本研究之目的為探討滴流與噴流在不同流體性質和流率下的轉換特徵變化。藉由不同濃度比例的甘油-水混合液(Ω)來產生不同性質之工作流體，並主要探討黏滯係數(μ)、液柱直徑(dj)及流率(Q)等參數，對於液柱的斷裂長度(Lj)、斷裂液滴直徑(D)、滴流與噴流之流體型態轉換等現象的影響性。由研究結果得知當Ω上升，會使得Lj及D分別地伸長與增加。在較大的液柱直徑(≥1146μm)會有遲滯現象(Hysteresis)的產生，即為當流體型態從滴流逐漸轉變成噴流(DJ)，與噴流逐漸轉變成滴流(JD)所對應到的臨界流率並不相同。研究結果發現，隨著Ω上升遲滯現象的範圍將會擴大並往較低We數的方向移動，尤其是在較大dj下更為顯著，此外原先無遲滯現象之液柱直徑也能透過增加Ω來產生。同時也分析親水性噴嘴的幾何形狀，並探討產生遲滯現象的原因，研究結果發現，噴嘴的壁厚與內部半徑之間的比值是個重要因素，若比值越大則越不容易產生遲滯現象；相反的比值越小則越容易產生。另外深入研究噴嘴幾何形狀對於滴流狀態下毛細上升(δh)的影響，並發現在δh中也會有遲滯現象的行為產生，亦即從DJ時上升的高度會不同且大於JD時所上升的高度。當Ω等於0%時，毛細現象在較小噴嘴會以不對稱方式爬升，而較大噴嘴則是沿著噴嘴孔並對稱爬升，而當Ω 增加時，由於流體與噴嘴之間的附著力上升，毛細現象將以不對稱的方式爬升，且爬升高度也更為顯著。

The objective of this research is to analyze the characteristics of a liquid jet under different working fluid properties and flow rates. In this study, glycerol-water mixtures with different concentrations (Ω) were used as the working fluids. The properties of the working fluid were varied in terms of the main viscosity (μ), the diameter of the liquid column (dj), and the flow rate (Q) to investigate the characteristics of the breakup length (Lj), the breakup droplet diameter (D), and the flow type transition between a dripping and jetting flow. From the research results, when the Ω were increased the Lj and D extended and increased, respectively. Hysteresis behavior occurred in the liquid column with a larger diameter of (≥ 1146μm), which indicated that the critical flow rate of the transition from dripping to jetting (DJ) was different from that from jetting to dripping (JD). The range of the hysteresis increased as the Ω increased and moved to a lower We number region, especially with a larger dj. It was found that increases in Ω also caused hysteresis behavior to occur in dj that without hysteresis. At the same time, the geometry of the hydrophilic nozzle is analyzed in detail, and to determine the reason to cause the hysteresis to happen. The results show that the ratio between the thickness and the inner radius of the nozzle is an important factor. If the ratio is larger, the hysteresis is less likely to occur, on the contrary, the lower the ratio is, the easier it is. Besides, the influence of the nozzle geometry on the capillary rise (δh) in the dripping flow is further studied, and it is found that there also is a hysteresis in the δh, that is, the δh from DJ will be different and greater than that from JD. When Ω is equal to 0%, the capillary phenomenon will rise asymmetrically in the smaller nozzle but rise symmetrically in the larger nozzle along with the nozzle orifice, and when increasing Ω, the adhesion force between the fluid and the nozzle will increase, and the δh is more significant and all rise in an asymmetrical way.

[1] Jiang, X. S., Qi, L. H., Luo, J., Huang, H., Zhou, J. M., “Research on accurate droplet generation for micro-droplet deposition manufacture,” Int. J. Adv. Manuf. Tech. 49, p. 535-541, 2010.
[2] Berkland, C., Kim, K., Pack, D. W., “Fabrication of PLG microspheres with precisely controlled and monodisperse size distributions,” J. Control. Release 73, p. 59-74, 2001.
[3] Xu, C., Chai, W., Huang, Y., Markwald, R. R., “Scaffold-free inkjet printing of three dimensional zigzag cellular tubes,” Biotechnol. Bioeng. 109, p. 3152-3160, 2015.
