臺灣博碩士論文加值系統

在Hele-Shaw流場中，因離心力所產生的界面不穩定問題，由於具旋轉塗覆技術(Spinning coating)的潛在應用價值而成為最近研究的主題。此一流場界面穩定性具有兩種相反作用的機制：「黏性驅使界面穩定的機制和離心力驅使界面不穩定的機制，此兩種相反作用彼此之間的競爭決定了界面之間的穩定性。」而且其於旋轉效應中，所產生的指狀化不穩定現象，與單純的徑向推斥所引發的指狀化不穩定性現象，亦有許多方面的差異，主要歸因於：「在旋轉效應中，可互溶流體間黏滯度的差異，會因擴散的效應，而隨著徑向距離的增加而衰減，使得黏滯度對界面的穩定效應相對的減小，然而不穩定的離心力，會因旋轉半徑增大而增強，此與徑向推斥其不穩定性隨徑向距離增加而減弱不同」。本文利用高準確率的數值方法，模擬旋轉Hele-Shaw流場中，可互溶液滴與液環界面不穩定性指狀化情形，其界面的不穩定性取決於五個主要的控制參數，即旋轉強度、黏滯度比控制參數、表面應力係數、科氏力控制參數及注入強度。液滴中心注入流體的強度，會導致界面的不穩定性成長被迫延遲；在高的旋轉強度及低的黏滯係數下，液滴的指狀化情形顯得較為活躍，且呈現較不穩定的現象；科氏力及表面應力將使界面的不穩定趨於緩和。

The Hele-Shaw flows driven by centrifugal force have been the subject of recent studies due to their potential applications of in the technology of spin coating. In the common practices of spin coating process, a liquid drop is initially deposited on the top of rotating target substrate, and spreads outward by the centrifugal force. Since the coating film is extremely thin, the process bears similarities to a rotating Hele-Shaw flow. The rotational effects to the fingering instability differ from the radial flows in many ways. Instabilities in radial flows are mainly due to the viscosity contrast, and decay as radial distance increases. Fingerings are triggered if the displacing fluid is less viscous and more vigorous near the origin. However, in the rotational Hele-Shaw cell, the centrifugal force is generated by the density difference, and proportional to the radial distance. A stronger unstable mechanism is expected if the heavier fluid, usually more viscous, is the driving fluid and more pronounced away from the center. Numerical simulations of interfacial stabilities for miscible interfaces of confined annulus in a rotating Hele-Shaw cell have been presented by means of highly accurate numerical schemes. The influences of Coriolis forces, rotating speed, viscosity contrast, Korteweg stresses and injection are simulated systematically. The fingering patterns are detailed demonstrated by images of concentration, vorticity fields and streamlines systematically to depict the influences of various parameters

封面內頁
簽名頁
授權書　　　　　　　　　　 iii
中文摘要　　　　 　　　　　 　　　　　v
英文摘要　　　　 　　　　　 　　　　vi
誌謝　　　　　　　　　　 　　　 vii
目錄　　　　　　　　　　 　　　 viii
圖目錄　　　　　　　　　 　　　　 　　　x
符號說明　　　　 　　　　　 　　　　xiii
第一章　緒論　　　 　　　　　　　　　　　　　1
1.1 研究背景　 　　　　　　　　　　　1
1.2 研究目的　　　　　 　　　　　　　　　　4
第二章 研究方法與進行步驟　　 　　　　　　 　 7
第三章 結果與討論　　 　　　　　 　　　　 　13
3.1 Hele-Shaw流場可互溶流體液滴之界面探討 　13
3.1.1參考範例的探討　 　　　　　　　 　15
3.1.2科氏力的影響　　　　　　　　　　 　17
3.1.3表面應力的影響　　 　　　　　　 　18
3.1.4無因次旋轉強度的影響　　　　　　 　19
3.1.5注入強度的影響　　 　　　　 　21
3.1.6黏滯度比控制參數的影響 　　　　 　23
3.2 Hele-Shaw流場中可互溶流體液環之界面探討　　25
3.2.1液環的參考範例探討　 　　　　　 　26
3.2.2在液環中添加擾動的影響　　　 　　　 27
3.2.3在液環中科氏力的影響　　　　　　 　27
3.2.4在液環中無因次旋轉強度的影響　　　 　28
3.2.5在液環中表面應力的影響　　　　　 　29
3.2.6在液環中注入強度的影響 　　 　30
第四章 結論　　 　　　　　 　　　　 　31
參考文獻　　 　　　　　　　 　　　 　33

