{"title":"粒子对声场响应的理论研究","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":"{\"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}","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}
Theoretical investigation of the particle response to an acoustic field
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.
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.