In an impingement atomizer, a thin sheet of liquid generates by impinging two identical jets. The thickness is one of the most crucial parameters in quantifying the spray characteristics for which several non-unique solutions have been acquired theoretically, so far. Among all, three theoretical solutions presented by Hasson and Peck, Ranz, and Miller are the most reliable expressions in terms of precision. Apparently, all these distinctive solutions cannot be physical simultaneously. However, a theoretical satisfactory explanation for having various non-unique solutions has not been presented. Moreover, a meaningful criterion to recognize the most physical solution is highly desirable. To address this gap, it is hypothesized that an additional constraint should be considered in couple with the continuity and momentum equations to have a unique prediction for the liquid sheet thickness. By employing the minimum energy principle, the minimum stored energy in the liquid sheet is considered the crucial constraint to achieving a unique solution and rejecting non-physical ones. Since the inviscid flow assumption is reasonably valid for the liquid sheet, the minimum energy principle satisfies when the minimum lateral surface predicts. To quantify the lateral surface area the sheet shape is presented in terms of the sheet thickness and numerically calculated by the fourth-order Runge-Kutta method for the three mentioned expressions. Using the liquid shape, the lateral surface areas are calculated and compared in three different impingement angles of 58, 89, and 117 degrees. In addition, the liquid shapes are visually compared with the experimental results obtained by the Shadowgraph technique. In sum, it is proved that Hasson and Peck presented the most physical solution for the liquid sheet thickness.
Semi-analytical model for the rising sheet generated by droplet-pair impact
Institute of Thermal Science and Power Systems, School of Energy Engineering, Zhejiang University（浙江大学能源工程学院热科学和动力系统工程研究所）；State Key Laboratory of Clean Energy Utilization, Zhejiang University（浙江大学清洁能源利用国家重点实验室）；Department of Mechanical and Aerospace Engineering, Princeton University（普林斯顿大学机械与航空航天工程系）
Holes in Sheets: Double-Threshold Rupture of Draining Liquid Films
University of Twente（特温特大学）；City College of New York（纽约市立学院）；Sorbonne Université（索邦大学）；Institut Universitaire de France（法国高等研究院）；Max Planck Institute for Dynamics and Self-Organisation（马克斯·普朗克动力学与自组织研究所）；Durham University（杜伦大学）
Retraction Dynamics of a Highly Viscous Liquid Sheet
Massachusetts Institute of Technology（麻省理工学院）；Princeton University（普林斯顿大学）；University of Bristol（布里斯托大学）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
