Flows of thin fluid layers spreading, which have a distinguished history, have been studied since the days of Reynolds, who was among the early researchers to examine flows. Different from surfactant-driven spreading, which is currently the most common subject of study, we observe the spreading process of n-hexadecane driven by volatile silicone oil at the surface of the aqueous substrates and explore the influence of Marangoni flow caused by surface tension gradient on liquid-driven spreading. We find that on different substrates, the initial state of n-hexadecane is different, and there are two instability patterns during the spreading, subsequently, which are analyzed theoretically. While the n-hexadecane drop stationed on the liquid surface is small, it is driven to form a rim and then breaks up into beads, which shows the Rayleigh–Plateau instability patterns. When we put the n-hexadecane drop on the surface of the saturated sodium chloride solution, which spreads out more, it is driven to form a circular belt first and fingering instability subsequently occurs at the inner edge of the circular belt.
The Euler-Eytelwein equation indicates that the tension from one end of the rope to the other end decays exponentially with the wrapping angle after wrapping around a target object, and the tensions at two ends can differ by several orders of magnitude.The ability to scale the force magnitude of this wrapping structure may be exploited for space captures. This paper simplifies the modeling of the actual scene of space capture, analyzes the kinematic characteristics of the wrapping process of tethered projectile systems, and obtains the trajectory equation of the projectile. Carrying out the force analysis of the element, forces acting on the satellite and the target object under different friction coefficients are obtained. Finally, considering two constraints of rope tension and wrapping time, as well as the number of wrapping turns for safe, a design scheme of projectile velocity and initial rope length required for successful capture is proposed.
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