Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2307.12319

Time-Dependent Acoustic Waves Generated by Multiple Resonant Bubbles: Application to Acoustic Cavitation

Arpan Mukherjee·Mourad Sini
View original source ↗Read source document ↗Export metadata ↓

Abstract

We analyse the ultrasound waves reflected by multiple bubbles in the linearized time-dependent acoustic model. The generated time-dependent wave field is estimated close to the bubbles. The motivation of this study comes from the therapy modality using acoustic cavitation generated by injected bubbles into the region of interest. The goal is to create enough, but not too much, pressure in the region of interest to eradicate anomalies in that region. Here, we derive the dominant part of the generated acoustic field by a cluster of bubbles taking into account the (high) contrasts of their mass density and bulk as well as their general distribution in the given region. As consequences of these approximations, we highlight the following features: 1. If we use dimers (two close bubbles), or generally polymers, then we obtain a remarkable enhancement of the whole echo in the whole time. 2. If we distribute the bubbles every where in the region of interest,then we can derive the effective acoustic model which turns out to be a dispersive one. We show that, for a given desired pressure, we can tune the effective model to generate it.

Explore related subjects

math.AP

Keep this discovery

BibTeXRIS

Arpan Mukherjee, Mourad Sini. 2023-07-23. Time-Dependent Acoustic Waves Generated by Multiple Resonant Bubbles: Application to Acoustic Cavitation. https://arxiv.org/abs/2307.12319

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Well-posedness of the two-dimensional unsteady Prandtl system in Sobolev space with degenerate critical points

This paper is devoted to the well-posedness of classical Prandtl equations in a finite order Sobolev space. For a initial data with degenerate critical points and general outflow, we obtain the local-in-time existence and uniqueness of the solution to the Prandtl equations in a Sobolev space, by introducing a new iteration scheme and linear cancelation. This result shows that Oleinik's monotonicity condition is not a necessary condition for the Prandtl equations to be well-posed in Sobolev spaces and provides evidence to demonstrate that zero shear stress does not necessarily lead to boundary layer separation in two-dimensional unsteady boundary layers.

math.AP↗
arXiv2026

Global existence and time decay for a bipolar Euler-Poisson system with one pressureless and undamped fluid

We study the Cauchy problem for a three-dimensional bipolar Euler--Poisson system in which one fluid is pressureless and undamped, while the other is subject to momentum relaxation. For sufficiently small smooth perturbations of a constant equilibrium, we prove the global existence and uniqueness of smooth solutions under an irrotationality assumption on the initial velocity of the pressureless fluid, together with algebraic time-decay estimates. The main difficulty is that the velocity of the pressureless fluid is dissipated only indirectly through the Poisson coupling, and this mechanism degenerates strongly at high frequencies, leading to a regularity-loss structure. We overcome this difficulty by combining refined Green-function estimates, a low--middle--high frequency decomposition, and high-order nonlinear energy estimates adapted to the asymmetric regularity hierarchy. The result establishes a global small-data theory for this asymmetric regime, in which pressure and damping are simultaneously absent from the same fluid.

math.AP↗
arXiv2026

Boundary layer of 2D Chemotaxis Navier-Stokes equations with logarithmic Sensitivity. II. viscous vanishing limit

This is the second part of a two-part work concerning boundary layer solutions to the coupled Chemotaxis-Navier-Stokes system in the two-dimensional half-space. In the present work, we address the convergence of boundary layer solutions to singular chemotaxis-fluid equations under slip boundary conditions with respect to the chemical diffusion-viscosity parameter $\varepsilon$ in the two-dimensional half-plane. More precisely, we show that the boundary layer for $\varepsilon>0$ (viscous convection coefficient) converges to the superposition of the outer layer (solution with $\varepsilon=0$) and the inner layer as $\varepsilon\rightarrow0$. The outer and inner profiles are explicitly derived as in the first part\cite{WWZ}. Furthermore, the well-posedness results of the coupled Chemotaxis-Navier-Stokes system in conormal Sobolev spaces will be presented in Appendix. They answer the question mentioned in the first part of the two-part work. This study could help the understanding of the chemotactic movement of aerobic bacteria to the water-air surface observed experimentally in fluids, and enrich the theoretical results of boundary layer in chemotactic fluid models.

math.AP↗