Theoretical investigation of the particle response to an acoustic field

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2016-04-21 DOI:10.1177/1756827716641118

Javier Achury, W. Polifke

{"title":"Theoretical investigation of the particle response to an acoustic field","authors":"Javier Achury, W. Polifke","doi":"10.1177/1756827716641118","DOIUrl":null,"url":null,"abstract":"In this paper, the problem of a particle subjected to an acoustic field is addressed theoretically. Once the fundamental equation of motion is obtained, two nonlinearities are identified: one related to the drag law and one associated with the excitation. In order to face the nonlinearities, two cases are constructed: the first corresponds to the parametric numerical solution of a particle with nonlinear drag in an oscillating flow field (infinite wavelength) and the second refers to the particle submitted to an acoustic standing wave (finite wavelength). For the latter, an approximated analytical solution is formulated. The system is linearized around an equilibrium point and the parameters of the equation are grouped in three nondimensional numbers: the Stokes number (St), the acoustic Mach number (Ma), and the densities ratio (γ). Conditions of parametric resonance in the particle response are deduced for this system by means of the analytical method here proposed, based on Hill’s determinants. Comparison with numerical solutions of the linearized and nonlinearized equations close to an equilibrium point corroborates the analysis for different combinations of parameters.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2016-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/1756827716641118","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1177/1756827716641118","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 4

Abstract

In this paper, the problem of a particle subjected to an acoustic field is addressed theoretically. Once the fundamental equation of motion is obtained, two nonlinearities are identified: one related to the drag law and one associated with the excitation. In order to face the nonlinearities, two cases are constructed: the first corresponds to the parametric numerical solution of a particle with nonlinear drag in an oscillating flow field (infinite wavelength) and the second refers to the particle submitted to an acoustic standing wave (finite wavelength). For the latter, an approximated analytical solution is formulated. The system is linearized around an equilibrium point and the parameters of the equation are grouped in three nondimensional numbers: the Stokes number (St), the acoustic Mach number (Ma), and the densities ratio (γ). Conditions of parametric resonance in the particle response are deduced for this system by means of the analytical method here proposed, based on Hill’s determinants. Comparison with numerical solutions of the linearized and nonlinearized equations close to an equilibrium point corroborates the analysis for different combinations of parameters.

查看原文本刊更多论文

粒子对声场响应的理论研究

本文从理论上讨论了粒子受声场作用的问题。一旦得到基本的运动方程，就可以确定两个非线性:一个与阻力定律有关，另一个与激励有关。为了面对非线性，构造了两种情况:第一种情况对应于振荡流场(无限波长)中具有非线性阻力的粒子的参数数值解，第二种情况对应于声波驻波(有限波长)下的粒子。对于后者，给出了近似解析解。该系统围绕一个平衡点线性化，方程的参数被分组为三个非维数:斯托克斯数(St)、声学马赫数(Ma)和密度比(γ)。利用本文提出的基于希尔行列式的解析方法，推导了该系统的粒子响应参数共振条件。与接近平衡点的线性化和非线性化方程的数值解比较，证实了对不同参数组合的分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.