Acoustic Bessel beams: partial wave expansions and computational calculation of acoustic forces over spherical microparticles

• Grant number: 24/06124-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2024
• End date: July 31, 2025
• Field of knowledge: Engineering - Electrical Engineering
• Principal Investigator: Leonardo Andre Ambrosio
• Grantee: Lucas Lima Romero
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project aims at the theoretical study and subsequent development of algorithms in the Julia programming language for calculating acoustic forces exerted on isotropic and homogeneous spherical particles by ultrasonic Bessel beams. To this end, the schedule will consist of: (i) stages of literature review and theoretical studies in acoustic waves, continuity equations of mass and Navier-Stokes equations for compressible and incompressible Newtonian fluids, assuming non-viscous media; (ii) stages of theoretical studies in expansions of acoustic waves (velocity potencials) in partial spherical waves, which involves cylindrical and spherical Bessel functions and associated Legendre functions, with the calculation of beam shape coefficients associated with Bessel beams and, finally, (iv) stages of simulations and algorithm development for the reconstruction of Bessel beams using partial waves and the subsequent calculation of acoustic forces with reproduction of graphics and results available in the literature. It is expected that the grantee will be able to initiate high-level academic scientific research in the area of interest for the Applied Eletromagnetics Group (AEG) of the Department of Electrical and Computer Engineering (SEL), São Carlos School of Engineering (EESC), USP, with applications aimed in volumetric displays based on acoustic trapping of microparticles, acoustic holography, and structured ultrasonic beams. During the project period, there is an expectation of collaboration and exchange of information between the grantee and the Julia group of Massachusetts Institute of Technology (MIT), United States, and it may be even possible to request BEPE scholarship for a period of overseas internship at the said university.