[1] Hill, S. 1952 “Channeling in packed columns.” Chem. Eng. Sci.1.
[2] Saffman, P. and Taylor, G. 1958 “The penetration of a fluid in to a porous medium of Hele-Shaw cell containing a more viscous liquid.” Proc. R. Soc. London. Ser. A, 245, 312.
[3] Yortsos, Y. 1990 “Instabilities in displacement processes in porous media.” J. Phys. Con-dens. Matter 2, SA443.
[4] McCloud, K. V. and Maher, J. V. 1995 “Experimental perturbations to Saffman-Taylor Flow.” Physics Reports 260, 139.
[5] Melo, F. Jooanny, J. and Fauve, S. Phys. Rev. Lett., 1989. 63, 1958.
[6] Fraysse, N. and Homsy, G. 1994. “An experimental study of rivulet instabilities in centrifugal spin coating of viscous Newtonian and non-Newtonian fluids,” Phys. Fluids A, 6, 1491 .
[7] Spaid, M. and Homsy, G. 1997. “Stabilities of viscoelastic dynamic contact lines: An experimental study, ” Phys. Fluids A, 9, 823 .
[8] Carrillo, L., Magdaleno, F., Casademunt, J. and Ortin, J. 1996 “Experiments in a rotating Hele-Shaw cell.” Phys. Rev. E 54, 6260-6267.
[9] Carrillo, L., Soriano, J. and Ortin, J. 1998 “Radial displacement of a fluid annulus in a rotating Hele-Shaw cell.” Phys. Fluids 11, 4, 778-785.
[10] Carrillo, L., Soriano, J. and Ortin, J. 2000 “Interfacial instability of a fluid annulus in a rotating Hele-Shaw cell.” Phys. Fluids 12, 7, 1685-1698.
[11] Wang, M.-W. and Chou, F.-C. 2001 “Fingering Instability and Maximum Radius at High Rotational.” J. of The Electrochemical Society 148, 5, 283-290.
[12] Schwartz, L. 1989. “Instabilities and fingering in a rotating Hele-Shaw cell or porous medium, ” Phys. Fluids A 1, 167 .
[13] Schwartz, L. 2004. “Theorectical and numerical results for spin of viscous liquids, ” Phys. Fluids volume16,Number 3 .
[14] Chen, C.-Y. and Meiburg, E. 1998 “Miscible porous media displacements in the quarter five-spot configuration. Part 1: The homogeneous case.” J. Fluid Mech. 371, 233.
[15] Chen, C.-Y. and Meiburg, E. 1998 “Miscible porous medi displacements in the quarter five-spot configuration. Part 2: Effect of heterogeneities.” J. Fluid Mech. 371, 269.
[16] Chen, C.-Y. and Wang, S. 2001 “Miscible displacement of a layer with finite width in porous media.” Numerical Methods For Heat And Fluid Flow. 11, 8.
[17] Alvarez-Lacalle, E., Ortin, J., and Casademunt, J. “Low viscosity contrast fingering in a Hele-SHAW cell.” Phys. Fluids 16, 4, 908-924
[18] Korteweg, D.1901 ”Sur la forme que prennent les equations du movement des fluids si l’on tient compte des forces capillaries causes par des variations de densite.” Arch. Neel. Sci. Ex. Nat. (II) 6
[19] Hu H. and Joseph, D. 1992.“Miscible displacement in a Hele-Shaw cell,”Z angew. Math. Phys. 43. 626-644.
[20] Camhi, E., Meiburg, E. and Ruith, M. 1999 “ Miscible rectilinear displacements with gravity override. Part2: Hetergeneous porous media.”J. Fluid Mech.420,225.
[21] Rogerson, A. and Meiburg, E. 1993 ”Shear stabilization of miscible displacement of processes in porous media.” Phys. Fluids, A, 5, 1344
[22] Chen C.-Y. and Meiburg, E.1998 ”Miscible porous media displacements in the quarter five-spot configuration. Part 1: The homogeneous case, ” J. Fluid Mech. 371, 233 .