Liquid atomisation is the basis for various practical applications such as pharmaceuticals, cosmetics, food industry, etc. In this case, the main challenge is the development of high-performance, highly dispersed atomisation systems. Generally, high-throughput atomisation systems form aerosol with large droplet sizes, and high-disperse atomisation systems have low performance. Secondary ultrasonic atomisation can solve this problem by allowing non-contact crushing of already formed aerosol droplets with large droplet sizes by means of a high-intensity ultrasonic field. For this purpose, a pre-generated stream of liquid droplets is directed into a cylindrical region formed by an emitter in which a high-intensity ultrasonic field is generated. Ultrasonic radiator, is a tube of stepped-variable cross-section, providing the formation of bending-diametral or diametral oscillations at a frequency above 20 kHz. At sufficiently high ultrasound intensity, conditions for further crushing of liquid droplets are realised, which leads to the formation of a highly dispersed aerosol. This paper describes the proposed mathematical model of the atomisation process and finds the regularities of the process depending on the determining parameters of the ultrasonic field and physical and chemical properties of the liquid. Two mechanisms of jet destruction are revealed: direct destruction of droplets when they hit the ultrasonic wave front and cavitation mechanism of droplet and jet destruction. The dominant crushing mechanism depends on the problem parameters and, in turn, determines the minimum size of the resulting droplets. The results of this work will help to optimise the secondary ultrasonic atomisation process and improve liquid atomisation technologies in various applications.