper-Convected Maxwell Model, and it is applied computationally for the Phan-Thien/Tanner and Giesekus Models. Numerical solutions exist for the last two models [J.Y. Yoo, H.C. Choi, On the steady simple shear flows of the one-mode Giesekus fluid, Rheol. Acta 28 (1989) 13–24; P.J. Oliveira, F.T. Pinho, Analytical solution for fully developed channel and pipe flow of Phan-Thien–Tanner fluids, J. Fluid Mech. 387 (1999) 271–280; M.A. Alves, F.T. Pinho, P.J. Oliveira, Study of steady pipe and channel flows of a single-mode Phan-Thien–Tanner fluid, J. Non-Newtonian Fluid Mech. 101 (2001) 55–76], allowing verification of the computational technique. Subsequently, the computational algorithm is applied to the constant-volume polymer blend models of Maffettone and Minale [P.L. Maffettone, M. Minale, Equation of change for ellipsoidal drops in viscous flow, J. Non-Newtonian Fluid Mech. 84 (1999) 105–106 (Erratum), J. Non-Newtonian Fluid Mech. 78 (1998) 227–241] and Dressler and Edwards [M. Dressler, B.J. Edwards, The influence of matrix viscoelasticity on the rheology of polymer blends, Rheol. Acta 43 (2004) 257–282; M. Dressler, B.J. Edwards, Rheology of polymer blends with matrix-phase viscoelasticity and a narrow droplet size distribution, J. Non-Newtonian Fluid Mech. 120 (2004) 189–205]. Rheological and morphological properties of the model blends are thus obtained as functions of the spatial position within the channel, applied pressure drop, and shear rate at the wall.     

微管内气液两相流中液膜厚度的实验测量

微通道内气液两相流中气柱（plugbubble）与通道壁之间液膜厚度的实验测量，是微热管、微流动、微电子冷却以及气泡雾化等研究中普遍关注的问题。本文利用基于光学干涉和快速傅立叶变换的空间频谱分析方法，实验测量获取了含表面活性剂水中气柱在750μm通道内运动时其与通道壁面之间的液膜厚度。实验结果表明：表面活性剂对液膜厚度的影响比较明显，即当表面活性剂浓度在一定范围内增大时，液膜厚度会减小；此外，当气柱运动速度在一定范围内增大时，液膜厚度也会减小。     

Unsteady flow of viscoelastic fluid with fractional Maxwell model in a channel

The unsteady flow of viscoelastic fluid with the fractional derivative Maxwell model (FDMM) in a channel is studied in this note. The exact solutions are obtained for an arbitrary pressure gradient by means of the finite Fourier cosine transform and the Laplace transform. Two special cases of pressure gradient are discussed. Some results given by the classical models with integer-order are included in this note.     

奖惩机制下闭环供应链非正规渠道社会效应研究

针对闭环供应链非正规渠道在促进资源回收再利用的同时又对环境造成二次污染的情况,给出资源回收当量指标以综合考量渠道资源回收和再造污染效应,利用数学优化和数值仿真方法对比分析存在政府奖惩机制下非正规渠道的经济效应和资源回收效应,获得了非正规渠道积极社会效应的通用定理以及不同再造回收率和奖惩强度下非正规渠道社会效应的特点,给出了政府治理非正规渠道的参考建议和分析方法。     

On the Motion of Substance in a Channel of a Network: Extended Model and New Classes of Probability Distributions

We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network. This leads to an extension of the model of motion of substance and the extended model contains previous models as particular cases. We use a discrete-time model of motion of substance and consider a stationary regime of motion of substance in a channel containing a finite number of nodes. As results of the study, we obtain a class of probability distributions connected to the amount of substance in nodes of the channel. We prove that the obtained class of distributions contains all truncated discrete probability distributions of discrete random variable ω which can take values 0,1,⋯,N. Theory for the case of a channel containing infinite number of nodes is presented in Appendix A. The continuous version of the discussed discrete probability distributions is described in Appendix B. The discussed extended model and obtained results can be used for the study of phenomena that can be modeled by flows in networks: motion of resources, traffic flows, motion of migrants, etc.     

Self‐Assembly of a Tripod Aromatic Rod into Stacked Planar Networks

Threefold symmetric rigid‐core molecules with an internally grafted poly(ethylene oxide) (PEO) chain were synthesized, and their self‐assembled structures were characterized using differential scanning calorimetry, TEM, and 1D and 2D X‐ray scatterings in the solid state. The tripod compounds based on short PEO chains (n=8, 13, 17, 21), self‐assemble into 2D channel‐like network structures, whereas the compound with the longest PEO chain (n=34) forms a lamellar liquid crystalline phase. The interiors of the channel structures are filled with flexible PEO chains along the double‐walled aromatic circumference. In these channel‐like networks, three aromatic rods connected in the meta‐position to each other are superimposed in parallel to other adjacent molecules to form the double‐walled aromatic frameworks stacked perpendicular to the resulting channels. These are novel examples of supramolecular channel‐like structures developed using amphiphilic diblock molecules based on a threefold symmetric rigid scaffold.     

Reduced dimensionality (3,2)D NMR experiments and their automated analysis: implications to high‐throughput structural studies on proteins

Protein NMR spectroscopy has expanded dramatically over the last decade into a powerful tool for the study of their structure, dynamics, and interactions. The primary requirement for all such investigations is sequence‐specific resonance assignment. The demand now is to obtain this information as rapidly as possible and in all types of protein systems, stable/unstable, soluble/insoluble, small/big, structured/unstructured, and so on. In this context, we introduce here two reduced dimensionality experiments – (3,2)D‐hNCO canH and (3,2)D‐hN coCA nH – which enhance the previously described 2D NMR‐based assignment methods quite significantly. Both the experiments can be recorded in just about 2–3 h each and hence would be of immense value for high‐throughput structural proteomics and drug discovery research. The applicability of the method has been demonstrated using alpha‐helical bovine apo calbindin‐D9k P43M mutant (75 aa) protein. Automated assignment of this data using AUTOBA has been presented, which enhances the utility of these experiments. The backbone resonance assignments so derived are utilized to estimate secondary structures and the backbone fold using Web‐based algorithms. Taken together, we believe that the method and the protocol proposed here can be used for routine high‐throughput structural studies of proteins. Copyright © 2014 John Wiley & Sons, Ltd.