Grouping and trapping of evaporating droplets in an oscillating gas flow

A new approach to the analysis of droplet grouping in an oscillating gas flow is suggested. This is based on the investigation of droplet trajectories in the frame of reference moving with the phase velocity of the wave. Although the equations involved are relatively simple, the analysis shows distinctive characteristics of grouping and non-grouping cases. In the case of grouping, droplet trajectories converge to the points for which the ratio of flow velocity in this frame of reference and the amplitude of flow oscillations is less than 1, and the cosine of the arc sine of this ratio is positive. In the case of non-grouping, droplet trajectories in this frame of reference oscillate around the translational velocity close to the velocity of flow in the same frame of reference. The effect of droplet size on the grouping pattern is investigated. It has been pointed out that for the smaller droplets much more stable grouping is observed. The effect of droplet evaporation is studied in the limiting case when the contribution of the heat-up period can be ignored. It is shown that evaporation can lead to droplet grouping even in the case when the non-evaporating droplets are not grouped. This is related to the reduction in droplet diameter during the evaporation process. Coupling between gas and droplets is shown to decrease the grouping tendency. A qualitative agreement between predictions of the model and in-house experimental observations referring to Diesel engine sprays has been demonstrated.     

Synthesis of functional polymer particles by dispersion polymerization in organic media: A tool toward stable electrophoretic inks

In this article, a simple route to obtain particles in one step from functional ionizable monomers in organic media by the use of acrylate‐based macroinitiator synthesized by nitroxide‐mediated radical polymerization is presented. Different positively ionizable monomers like 4‐vinylpyridine, (dimethylamino)ethyl methacrylate, or negatively ionizable ones like methacrylic acid and acrylic acid were tested. Several parameters were studied to control the particles size, their stability in different organic media, and the possibility to crosslink them. Finally, well‐defined, depending of conditions, functional latexes in organic media were produced in a simple way. This synthetic process constitutes the first step to produce electrophoretic inks for display applications such as electronic paper. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4608–4617     

An upper bound for validity limits of asymptotic analytical approaches based on normal form theory

Perturbation methods are routinely used in all fields of applied mathematics where analytical solutions for nonlinear dynamical systems are searched. Among them, normal form theory provides a reliable method for systematically simplifying dynamical systems via nonlinear change of coordinates, and is also used in a mechanical context to define Nonlinear Normal Modes (NNMs). The main recognized drawback of perturbation methods is the absence of a criterion establishing their range of validity in terms of amplitude. In this paper, we propose a method to obtain upper bounds for amplitudes of changes of variables in normal form transformations. The criterion is tested on simple mechanical systems with one and two degrees-of-freedom, and for complex as well as real normal form. Its behavior with increasing order in the normal transform is established, and comparisons are drawn between exact solutions and normal form computations for increasing levels of amplitudes. The results clearly establish that the criterion gives an upper bound for validity limit of normal transforms.