Modeling and Analysis of Liquid Penetration into Soft Material with Application to Needle-Free Jet Injection

A mathematic model has been presented for a high speed liquid jet penetration into soft solid by a needle-free injection system. The model consists of a cylindrical column formed by the initial jet penetration and an expansion sphere due to continuous deposition of the liquid. By solving the equations of energy conservation and mass conservation, the penetration depth and the radius of the expansion sphere can be predicted. As an example, the calculation results were presented for a typical needle-free injection system injected into a silicon rubber.