Droplet collisions in turbulence

Abstract

Liquid droplets occur in many natural phenomena and play an important role in a large number of industrial applications. One of the distinct properties of droplets as opposed to solid particles is their ability to merge, or coalesce upon collision. Coalescence of liquid drops is of importance in for example the food industry, where the shelf life of emulsion type of products is often elongated with absence of coalescence, rocket propulsion, where fuel and oxidizer are separately injected and ignite upon coalescence, the semiconductor industry, where droplets of molten tin are targeted by a laser to produce extreme ultraviolet light, and during the formation of rain. One might not realize it immediately, but the outcome of a droplet collision is not always coalescence, but also bouncing can occur. In most of the mentioned cases the droplet collisions do not take place in a stationary environment but in an environment that flows with respect to the droplets or is even turbulent. The aim of the current study is to gain insight into the effect of external turbulence on the outcome of droplet collisions. When two droplets collide it might appear that the drops are in contact, but in reality there will be a thin film of surrounding fluid in between the droplets. When this film becomes so thin that Van der Waals forces between the molecules of the two drops come into effect a hole will be initiated in the film and the droplets will coalesce. The associated thickness is in the order 60 nm. If the film thickness does not decrease to this value, the droplets will bounce. The time it takes from the start of drop interaction to film rupture is called the drainage time, denoted by t_drainage. The time during which the drops are in apparent contact is called the interaction time t_interaction. A droplet collision will thus lead to coalescence when t_{drainage} < t_{interaction}, otherwise the collision results in bouncing. To investigate film drainage an experiment was performed where a droplet of silicone oil was released in a layer of water below a layer of silicone oil. A film of water will form between the drop and the top liquid. Because the interaction time t_interaction is always larger than the drainage time t_drainage, the film will eventually always rupture. Refractive index matching and laser induced fluorescence (LIF) were used to image the film and determine its thickness and rupture location. The measurements show that the film attains a specific geometry. The film is thick at the center and thin at an off center ring. This geometry is termed a 'dimple'. The measurements also show that the film ruptures faster than simple analytical models predict and that the film thins asymmetrically. The rupture locations correlate with the region of minimal thickness. After the investigation of film drainage, investigation of droplet collisions with realistic values for the interaction time become of interest together with the influence of external turbulence. In order to investigate both phenomena a cylindrical tank was designed with discs at the top and bottom which could counter rotate at fixed frequency. The flow between counter rotating discs is referred to as Von Karman flow. At the center of the flow facility a small volume exists where the average flow is approximately zero, but the turbulent velocity fluctuations are finite. Nozzles were mounted in the Von Karman flow facility to inject droplets to produce collisions at this location. Droplets could be collided in a stationary flow and in a turbulent flow and using three high speed cameras the droplets could be tracked in 3D. The Reynolds number based on the Taylor micro scale and the turbulent fluctuations, denoted as Re_l, is zero in case of a stationary flow Re_l = 0 and for the turbulent case it holds that Re_l = 141. The collisions are characterized using the Weber number We = rho_d U^2 D/sigma based on the drop density rho_d, the relative drop velocity U, the drop diameter D and the interfacial tension sigma. The Weber number is an indicator for the balance of inertial forces over surface tension forces. In case of droplet collisions in a stationary liquid (Re_l = 0) for low values of the Weber number the outcome of collision events is bouncing. For large values of the Weber number the outcome is coalescence and for the largest achievable values of the Weber number the droplets would coalesce, the coalesced drop would form a flat disc which would eventually break up into two separate drops and one small satellite drop. This behavior with increasing values of the Weber number was shown before for droplets in air by Qian and Law, see (1). Droplet collisions in a liquid are thus similar to droplet collisions in air. In case of a stationary outer liquid the value of the Weber number at the boundary between bouncing and coalescence is approximately Wen_(II,III) = 20. In case of bouncing the interaction time was found to be equal to the theoretical drop oscillation period as derived by Miller and Scriven (2), and the drainage time was found to decrease with increase of the Weber number. For droplet collisions in a turbulent outer flow (Re_l = 141) on average collisions only lead to coalescence for values of the Weber number larger than 30 (We_(II,III) > 30). The external flow is thus of significant influence on the outcome of droplet collisions in terms of bouncing or coalescence. A possible explanation for this hindered coalescence is the fact that a compressional flow in the direction of the collision axis induces an internal drop flow which counteracts film drainage. If this explanation is valid the measured effect is not due to turbulence. References (1) Qian and Law, Regimes of coalescence and separation in droplet collision. J. Fluid Mech 331, 1997. (2) Miller and Scriven, The oscillations of a fluid droplet immersed in another fluid. J. Fluid Mech 32, 1968.