1 Introduction
2 Droplet–droplet collisional theory
2.1 Dimensionless collision parameters
2.2 Current models for regime boundaries
Authors | Model boundaries | Viscosity range (mPa s) | Viscous dissipation |
---|---|---|---|
Ashgriz and Poo (1990) | RS-C, SS-C | 1 | Neglected |
Jiang et al. (1992) | RS-C, SS-C | 0.4 –3.5 | Via \(\mu\) to \(\sigma\) ratio |
Qian and Law (1997) | RS-C | 2 | Via Oh number |
Estrade et al. (1999) | B-(C,SS) | 1.22 | Neglected |
Willis and Orme (2003) | RS-C | 10–30 | Via Oh number |
Gotaas et al. (2007) | RS-C | 0.9–48 | Via Oh number |
3 Milk properties
3.1 Surface tension
3.2 Viscosity and rheology
4 Materials and methodology
4.1 Liquids characterization
Liquids |
ρ (kg/m3) | μ (mPa s) |
\(\sigma\) (mN/m) |
---|---|---|---|
Milk \(20\%\) TS content | 1041 | 4.3 | 46.8 |
Milk \(30\%\) TS content | 1061 | 8.8 | 46.1 |
Milk \(46\%\) TS content | 1094 | 83 | 46.9 |
Glycerol 40 \(\hbox {vol}\%\)
| 1104 | 5.01 | 68.5 |
Glycerol 60 \(\hbox {vol}\%\)
| 1158 | 15.5 | 67.9 |
Glycerol 80 \(\hbox {vol}\%\)
| 1211 | 88.8 | 65.1 |
4.2 Reconstitution of milk concentrates
Milk concentrate | Total weight (g) | Water (g) | Powder (g) |
---|---|---|---|
\(20\%\) TS content | 1000 | 800 | 200 |
\(30\%\) TS content | 1000 | 700 | 300 |
\(46\%\) TS content | 1000 | 540 | 460 |
4.3 Experimental set-up
4.4 Droplet collision tracking
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The viscosity, density and surface tension of the colliding liquid in the recording are entered in the script. Furthermore, the pixel-to-meter ratio is entered, as well as the average droplet radius. A ruler is used to calibrate the pixel-to-meter ratio, once the camera position is set.
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The pre-collision area is selected manually, the drops are distinguished from the background using the edge and imfill image analysis commands and the locations of all droplets are determined with the imfindcircles function (step 1–3 in Fig. 7).
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The frame is divided into two vertical sides so that one droplet from one stream collides with one droplet belonging to the other jet. The drop on the left side is associated with the one on the right side which has the smallest vertical distance. This is illustrated by step 4 in Fig. 7. The pair is labelled with a number which remains the same for the entire recording. For the new pairs appearing in the next frames, new labels are provided.
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The script now continues with Frame 2. All droplets are again localized, the droplet pair of the colliding droplets is found by using the location of the droplet pair of the previous frame. Once the droplet pair has again been identified, the horizontal and vertical displacements from the previous frame are measured and velocity coordinates are derived. The script continues with the next frame.
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The process for a pair stops when the circles around the two droplets overlap.
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With the displacements and position of droplets at the moment of collision, the relative velocity and impact parameter are calculated for each pair in the recording. The distance b between the two droplet centres is calculated according to:In case the two drops have no point of contact in the last frame before merging, an extrapolated position, based on the previous velocity and displacement of the drops, is considered for calculating the impact parameter. Therefore, the relevant dimensionless numbers are calculated and then stored in a matrix.$$\begin{aligned} b=\left| \frac{\Delta y \Delta v_{x} - \Delta x \Delta v_{y}}{v_{\text{rel}}} \right| \end{aligned}$$(24)
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When the droplet pairs are detected, a video in which the pair label is shown next to the moving droplets is created.