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Research Papers: Fundamental Issues and Canonical Flows

Numerical Investigation of an Efficient Method (T-Junction With Valve) for Producing Unequal-Sized Droplets in Micro- and Nano-Fluidic Systems

[+] Author and Article Information
Ahmad Bedram

Center of Excellence in Energy Conversion (CEEC),
School of Mechanical Engineering,
Sharif University of Technology,
Azadi Avenue, P.O. Box 11365-9567,
Tehran 11365-9567, Iran
e-mail: a_bedram@yahoo.com

Amir Ebrahim Darabi

Center of Excellence in Energy Conversion (CEEC),
School of Mechanical Engineering,
Sharif University of Technology,
Azadi Avenue, P.O. Box 11365-9567,
Tehran 11365-9567, Iran
e-mail: amir.adarabi@gmail.com

Ali Moosavi

Associate Professor
Center of Excellence in Energy Conversion (CEEC),
School of Mechanical Engineering,
Sharif University of Technology,
Azadi Avenue, P.O. Box 11365-9567,
Tehran 11365-9567, Iran
e-mail: moosavi@sharif.edu

Siamak Kazemzade Hannani

Professor
Center of Excellence in Energy Conversion (CEEC),
School of Mechanical Engineering,
Sharif University of Technology,
Azadi Avenue, P.O. Box 11365-9567,
Tehran 11365-9567, Iran
e-mail: hannai@sharif.edu

For the initial lengths of the droplet that are smaller than a specific value (critical length), the droplet doesn't break.

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 16, 2014; final manuscript received September 2, 2014; published online October 21, 2014. Assoc. Editor: Daniel Maynes.

J. Fluids Eng 137(3), 031202 (Oct 21, 2014) (9 pages) Paper No: FE-14-1136; doi: 10.1115/1.4028499 History: Received March 16, 2014; Revised September 02, 2014

We investigate an efficient method (T-junction with valve) to produce nonuniform droplets in micro- and nano-fluidic systems. The method relies on breakup of droplets in a T-junction with a valve in one of the minor branches. The system can be simply adjusted to generate droplets with an arbitrary volume ratio and does not suffer from the problems involved through applying the available methods for producing unequal droplets. A volume of fluid (VOF) based numerical scheme is used to study the method. Our results reveal that by decreasing the capillary number, smaller droplets can be produced in the branch with valve. Also, we find that the droplet breakup time is independent of the valve ratio and decreases with the increase of the capillary number. Also, the results indicate that the whole breakup length does not depend on the valve ratio. The whole breakup length decreases with the decrease of the capillary number at the microscales, but it is independent of the capillary number at the nanoscales. In the breakup process, if the tunnel forms the pressure drop does not depend on the valve ratio. Otherwise, the pressure drop reduces linearly by increasing the valve ratio.

Copyright © 2015 by ASME
Topics: Drops , Valves , Junctions , Fluids
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References

Figures

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Fig. 1

The geometry of the T-junction with valve and representation of the involved parameters

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Fig. 2

3D configuration of the system

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Fig. 3

Checking the grid independency of the results. The droplet deforms and breaks up into two parts. In this case, Ca = 0.04 and volume ratio = 0.6 and the droplet is in the center of the junction. The grids that have more than 6605 nodes are confident and we use the grid with 11,542 nodes for simulation of our cases.

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Fig. 4

Droplet critical length as a function of capillary number. Dotted line is the analytical relation (l/w = 1.3Ca-0.21). The critical length became dimensionless by width of channel.

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Fig. 5

Droplet velocity as a function of mean velocity of carrier fluid in tube. In the values of mean velocity of carrier fluid larger than 0.03, a small difference exists between the analytical and numerical results. It is because that the analytical results are derived by assumption of low value of carrier fluid mean velocity.

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Fig. 6

The breakup process of unequal-sized droplets. For the shown case, the capillary number is 0.1, the valve ratio is 0.4, and the volume ratio is 0.48.

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Fig. 7

Droplet volume ratio as a function of the valve ratio and the capillary number. When the valve ratio is equal to 1 (symmetric T-junction), the droplets that enter the branches have the same size. Also for a specific volume ratio as the capillary number decreases, the valve should be opened further and, as a result, the T-junction becomes more symmetric.

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Fig. 8

Generation of equal-size droplets using consecutive symmetric T-junctions

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Fig. 9

tbreakup is the time between the situation displayed in part (a) and part (b). The valve ratio is equal to 0.5 and the capillary number is Ca = 0.1.

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Fig. 10

Breakup time as a function of valve ratio. The average value of breakup time for Ca = 0.04, Ca = 0.1 (2D), and Ca = 0.1 (3D) are 5.84 × 10−4, 1.55 × 10−4, and 1.41 × 10−4 (second dimension), respectively.

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Fig. 14

Droplet breakup. (a) without tunnel, Ca = 0.1 and valve ratio = 0.4. (b) with tunnel, Ca = 0.1 and valve ratio = 0.8.

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Fig. 13

Pressure drop as a function of valve ratio. In the above diagram, the pressure drop is calculated at the breakup moment. The results have shown that approximately at this moment the maximum pressure drop occurs.

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Fig. 12

Breakup length as a function of valve ratio. The breakup length of droplet is dimensionless (w is the width of the branches). For the valve ratio near 1 (symmetric T-junction), in each capillary number, the droplets that enter the branches have the same size; therefore, the breakup lengths of them are equal.

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Fig. 11

Droplet breakup length. The vertical dashed line (in the junction center) is the centerline of the inlet channel. The whole breakup length, namely, the length of the droplet at the breakup moment, is composed of the large part length and the small part length.

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Fig. 19

Droplet breakup for the nanoscale case. (a) Ca = 0.3 and valve ratio = 0.8. (b) Ca = 0.5 and the valve ratio = 0.65. As can be seen in both the cases, the tunnel does not form. Therefore, by the increase of the valve ratio, the pressure drop reduces linearly.

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Fig. 18

Pressure drop as a function of valve ratio for the nanoscale case. In the diagram the pressure drop is calculated at the breakup moment.

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Fig. 17

Droplet breakup length as a function of the valve ratio for the nanoscale case. The breakup length is scaled by the channel width w. As it can be deduced, for the valve ratios near 1 (symmetric T-junction), for all the capillary numbers, the droplets that enter the branches have the same size. Therefore, their breakup lengths are equal.

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Fig. 16

Breakup time as a function of valve ratio for the nanoscale case. The average of the breakup time is 2.86 × 10−7 s and 1.57 × 10−7 s for Ca = 0.3 and Ca = 0.5, respectively.

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Fig. 15

Droplet volume ratio as a function of the valve ratio for two capillary numbers for the nanoscale case. In the valve ratio equal to 1, the equal-size droplets enter each branch and the volume ratio becomes 1. Also to obtain a specific volume ratio, if we select a smaller capillary number, the required valve ratio increases. This means that the junction becomes more symmetric.

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