Theoretical Modelling Of The Interaction Force Between Ultrasound Contrast Agents

Nowadays, Ultrasound contrast agents (UCA for short) are playing important roles in the fields of imaging with ultrasound, drag delivery carrier, and organizations destroy. For example, image quality will be improved because of strong ability of diffusivity of UCAs. The mutual interaction between UCAs is called secondary Bjerknes Force which may lead to aggregations of UCA micro bubbles. One method of controlling the motion of UCAs is to use ultrasound field which will send UCA bubbles to ideal location to complete the drug delivery. Literature shows that study on secondary Bjerknes Force is not intensive. This paper analyze this force and its influence factors by perturbation method and theoretical deduction.Firstly, this paper focuses on the relationship between UCAs. The equations of mutual interaction between UCAs are deduced and oscillation equations of UCAs are found. The main differences between UCAs and micro bubbles without shells are properties of shells including materials types, kinetic viscosity, inside and outside surface tensions. Besides, change of damping coefficient contributes to the secondary Bjerknes Force by comparing equations.Secondly, the analysis solutions are worked out to get the expression of linear secondary Bjerknes Force and calculate classic examples. These examples include parameters of geometrical relationship, properties of shell, and acoustic field. The main conclusions are with the increase of thickness of shell, the natural frequency will increase at the same time to affect the sign of secondary Bjerknes Force; And the kinetic viscosity’s increase will also add natural frequency.Thirdly, the characteristic other parameters of bubbles are focused. Main conclusions include, with the increase of the UCA diameter, the natural frequency will decrease and bring about sign change of secondary Bjerknes Force; when diameters of UCAs with respect to the distance between two UCAs become large, the change of rule of secondary Bjerknes Force will take place. The distance between two UCAs and the acoustic angular frequency have the relationship with natural frequency of UCAs to influence secondary Bjerknes Force. These parameters can be changed to control bubble motion to weaken UCA aggregation.Forthly, the numerical solution is found and the differences between the analysis and numerical solution are compared to validate the analysis solution.