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Investigation of droplet collisions for solutions with different solids content

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Abstract

The collision behaviour of droplets and the collision outcome are investigated for high viscous polymer solutions. For that purpose, two droplet chains produced by piezoelectric droplet generators are directed towards each other at a certain angle so that individual droplet pairs collide. For recording the collision event, one double-image and one high-speed CCD camera were used. One camera is positioned perpendicular to the collision plane recording the outcome of the collision, and the second camera is aligned parallel to the collision plane to assure that the droplet chains are exactly in one plane. A new approach for tracking droplets in combination with an extended particle tracking velocimetry algorithm has been developed. Time-resolved series of pictures were used to analyse the dynamics of droplet collisions. The three different water soluble substances were saccharose and 1-Ethenyl-2-pyrrolidone (PVP) with different molecular weights (K17, K30). The solvent was demineralised water. The solids contents ranged from 20 to 60 %, 5 to 25 % and 5 to 35 %, yielding dynamic viscosities in the range of 2–60 mPa s. Results were collected for different pairs of impact angles and Weber numbers in order to establish common collision maps for characterising the outcomes. Here, relative velocities between 0.5 and 4 m/s and impact parameters in the interval from 0 to 1 for equal-sized droplets (Δ = 1) have been investigated. Additionally, satellite formation will be discussed exemplarily for K30. A comparison with common models of different authors (Ashgriz and Poo in J Fluid Mech 221:183–204, 1990; Estrade et al. in Int J Heat Fluid Flow 20:486–491, 1999) mainly derived for low viscous droplets revealed that the upper limit of their validity is given by an Ohnesorge number of Oh = 0.115 and a capillary number of Ca = 0.577. For higher values of these non-dimensional parameters and hence higher dynamic viscosities, these models are unable to predict correctly the boundaries between collision scenarios. The model proposed by Jiang et al. (J Fluid Mech 234:171–190, 1992), which includes viscous dissipation, is able to predict the boundary between coalescence and stretching separation for higher viscosities (i.e. Oh > 0.115 and Ca > 0.577). However, the model constants are not identical for different solution properties. As a conclusion, an alteration of the collision appearance takes place because of the relative importance between surface tension and viscosity.

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Abbreviations

b :

Lateral displacement of the centres of mass upon collision

B :

Non-dimensional impact parameter

m 1, m 2 :

Mass of droplet 1 and 2 (kg)

Oh :

Ohnesorge number

Ca :

Capillary number

PTV:

Particle tracking velocimetry

r 1, d 1 :

Radius; diameter of the larger droplet

r 2, d 2 :

Radius; diameter of the smaller droplet

u rel :

Relative velocity

u 1, u 2 :

Velocity of droplet 1 and 2 (m/s)

We :

Weber number

α 1, α 2, α 3 :

Angles between the x-axis and u 1, u 2, u 3 (°)

φ :

Enclosed angle between the relative velocity vector and the position vector

σ l :

Surface tension of the liquid

ρ l :

Density of the liquid

η l :

Dynamic viscosity of the liquid

Δ:

Diameter ratio

λ C :

Wave length at 50 % light transmission

λ :

Gap between two subsequent images for the extended PTV criterion

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Acknowledgments

The authors acknowledge the financial support of this research project by the Deutsche Forschungsgemeinschaft (DFG) under contract no. SO 204/35-1 and 2. Furthermore, the delivery of species data by the Technical University Freiberg within the Priority Program SPP 1423 is acknowledged.

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Authors and Affiliations

  1. Zentrum für Ingenieurwissenschaften, Martin-Luther-Universität Halle-Wittenberg, 06099, Halle (Saale), Germany

    Matthias Kuschel & Martin Sommerfeld

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  1. Matthias Kuschel
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  2. Martin Sommerfeld
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Correspondence to Martin Sommerfeld.

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Kuschel, M., Sommerfeld, M. Investigation of droplet collisions for solutions with different solids content. Exp Fluids 54, 1440 (2013). https://doi.org/10.1007/s00348-012-1440-z

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  • DOI: https://doi.org/10.1007/s00348-012-1440-z

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