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Research Papers

Modeling on Microdroplet Formation for Cell Printing Based on Alternating Viscous-Inertial Force Jetting

[+] Author and Article Information
Long Zhao, Rui Yao, Feng Lin

Biomanufacturing Engineering Research Center,
Mechanical Engineering,
Tsinghua University,
Beijing 100084, China;
Biomanufacturing and Rapid Forming
Technology Key Laboratory of Beijing,
Beijing 100084, China

Karen Chang Yan

Department of Mechanical Engineering,
The College of New Jersey,
Ewing, NJ 08628

Wei Sun

Biomanufacturing Engineering Research Center,
Mechanical Engineering,
Tsinghua University,
Beijing 100084, China;
Biomanufacturing and Rapid Forming Technology Key Laboratory of Beijing,
Beijing 100084, China;
Department of Mechanical Engineering,
Drexel University,
Philadelphia, PA 19104
e-mails: weisun@tsinghua.edu.cn, sunwei@drexel.edu

1Co-corresponding authors.

Manuscript received February 4, 2015; final manuscript received January 11, 2016; published online August 9, 2016. Assoc. Editor: Yong Huang.

J. Manuf. Sci. Eng 139(1), 011005 (Aug 09, 2016) (10 pages) Paper No: MANU-15-1072; doi: 10.1115/1.4032768 History: Received February 04, 2015; Revised January 11, 2016

Drop-on-demand (DOD) microdroplet jetting technology has diverse applications ranging from additive manufacturing (AM) and the integrated circuit (IC) industry to cell printing. An engineering model of droplet formation can provide insights for optimizing the process and ensuring its controllability and reproducibility. This paper reports a development of an engineering model on the fluid outflow and microdroplet formation based on alternating viscous-inertial force jetting (AVIFJ). The model provides a fundamental understanding on the mechanism of droplet formation driven by the alternating viscous force and inetial force. Furthermore, the model studies the fluid acceleration, velocity, and displacement under the conditions of a uniform cylindrical nozzle and a nonuniform cylindrical nozzle. In conjunction with an energy-based criterion for droplet formation, the model is applied to predict the formability of single microdroplets and the volume and velocity of formed microdroplets. A series of experiments was conducted to validate the developed model. The results show that the model predictions agree well with the experimental results. Specifically, comparing the model prediction and experimental results, the maximum difference of drop diameter is 4 μm, and the maximum difference of drop velocity is 0.3 m/s. These results suggest that the developed theoretical model will provide guidance to the subsequent cell printing applications.

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Figures

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Fig. 1

(a) Schematic diagram of microdroplet deposition system based on AVIFJ, (b) principle of microdroplet jetting based on AVIFJ, and (c) a typical printing nozzle

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Fig. 2

Progression of the micromotion-based microdroplet formation process (images taken for 0.5% (w/v) sodium alginate solution)

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Fig. 3

Force analysis diagram of fluid in two different capillary tubes: (a) straight cylindrical tube and (b) nonuniform cylindrical tube

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Fig. 4

Quadratic waveform applied as a driving signal: (a) the displacement of the nozzle versus time and (b) the acceleration of the nozzle versus time

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Fig. 5

Force analysis diagram of three zones in a nonuniform tube: (a) zone I, (b) zone II, and (c) zone III

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Fig. 6

Spherical coordinate system used for zone II

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Fig. 7

(a) Alternating viscous (sharp shape) and inertial force (square shape) in a straight cylindrical tube and (b) alternating viscous (sharp shape) and inertial force (square shape) in a nonuniform cylindrical tube

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Fig. 8

Acceleration (a), velocity (c), and displacement (e) of fluid shown in a straight cylindrical tube, the counterparts for the nozzle are shown in lower left in each figure; acceleration (b), velocity (d), and displacement (f) of fluid shown in a nonuniform cylindrical tube, the counterparts for the nozzle are shown in upper right of each figure

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Fig. 9

Relative displacement for comparing with predicted fluid flow motion: (a) captured images and measurement at selected time points and (b) comparison of the model prediction and the experimental measurements (printing conditions: 45 μm nozzle diameter, 90 V, 50 Hz, and 0.5%w/v alginate solution)

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Fig. 10

Experiment result and model prediction of (a) microdroplet diameter and (b) microdroplet velocity (For all experimental data presented, N = 20 for each data point. Printing conditions: 45 μm nozzle diameter, 50 Hz, and 0.5%w/v alginate solution). Experiment result and model prediction of (c) microdroplet diameter and (d) microdroplet velocity (For all experimental data presented, N = 20 for each data point. Printing conditions: 45 μm nozzle diameter, 90 V, and 50 Hz). Experiment result and model prediction of (e) microdroplet diameter and (f) microdroplet velocity (For all experimental data presented, N = 20 for each data point. Printing conditions: 90 V, 50 Hz, and 0.5%w/v alginate solution).

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Fig. 11

The minimum and maximum applied voltage for single droplet formation obtained from the model prediction and theexperimental data with varying process parameters: the nozzle diameter (a), the material viscosity (b), and the signal frequency (c)

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Fig. 12

Printed Hela cells on the cross-linked sodium alginate spread substrate: the cell viability of printed cells is about 95%

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