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Research Papers

Drawback During Deposition of Overlapping Molten Wax Droplets

[+] Author and Article Information
Ri Li, Sanjeev Chandra

Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON, M5S 3G8, Canada

Nasser Ashgriz1

Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON, M5S 3G8, Canadaashgriz@mie.utoronto.ca

John R. Andrews, James Williams

 Xerox Corporation, Wilson Center for Research and Technology, 800 Phillips Road, M∕S 114-44D, Webster, NY 14580

1

Corresponding author.

J. Manuf. Sci. Eng 130(4), 041011 (Jul 15, 2008) (10 pages) doi:10.1115/1.2952821 History: Received August 02, 2007; Revised May 12, 2008; Published July 15, 2008

Two overlapping droplets impacting on a solid surface coalesce and recoil so that the edges of the droplets are drawn back, a phenomenon called drawback. A series of experiments were conducted on the merging of two overlapping wax droplets deposited on an aluminum drum to characterize the drawback process between the two droplets. Drum temperature, droplet overlap ratio, and the time interval between impacts of droplets were varied. Wax bumps, formed by coalescence of two droplets on the drum surface, were photographed and their length and width measured. An aspect ratio and dimensionless drawback index, quantifying the extent of drawback, were calculated from these measurements. When drum temperature is increased, or the time interval between impacts of the two droplets is reduced, there is more drawback and the ink bumps become round, since the cooling rate of droplets is slower and droplets have a longer time to change shape due to surface tension. A simple heat transfer model was developed to predict changes in droplet-cooling rate with changes in droplet overlap, substrate temperature, or time interval (deposition frequency). Experiments were also conducted on the formation of lines by depositing 20 droplets. Measurements on the drawback of two droplets were used to predict conditions under which broken lines are obtained.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Two droplets are generated at frequency f and initial temperature Ti. They land at a time interval Δt on a substrate at temperature Ts and moving at velocity u. If L<Ds, the two droplets eventually coalesce. If Ts is less than the melting temperature of droplets, solidification occurs.

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Figure 2

Drawback process of two droplets that are deposited sequentially on a substrate surface: (a) maximum spread; (b) final shape. The arrows show the drawback directions of the two edges and indicate asymmetric drawback due to sequential deposition and solidification.

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Figure 3

(a) Experiments illustrated in Fig. 1 were conducted using a SIJ printer to study the deposition of multiple droplets on a rotating drum. Looking from the right hand side, the first droplet is located at the lower part of the picture. (b) Two dimensions Dy and Dx are measured. Dy is the length of wax bump in the rotating direction of the drum.

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Figure 4

Wax bumps formed by deposition of two overlapped wax droplets on a drum. The symbols Δt, L, and λ represent time interval, center-to-center distance, and overlap ratio, respectively. (a) Drum temperature Ts=60°C; (b) Ts=75°C.

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Figure 5

Measurements of wax bumps formed by deposition of two overlapped wax droplets as shown in Fig. 5. (a) Drawback index θ=Dy∕(Ds+L); (b) aspect ratio β=Dy∕Dx.

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Figure 6

Measurements of wax bumps formed by two wax droplets deposited on drum surface with varied drum temperatures (0.28<λ<0.45; Δt=250μs). (a) Drawback index θ=Dy∕(Ds+L); (b) aspect ratio β=Dy∕Dx.

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Figure 7

Measurements of wax bumps formed by two wax droplets deposited with varied time intervals (λ=0.45, Ts=60°C). (a) Drawback index θ=Dy∕(Ds+L); (b) aspect ratio β=Dy∕Dx.

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Figure 8

The shapes of wax bumps show the effect of time interval. (a) Wax bumps formed by two droplets generated from two different nozzles and deposited at longer time intervals. (b) Wax bumps formed by two droplets generated from the same nozzle and deposited at shorter time intervals. The two pictures have been shown in Fig. 5.

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Figure 9

Critical time interval Δtc (and hence a critical droplet generation frequency fc=1∕Δtc), as a function of drum temperature Ts for varied spread factors B. Here, Eq. 10 is plotted in its dimensional form.

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Figure 10

(a) The initial shape of the second droplet is modeled as a spherical cap to merge with the overlapped part of the first droplet. (b) A side-view scanning electron microscopic (SEM) picture of a single droplet deposited on drum surface shows a final shape of a spherical cap.

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Figure 11

Equation 19 is plotted in a dimensional form, ts as a function of drum temperature Ts. The embedded pictures and the line (λ=0.4, Δt=0.25ms) correspond to the experimental test shown in Fig. 7.

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Figure 12

Equation 19 is plotted in a dimensional form, ts as a function of time interval Δt (a) and overlap ratio λ (b); a constant spread factor B=1.6 is used for all the cases in this figure

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Figure 13

Lines formed by 20 wax droplets deposited on the drum surface with large overlaps (drum temperature Ts=75°C)

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Figure 14

Lines formed by 20 wax droplets deposited on drum surface with intermediate and relatively low overlaps for different drum temperatures: (a) Ts=60°C, (b) Ts=75°C, and (c) Ts=80°C

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Figure 15

Drawback indices of lines formed by 20 wax droplets deposited on drum surface

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Figure 16

Three droplets are generated from a nozzle moving at u and land on a stationary substrate. The relative distance ΔX can be found by separately considering the deposition of 1 the first and second droplets and the deposition of the third droplet.

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Figure 17

Data for Ts=60°C and 75°C presented in Fig. 6 are substituted into Eq. 22. The pictures of printed lines are arranged according to the deposition conditions.

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Figure 18

Equation 23 is plotted as a curved line that divides the first quadrant into break-up and non-break-up regions. The data of two droplets’ deposition presented in Fig. 6 are shown. Discontinuous lines are predicted for conditions represented by empty symbols in the breakup region, while continuous lines are predicted for conditions represented by solid symbols in the non-break-up region.

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