The prime objective of this study is to answer the question: How large is the pressure developed at the instant of a spherical liquid droplet impact on a solid surface? Engel first proposed that the maximum pressure rise generated by a spherical liquid droplet impact on a solid surface is different from the one-dimensional water-hammer pressure by a spherical shape factor (Engel 1955 J. Res. Natl Bur. Stand. 55(5), 281–298). Many researchers have since proposed various factors to accurately predict the maximum pressure rise. We numerically found that the maximum pressure rise can be predicted by the combination of water-hammer theory and the shock relation; then, we analytically extended Engel’s elastic impact model, by realizing that the progression speed of the contact between the gas–liquid interface and the solid surface is much faster than the compression wavefront propagation speed at the instant of the impact. We successfully correct Engel’s theory so that it can accurately provide the maximum pressure rise at the instant of impact between a spherical liquid droplet and solid surface, that is, no shape factor appears in the theory.

A two-fluid spray cleaning technique has been gaining popularity as a cleaning process in the semiconductor industry. The most essential physical process in this technique is the impact of droplets with a velocity of O(10 m/s) on a solid surface. This study aims to experimentally and numerically investigate water-droplet impacts with velocities of up to 50 m/s and their subsequent flow fields, especially the gas flow field in the strictly limited area in the vicinity of the contact line. First, we experimentally evaluated the velocity of the splash and numerically calculated the gas velocities. Comparison of these velocities supported our assumption that the maximum gas velocity may be on approximately the same order as the velocity of the splash. Therefore, we concluded that the gas velocity field of the order of 500 m/s indeed develops at the impact of droplet with a velocity of the order of 50 m/s. Moreover, we determined that the gas pressure was of the order of 1.0 MPa by numerical analysis. Such a high pressure leads to shock wave propagation, which can contribute to the cleaning process in semiconductor production. To manufacture semiconductors, cleaning techniques that use physical action, such as megasonic agitation, are generally employed 1 together with those using chemical action to enhance the cleaning efficiency. A deionized water/gas-mixture jet spray cleaning technique, in other words, a two-fluid spray cleaning technique, is also gaining popularity.1-4 The advantage of this technique over megasonic agitation is the magnitude of the physical action generated by a highspeed droplet impacting a solid surface. However, most cleaning techniques that use physical action tend to cause structural damage and pattern collapse; therefore, the particle removal force should be quantitatively understood and measured. 5,6 The development of advanced spray technology offers the possibility of preventing this damage by controlling both the sizes and velocities of the droplets with extremely high accuracy. 7,8 It should be emphasized here that the most essential physical process in this two-fluid spray cleaning technique is the droplet impact upon the solid surface with a velocity of several tens of meters per second. Until recently, the velocities of liquid droplets in most experimental studies on liquid-droplet impacts were restricted to the range of several meters per second, 9-11 mainly due to the difficulties associated with high-speed observation. On the other hand, Mehdizadeh et al., 12 Pan et al., 13 and Visser et al. 14 reported on experimental studies that utilized droplet impacts at velocities of the order of 10 m/s. Mehdizadeh et al.12 observed the impacts of water droplets with radii of about 1 mm on stainless steel surface mounted on the end of a rotating arm whose linear velocities of up to 50 m/s. They measured the number of fingers and maximum diameter of the droplet after spreading. Pan et al. 13 observed the collision between a solid plate and a droplet with a radius of about 0.5 mm and a speed...

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