Experiments and Direct Numerical Simulations of binary collisions of miscible liquid droplets with different viscosities

Binary droplet collisions are of importance in a variety of practical applications comprising dispersed two-phase flows. The background of our research is the prediction of properties of particulate products formed in spray processes. To gain a more thorough understanding of the elementary sub-processes inside a spray, experiments and direct numerical simulations of binary droplet collisions are used. The aim of these investigations is to develop semi-analytical descriptions for the outcome of droplet collisions. Such collision models can then be employed as closure terms for scale-reduced simulations. In the present work we focus on the collision of droplets of different liquids. These kinds of collisions take place in every spray drying process when droplets with different solids contents collide in recirculation zones. A new experimental method has been developed allowing for high spatial and time resolved recordings via Laser-induced fluorescence. The results obtained with the proposed method will be compared with DNS simulations. The viscosities of the droplets are different whereas the interfacial tension and density are equal. The liquids are miscible and no surface tension is acting between the two liquids. Our intention is to discover elementary phenomena caused by the viscosity ratio of the droplets. Introduction In numerous industrial areas spray drying is used for producing powders of desired properties. The first step of this process is the atomization of a solution or suspension to produce fine droplets which are subsequently dried in a hot air stream. Normally, the atomisation and subsequent droplet break-up yield a broad size distribution of droplets. Owing to their size, the residence time of droplets will vary and their viscosity will be increased as a result of the drying process. During spray drying processes droplet collisions will occur not only close to the nozzle [6] but also in recirculation zones further downstream in the dryer. Here droplets of different drying state (i.e. different solids content and viscosity) may collide with each other. Depending on the relative velocity, the impact parameter and the diameter ratio, different collision outcomes can be observed [7] (i.e. bouncing, coalescence, separation). Due to the evaporation of the solvent, collisions of unlike viscous droplets will mostly exhibit also a diameter ratio less than unity. In the experiments a fluorescent marker is used to visualise mixing processes. This was already done for water or water ethanol mixtures in [1, 3], but both studies had in common that they used a frozen image technique yielding only time averaged data. The observation of deformations, mixing and penetration processes of single droplets was not possible and hence some features belonging to a certain collision type were hidden. The proposed experimental method offers high time resolution and still a very good contrast where no in-motion unsharpness occurs. Thus it is possible to study not only the dynamical behaviour of the collision complex (outer surface) but also the internal mixing and even penetration can be analysed quantitatively. Another advantage which comes with the new method is based on the fact that numerical researchers now have better validation data due to the high time resolution. In the numerical part of the work we investigate the collision of droplets of different liquids and assume that surface tension and density are equal. The liquids are miscible, so no surface tension is acting at the liquid-liquid interface. The experimental data is used to validate the effect of non-constant viscosity transported using a species equation. Subsequently, the local field data is used to gain a deep insight in the flow inside the colliding droplets. This study is devoted to the investigation of such collisions experimentally as well as numerically in order to analyse the effects of penetration and mixing. Experimental Facility For the investigation of droplet collisions with equal und unequal viscosity, uniform droplets have to be produced which was realised by using two piezo-electric droplet generators. The excited jets break up into monodis∗Corresponding author numerical part: [email protected] †Corresponding author experimental part: [email protected] 1 ar X iv :1 21 0. 62 34 v1 [ ph ys ic s. fl udy n] 2 3 O ct 2 01 2 12 ICLASS 2012 Experiments and Direct Numerical Simulations of binary collisions of miscible liquid droplets with different viscosities perse droplets chains. The angle between the resulting droplet chains was varied in order to change the relative velocity in a range of 1 to 3 m/s. The liquid was pressed through the nozzles (producer: encap biosystems) with a diameter of 200 or 300 μm, resulting in droplets of around 380 and 580 μm in size. The temperature was kept constant at about 22 ◦C by a thermostat. The impact parameter was modified by using the aliasing method (frequency shift) [4]. Three high speed cameras (two PHOTRON SA 4 and one PCO 1200 HS), whereas the two PHOTRON cameras operated synchronously, were used to observe the collision event from different viewpoints (two cameras front or collision plane view and one camera side view). The synchronous cameras were equipped with the same lens yielding a calibration factor of 11.86 μm/Pixel. Both cameras observed the collision from the same view point via a beam splitter (50/50) but with different requirements. Whereas one camera recorded a combination of green LED back light and fluorescence of the droplets, the other camera looked for the fluorescence of the single droplets and their mixture only. Therefore special glass filters (SCHOTT) were applied to meet the requirements (see Fig. 1). First, all filters had to extinguish the scattered laser light but had to be able to pass the LED back light. Figure 1. Emissionsspectra of different light sources Additionally, the filter of the fluorescent recording camera also had to eliminate the LED back light. So the filters were chosen as follows: 530 nm for the camera which recorded the combination of back light and fluorescence and a 590 nm filter was equipped on the other camera. The PCO camera has been positioned parallel to the collision plane to assure central collisions in that plane and was also equipped with a 530 nm filter to reduce the scattered laser light in order to protect the camera from too much light intensity. The mixing and penetration processes have been visualised with the help of the fluorescent marker Rhodamin B with a concentration of 200 mg/kgLiquid. The Laser light sheet was created by a AR+ Laser (LEXEL 3500) and has been expanded to 20 mm in height and 1 mm in width at the collision point, generating a mean Laser intensity of around 150 kW/m (see Fig.2). With the experimental setup it is now possible to observe the collision as well as the mixing/penetration process timeand spatial resolved due to the application of two synchronous operating cameras, which either record a combination fluorescent droplets and non-fluorescent droplets or only the fluorescence of the collision complex at arbitrary frame rates up to 30.000 frames per second and a shutter rate of 10 μs. Numerical Methods Model description The numerical method (FS3D) employed here is based on the Volume-of-Fluid (VOF) method by Hirt and Nichols [5]. The VOF method solves the Navier-Stokes equations for an incompressible transient two-phase flow. The fundamental idea of this method is to capture the interface position implicitly by means of a phase indicator function, i.e. a scalar function f = f(t, x) with, say, f = 1 in the dispersed phase and f = 0 in the continuous phase. Due to the absence of phase change, the transport of f is governed by the advection equation ∂tf + u · ∇f = 0. (1) Therefore, the VOF-method inherently conserves phase volume. This is an important issue especially if the long term behaviour of solutions is to be studied, where other methods like Level Set or Front tracking could lose too much of the droplet volume. In case of Level Set methods it is possible to include correction steps in order to