Analysis of multi-frequency ultrasound effect on acoustic microcavitations in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math>-dimensional fluid

Acoustic microcavitation and associated mechanical effects, such as stress and strain, are significant in decreasing cavitation thresholds and improving cavitation effects at multiple (i.e., single, dual, and triple) frequencies. Ultrasonic excitation and the introduction of microbubbles as cavitation nuclei are both extremely successful techniques. Besides, the enhancing effects brought on by a dual and triple frequency approach, the cavitation dynamics of microbubbles in viscoelastic tissues under the influence of dual and triple frequency excitation are poorly known. This work deals with the modelling and numerical investigation of acoustic cavitation in N -dimensional fluid based on the multifrequency of ultrasound fields. The mathematical model of ultrasonic microcavitation bubble dynamics is formulated by continuity and Navier-Stokes equations in N -dimensions and the equation of pressure due to acoustic multifield. The proposed model is solved and investigated numerically based on the hybrid-B-Spline method. The numerical results illustrate that the behaviour of the microcavitation bubble dynamics increases with a decrease of the value of the N- dimensional fluid. Moreover, the results of the numerical simulation show the importance of the effect of different multifrequency on the behaviour of the microbubble dynamics, as the results obtained showed that in the case of a single frequency, the radius of the microbubbles is higher than in the cases of dual and triple frequency. Additionally, at different initial radii values for cavitation microbubbles, the growth and departure rates for microcavitation dynamics were examined. Finally, in the proposed model, numerical solutions are studied, their stability is verified, and they are compared with previous theoretical works. • A numerical simulation of the nonlinear dynamics of microcavitation dynamics in N-dimensional fluids is presented. • A modified Rayleigh-Plesset equation in N dimensions serves as the foundation for a mathematical model of microcavitation. • A numerical investigation of microcavitation under the influence of the multifrequency of ultrasound is investigated. • Numerical calculations and stability for the presented solutions are introduced.