Effects of viscosity on droplet formation and mixing in microfluidic channels

This paper characterizes the conditions required to form nanoliter-sized droplets (plugs) of viscous aqueous reagents in flows of immiscible carrier fluid within microfluidic channels. For both non-viscous (viscosity of 2.0 mPa s) and viscous (viscosity of 18 mPa s) aqueous solutions, plugs formed reliably in a flow of water-immiscible carrier fluid for Capillary number less than 0.01, although plugs were able to form at higher Capillary numbers at lower ratios of the aqueous phase flow rate to the flow rate of the carrier fluid (in all the experiments performed, the Reynolds number was less than 1). The paper also shows that combining viscous and non-viscous reagents can enhance mixing in droplets moving through straight microchannels by providing a nearly ideal initial distribution of reagents within each droplet. The study should facilitate the use of this droplet-based microfluidic platform for investigation of protein crystallization, kinetics, and assays.     

TiO2-Al2O3复合载体的比较研究

对用混胶法和共沉淀法分别制备的ＴｉＯ２－Ａｌ２Ｏ３复合载体（ＴｉＯ２含量为０．０８ｇ／ｇγ－Ａｌ２Ｏ３）进行了对比研究，采用的表征方法有ＸＲＤ，ＸＲＳ，ＬＲＳ等，得出的结论如下：两种载体均保持了γ－Ａｌ２Ｏ３的骨架结构，但ＴｉＯ２的分散状态不尽相同，混胶样品中ＴｉＯ２主要以表面富集的形式分散在γ－Ａｌ２Ｏ３表面，这有利于集二者的优点于一体，共沉淀样品中ＴｉＯ２趋于整个体相均匀分散，这有利于相互作用     

Estimating the mixing time of concert halls using the eXtensible Fourier Transform

In room acoustics, we measure room impulse responses (RIRs) in order to fully describe the hall. RIRs are composed of a succession of arrivals (i.e., some sound rays which have undergone one or more reflections on their way from the source to the receiver). We propose the eXtensible Fourier Transform (XFT) in order to investigate the time evolution of spectral components of RIRs. The phase evolution versus time allows to estimate the mixing time, which is defined as the time it takes for initially adjacent sound rays to spread uniformly across the room. After presenting some properties of the XFT, we show why one must compensate the natural energy decay of the RIR in order to obtain stationary signals. We estimate mixing times for a set of experimental RIRs and several that are synthesized using a stochastic model. Then, we estimate the dependance of mixing time upon the source/receiver distance in all these RIRs. Results are consistent up to the lack of reproducibility of the sound sources, but are strongly dependent on some parameters used for computing the XFT. We finally discuss the relevance of the name mixing time with respect to the theory and in regard to the time we estimate, that we propose to call cross-over time.     

Molecular Mixing and Flowfield Measurements in a Recirculating Shear Flow. Part I: Subsonic Flow

The mixing and flowfield of a complex geometry, similar to a rearward-facing step flow but with injection, is studied. A subsonic top-stream is expanded over a perforated ramp at an angle of 30°, through which a secondary stream is injected. The mass flux of the second stream is chosen to be insufficient to provide the entrainment requirements of the shear layer, which, as a consequence, attaches to the lower guidewall. Part of the flow is directed upstream forming a re-entrant jet within the recirculation zone that enhances mixing and flameholding. A control-volume model of the flow is found to be in good agreement with the variation of the overall pressure coefficient of the device with variable mass injection. The flowfield response to changing levels of heat release is also quantified. While increased heat release acts somewhat analogously to increased mass injection, fundamental differences in the flow behaviour are observed. The hypergolic hydrogen-fluorine chemical reaction employed allows the level of molecular mixing in the flow to be inferred. The amount of mixing is found to be higher in the expansion-ramp geometry than in classical free-shear layers. As in free-shear layers, the level of mixing is found to decrease with increasing top-stream velocity. Results for a similar configuration with supersonic flow in the top stream are reported in Part II of this two-part series.     

Lot-sizing on a tree

For the problem of lot-sizing on a tree with constant capacities, or stochastic lot-sizing with a scenario tree, we present various reformulations based on mixing sets. We also show how earlier results for uncapacitated problems involving (Q,S_Q) inequalities can be simplified and extended. Finally some limited computational results are presented.     

A parallel search game

We answer in negative a question of Gál and Miltersen [Proc 30th Int Coll Automata, Languages, and Programming (ICALP) 2003, pp. 332–344] about a combinatorial game arising in the study of time‐space trade‐offs for data structures. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

Optimizing the source distribution in fluid mixing

A passive scalar is advected by a velocity field, with a nonuniform spatial source that maintains concentration inhomogeneities. For example, the scalar could be temperature with a source consisting of hot and cold spots, such that the mean temperature is constant. Which source distributions are best mixed by this velocity field? This question has a straightforward yet rich answer that is relevant to real mixing problems. We use a multiscale measure of steady-state enhancement to mixing and optimize it by a variational approach. We then solve the resulting Euler-Lagrange equation for a perturbed uniform flow and for simple cellular flows. The optimal source distributions have many broad features that are as expected: they avoid stagnation points, favour regions of fast flow, and their contours are aligned such that the flow blows hot spots onto cold and vice versa. However, the detailed structure varies widely with diffusivity and other problem parameters. Though these are model problems, the optimization procedure is simple enough to be adapted to more complex situations.     

Cryptographic properties of nonlinear pseudorandom number generators

The cryptographic properties of keystreams generated by stream ciphers based on t-functions are studied. These constructions are of great interest as they allow building highly efficient and secure cryptographic primitives. The randomness of the coordinate sequences generated by such mappings is analyzed in terms of the autocorrelation function. The results derived are valid for all t-functions regardless the type of construction and indicate the existence of nonrandomness. As the problem of the efficient implementation of secure s-boxes is open, the nonlinearity of t-functions is also analyzed. It is shown how some cryptographically undesirable properties, can be solved by application of similarity transformations.      

Mixing is an aggregation processLe mélange est un processus d'agrégation

With the aid of several demonstration experiments, it is shown how a stirred scalar mixture relaxes towards uniformity through an aggregation process. The elementary bricks are stretched sheets whose rates of diffusive smoothing and coalescence build up the overall mixture concentration distribution. The cases studied, in particular, include mixtures in two and three dimensions, with different stirring protocols, which all lead to a family of concentration distributions stable by self-convolution. To cite this article: E. Villermaux, J. Duplat, C. R. Mecanique 331 (2003).