High-Speed Stress Field Measurement In A Soft Substrate During Droplet Impact

Abstract

In this study, we utilized high-speed photoelastic tomography to quantify dynamic stress fields within a soft substrate during droplet impact. This manuscript details the measurement technique, which employs a high-speed polarization camera and the principles of photoelastic tomography. Our method successfully enabled the quantitative measurement of dynamic stress fields in a soft substrate during droplet impact. Additionally, we conducted an analysis of the impact force derived through the spatial integration of the measured stress field. The discussion explored the interplay between the maximum impact force, droplet viscosity, and substrate elasticity. Our findings indicate that the maximum impact force 𝐹max can be expressed as a function with a self-similar variable of 𝑅𝑒 / 𝐶𝑎^2 , where 𝑅𝑒 is Reynolds number representing the droplet inertial force and droplet viscous force and 𝐶𝑎 is Cauchy number representing the ratio of the droplet inertial force and substrate elastic force. This combination, 𝑅𝑒 / 𝐶𝑎^2 , represents the relationship between the relaxation time of droplet and substrate deformation ( 𝜂/ 𝐸), the contact time of the droplet (𝑅 / 𝑉), and the ratio of substrate elastic force to droplet inertial force. Consequently, the maximum impact force 𝑅𝑒 / 𝐶𝑎^2 is determined by the balance between the relaxation and contact times. We believe that our developed method will significantly enhance the understanding of droplet impact phenomena. Furthermore, it holds potential for broader applications in various engineering processes, such as analyzing stress distribution in materials caused by liquid jet impact and studying cavitation bubbles in viscoelastic materials. This method's ability to provide detailed quantitative measurements of dynamic stress fields offers a valuable tool for future research and technological advancements in related fields.