[4] Savart, F., “Mémoire sur la constitution des veines liquides lancées pardes orifices circulaires en mince paroi,” Ann. Chem. Phys., Vol. 53, p.337, 1883.
[5] Lord Rayleigh, “On the capillary phenomena of jet,” Proc. R. Soc. London, Vol. 29, p. 71, 1879.
[6] Weber, C., “On the breakdown of a fluid jet,” ZAMM 1, Vol. 11, p. 136-154. 1931.
[7] Chandrasekhar, S., Hydrodynamics and Hydromagnetic Stability, Oxford University Press, Oxford, 1961.
[8] Tomotika, S., “On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid,” Proc. R. Soc. London, Ser. A, Vol. 150, p. 322, 1935.
[9] Tyler, E., and Richardson, E. G., “The characteristic curves of liquid jets,” Proc. Phys. Soc. London, vol. 37, p. 297, 1925.
[10] Haenlein, A., “Disintegration of a liquid jet.” NACA Tech, Note TN 659, 1932.
[11] Grant, R. P., Middleman, S., “Newtonian jet stability.” AIChE Journal, Vol. 12, p. 669-678, 1966.
[12] Mccarthy, M. J. and Molloy, N. A., “Review of stability of liquid jets and the influence of nozzle design.” Chem. Eng. J., Vol. 7, p. 1, 1974.
[13] Langhaar, H. L., “Steady flow in the transition lengths for incompressible laminar flow in rectangular ducts.” J. Appl. Mech. A, Vol. 9, p. 55, 1942.
[14] Lin, S. P. and Reitz, R. D., “Drop and spray formation from a liquid jet,” Ann. Rev. Fluid Mech., Vol. 30, p. 85, 1998.
[15] Goedde, E. F. and Yuen, M. C., “Experiments on liquid jet instability,” J. Fluid Mech., Vol. 40, p. 495, 1970.
[16] Pimbley, W. T. and Lee, H. C., “Satellite droplet formation in a liquid jet,” IBM J. Res. Dev., Vol. 21, p. 21, 1977.
[17] Chaudhary, K. C. and Maxworthy, T., “The nonlinear capillary instability of a liquid jet. Part 2. Experiments on jet behavior before droplet formation,” J. Fluid Mech., Vol. 96, p. 275, 1980.
[18] Chaudhary, K. C. and Redekopp, L. G., “The nonlinear instability of a liquid jet. Part 2. Experiments on jet behavior before droplet formation.” J. Fluid Mech. 96, p. 275-286, 1980.
[19] Bogy, D. B., “Drop formation in a circular liquid jet.” Annu. Rev. Fluid Mech., Vol. 11, p. 207-228, 1979.
[20] Yuen, M. C., “Non-linear capillary instability of a liquid jet.” J. Fluid Mech., Vol. 33, p. 151-163, 1968.
[21] LaFrance, P., “Non-linear breakup of a laminar liquid jet.” Phys. Fluids, Vol. 18, p. 428, 1975.
[22] Lord Rayleigh, “On the instability of jets.” Proc. London Math. Soc. 4, p. 10, 1878.
[23] Lee, H. C., “Drop formation in a liquid jet.” IBM J. Res. Dev., Vol. 18, p. 364-369, 1974.
[24] Vassallo, P. and Ashgriz, N., “Satellite formation and merging in liquid jet,” Proc. R. Soc. London, Ser. A, Vol. 433, p. 269, 1991.
[25] Kasyap, T. V., Sivakumar, D., Raghunandan, B. N., “Flow and breakup characteristics of elliptical liquid jets.” Int. J. Multiphase Flow, Vol. 35, p. 8-19, 2009.
[26] Rajesh, K. R., Sakthikumar, R., Sivakumar, D., “Interfacial oscillation of liquid jets discharging from non-circular orifices.” International Journal of Multiphase Flow,
Vol. 87, p. 1-8, 2016.
[27] Ashgriz, N., Mashayek, F., “Temporal analysis of capillary jet breakup.” J. Fluid Mech., Vol. 291, p. 163-190, 1995.
