Abstract: Aimed at a scientific consideration of the dynamic mechanism of droplet deformation on the surface of a jet nappe, this paper presents new backward stochastic differential equations describing the movement and deformation of droplets on the nappe surface with the final droplet state specified, and examines what initial conditions can develop into this final state. The results show that during the deformation of a single adhesive droplet on the nappe surface, its stretching probability is about 50%. Droplet forming has four deforming modes: long-axis stretching, short-axis stretching; long-axis stretching, short-axis shrinking; long-axis shrinking, short-axis stretching; long-axis shrinking, short-axis shrinking. Their probabilities are 18.9%, 31.2%, 18.7% and 30.5%, respectively. In the process of droplet group stretching, the droplets will undergo short-axis shrinking, which means a tendency for them to fragment. A variation in the evolving time into the final state, or the final state’s droplet morphology or long-axis growth rate, would not change this droplet group trend. The results of this study are of great significance for exploring droplet deformation process, and provide a new method for mathematical description of the deformation.

Key words: jet, adhesive droplets, deformation, fluctuating velocity, backward stochastic differential equation