Shape reconstruction of an inverse boundary value problem of two‐dimensional Navier–Stokes equations

This paper is concerned with the problem of the shape reconstruction of two‐dimensional flows governed by the Navier–Stokes equations. Our objective is to derive a regularized Gauss–Newton method using the corresponding operator equation in which the unknown is the geometric domain. The theoretical foundation for the Gauss–Newton method is given by establishing the differentiability of the initial boundary value problem with respect to the boundary curve in the sense of a domain derivative. The numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible. Copyright © 2009 John Wiley & Sons, Ltd.     

On non-Newtonian p-fluids. The pseudo-plastic case

In the following we study a class of stationary Navier-Stokes equations with shear dependent viscosity, under the non-slip (Dirichlet) boundary condition. We consider pseudo-plastic fluids. A fluid is said pseudo-plastic, or shear thinning, if in Eq. (1.1) below one has p<2. We are interested in global (i.e., up to the boundary) regularity results, in dimension n=3, for the second order derivatives of the velocity and the first order derivatives of the pressure. We consider a cubic domain Ω and impose the non-slip boundary condition only on two opposite faces. On the other faces we assume periodicity, as a device to avoid effective boundary conditions. This choice is made so that we work in a bounded domain Ω and simultaneously with a flat boundary.     

Numerical simulations of droplet formation in a cross‐junction microchannel by the lattice Boltzmann method

An immiscible liquid–liquid multiphase flow in a cross‐junction microchannel was numerically studied using the lattice Boltzmann method. An improved, immiscible lattice BGK model was proposed by introducing surface tension force based on the continuum surface force (CSF) method. Recoloring step was replaced by the anti‐diffusion scheme in the mixed region to reduce the side‐effect and control the thickness of the interface. The present method was tested by the simulation of a static bubble. Laplace's law and spurious velocities were examined. The results show that our model is more advantageous for simulations of immiscible fluids than the existing immiscible lattice BGK models. Computational results of multiphase flow in a cross‐junction microchannel were obtained and analyzed based on dimensionless numbers. It is found that the flow pattern is decided mostly by the capillary number at a small inlet flux. However, at the same capillary number, a large inlet flux will lead to much smaller droplet generation. For this case, the flow is determined by both the capillary number and the Weber number. Copyright © 2007 John Wiley & Sons, Ltd.     

A note on the second problem of Stokes for Maxwell fluids

New exact solutions corresponding to the second problem of Stokes for Maxwell fluids have been established by means of Laplace transforms. For large times, these solutions reduce to the well-known steady-state solutions which are periodic in time and independent of the initial conditions. Furthermore, the transient solutions are in accordance with the previous solutions obtained using the Fourier sine transform. The required time to get the steady-state is determined by graphical illustrations. This time decreases if the frequency of the velocity increases. The effects of the material parameters on the decay of the transients in time are also investigated by graphs.     

Topology optimization of microfluidic mixers

This paper demonstrates the application of the topology optimization method as a general and systematic approach for microfluidic mixer design. The mixing process is modeled as convection dominated transport in low Reynolds number incompressible flow. The mixer performance is maximized by altering the layout of flow/non‐flow regions subject to a constraint on the pressure drop between inlet and outlet. For a square cross‐sectioned pipe the mixing is increased by 70% compared with a straight pipe at the cost of a 2.5 fold increase in pressure drop. Another example where only the bottom profile of the channel is a design domain results in intricate herring bone patterns that confirm findings from the literature. Copyright © 2008 John Wiley & Sons, Ltd.     

Study of adsorption processes of model drugs at supercritical conditions using partial least squares regression

The characterisation of adsorption or impregnation processes using conventional or supercritical fluid technologies becomes an increasing part of the research on drug formulations. The complexity of the relationships between these adsorption processes and the experimental variables potentially influencing them, however, makes these studies more problematic. In this paper, a chemometric approach based on nonlinear partial least squares (NL-PLS) modelling is applied to characterise the effect of the experimental variables on the supercritical impregnation process. Various adsorbent materials such as silica gel, zeolite and amberlite were investigated using the following model compounds as adsorbates: benzoic, salicylic and acetylsalicylic acids.     

广义旋转Navier-Stokes方程解的整体适定性和解析性

在α和q满足适当的条件下，当初值属于Fourier-Herz空间?_q^1-2α（R³）时，我们建立了广义3维不可压旋转Navier-Stokes方程温和解的整体适定性和解析性.作为推论，我们也给出了广义Navier-Stokes方程的相应结论.     

Capillary instability of an annular liquid jet surrounding a solid cylinder

Summary The capillary instability of an annular liquid jet surrounding a solid cylinder is presented. A general dispersion equation is derived based on the linear-perturbation technique. The instability as well as stability characteristics of that model are identified analytically and confirmed numerically. The model is unstable only to the axisymmetric perturbation whose wavelengths are longer than the circumference of the liquid jet, while it is stable to all other perturbations. The maximum temporal amplification values prevailing on such a model are fairly lower than those of the full liquid jet. The thicker the solid cylinder, whether it is regular or irregular, the larger is its stabilizing effect.

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Riassunto Si presenta l’instabilità capillare di un getto anulare di liquido che circonda un cilindro solido. Si deduce un’equazione generale di dispersione basata sulla tecnica di perturbazione lineare. Le caratteristiche d’instabilità cosí come quelle di stabilità di quel modello si identificano analiticamente e sono confermate numericamente. Il modello è instabile solo rispetto alla perturbazione assisimmetrica, le cui lunghezze d’onda sono piú lunghe della circonferenza del getto di liquido, mentre è stabile rispetto a tutte le altre perturbazioni. I valori massimi dell’amplificazione temporale che prevalgono in tale modello sono molto piú bassi di quelli del pieno flusso di liquido. Piú spesso è il cilindro solido sia esso regolare o irregolare, maggiore il suo effetto stabilizzante.

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Резюме Анализируется капиллярная неустойчивость кольцевой жидкой струи. окружающей твердьй цилиндр. Выводится общее дисперсионное уравнение. основанное на линейной пертурбационной технике. Неустойчивость, а также характеристики устойчивости в этой модели определяются аналитически и подтверждаются численно. Предложенная модель оказывается неустойчнвой только для осесимметричных возмушений, длины волн которых превышают окружность жидкой струи, и является устойчивой для всех других возмущений. Максимальные значения временного увеличения в такой модели оказываются довольно низкими. Стабилизирующий эффект увеличивается с толщиной твердого цилиндра.