[28] Rutland, D. F. and Jameson, G. J., “Theoretical prediction of the sizes of drops formed in the breakup of capillary jets,” Chem. Eng. Sci., Vol. 25, p. 1689, 1970.
[29] Teng, H., Kinoshita, C. M., Masutani, S. M., “Prediction of droplet size from the breakup of cylindrical liquid jets.” Int. J. Multiphase Flow, Vol. 21, No. 1, p.129-136, 1995.
[30] Kinoshita, C. M., Teng, H., Masutani, S. M., “A study of the instability of liquid jets and comparison with Tomotika's analysis.” Int. J. Multiphase Flow 20, p. 523-533, 1994.
[31] Tate, T., “On the magnitude of a drop of liquid formed under different circumstances.” Phil. Mag., Vol. 27, p. 176, 1864.
[32] Harkins, W. D., Brown, F. E., “The determination of surface tension (Free surface energy), and the weight of falling drops: the surface tension of water and benzene by the capillary height method.” J. Am. Chem. Soc., Vol. 41, p. 499-524, 1919.
[33] Martien, P., Pope, S. C., Scott, P. L., Shaw, R. S., “The chaotic behavior of the leaky faucet.” Phys. Rev. Lett., Vol. 110A, p. 399-404, 1985.
[34] Sartorelli, J. C., Gonçalves, W. M., Pinto, R. D., “Crisis and intermittence in a leaky-faucet experiment.” Phys. Rev. E, vol. 49, 3963, 1994.
[35] Viswanathan, H., “Breakup and coalescence of drops during transition from dripping to jetting in a Newtonian fluid.” Int. J. Multiphase Flow, Vol. 112, p. 269-285, 2019.
[36] Clanet, C., and Lasheras, J. C., “Transition from dripping to jetting,” J. Fluid Mech, Vol. 383, pp. 307-326, 1999.
[37] Deka, H., Tsai, P. H., Biswas, G., Dalal, A., Ray, B., Wang, A. B., “Dynamics of Formation and Oscillation of Non-Spherical Drops.” Chemical Engineering Science 201, p. 413-423, 2019.
[38] Tyler, E., and Richardson, E. G., “The characteristic curves of liquid jets,” Proc. Phys. Soc. London, vol. 37, p. 297, 1925.
[39] Tylor, G. I., “The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets.” Proc. R. Soc. Lond. A 253, p.313-321, 1959.
[40] Meister, B. J., Scheele, G. F., “Prediction of jet length in immiscible liquid systems.” AIChE J., Vol. 15, p. 689-699, 1969.
[41] Basaran, O. A., “Small-scale free surface flows with breakup: Drop formation and emerging applications.” AIChE J., Vol. 48, p. 1842, 2002.
[42] Ambravaneswaran, B., Subramani, H. J., Phillips, S. D., Basaran, O. A., “Dripping-Jetting Transitions in a Dripping Faucet.” Phys. Rev. Lett. 93, 0345011-0345014, 2004.
[43] Subramani, H. J., Yeoh, H. K., Suryo, R., Xu, Q., Ambravaneswaran, B., Basaran, O. A., “Simplicity and complexity in a dripping faucet.” Phys. Fluids 18, 03210613, 2006.
[44] Coullet, P., Mahadevan, L., Riera, C. S., “Hydrodynamical models for the chaotic
dripping faucet.” J. Fluid Mech., vol. 526, p. 1-17, 2005.
[45] Hoeve, W., Gekle, S., Snoeijer, J. H., Versluis, M., Brenner, M.P., Lohse, D., “Breakup of diminutive Rayleigh jets.” Phys. Fluids., Vol. 22, 122003, 2010.
[46] Mariano, R. R., Paloma, T., Alejandro, S., “Dripping dynamics and transitions at high Bond numbers.” Int. J. Multiphase Flow, Vol. 104, p. 206-213, 2018.
[47] Chang, C., C., “A Study on the Breakup of a Rotating Liquid Jet,” Unpublished Master Dissertation, Department of Mechanical Engineering National Cheng Kung University, 2018.