Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Sự không ổn định nhiệt mao dẫn bậc hai phi tuyến của một lớp phim mỏng bọc bên trong một silanh có thành dày và độ dẫn nhiệt hữu hạn trong điều kiện không trọng lực
Tóm tắt
Nghiên cứu về sự không ổn định nhiệt mao dẫn bậc hai phi tuyến của một lớp phim lỏng mỏng bao phủ bên trong một silanh được gia nhiệt trong điều kiện không có trọng lực. Kết quả cho thấy, đối với chất lỏng Newton và dưới sự xấp xỉ về số sóng nhỏ và bán kính lớn của silanh, các chế độ trục và tất cả các chế độ azimuthal với số sóng kmax > 0 đều có cùng tốc độ phát triển tối đa tuyến tính, tương tự như trong các bài báo trước đây về dòng chảy bên ngoài silanh. Tại đây, sự không xác định của bài toán tuyến tính này được giải quyết phi tuyến bằng cách tìm kiếm khoảng giá trị của các tham số trong đó chế độ trục chiếm ưu thế và chế độ này không ổn định với chế độ azimuthal đầu tiên của sự không ổn định nhiệt mao dẫn.
Từ khóa
#nhiệt mao dẫn; không ổn định phi tuyến; lớp phim lỏng mỏng; silanh có thành dày; mất trọng lựcTài liệu tham khảo
Assaf, A, Alkharashi, S.A.: Hydromagnetic instability of a thin viscoelastic layer on a moving column. Phys. Scr. 94(045201), 1–19 (2019). https://doi.org/10.1088/1402-4896/aaf948
Benjamin, T.B., Hasselmann, K.: Instability of periodic wavetrains in nonlinear dispersive systems [and Discusssion]. Proc. Royal Soc. London A 299-1456, 59–76 (1967). https://doi.org/10.1098/rspa.1967.0123
Benney, D.J.: Long waves on liquid films. J. Math. Phys. 45, 150–155 (1966). https://doi.org/10.1002/sapm1966451150
Binnie, A.M.: Experiments on the onset of wave formation on a film of water flowing down a vertical plane. J. Fluid Mech. 2, 551–553 (1957). https://doi.org/10.1017/S0022112057000361
Bocharov, A.A., Tsveloduv, O.Yu.: Wave regimes of viscous film flow down a vertical cylinder. Fluid Dyn. 38, 321–327 (2003). https://doi.org/10.1023/A:1024237506130
Chao, Y.C., Ding, Z.Y., Liu, R.: Dynamics of thin liquid films flowing down the uniformly heated/cooled cylinder with wall slippage. Chem. Eng. Sci. 175, 354–364 (2018). https://doi.org/10.1016/j.ces.2017.10.013
Cheng, M.Q., Chang, H.-C.: Stability of axisymmetric waves on liquid films flowing down a vertical column to azimuthal and streamwise disturbances. Chem. Eng. Comm. 118, 327–340 (1992). https://doi.org/10.1080/00986449208936101
Dávalos-Orozco, L.A.: The effect of the thermal conductivity and thickness of the wall on the nonlinear instability of a thin film flowing down an incline. Int. J. Nonlinear Mech. 47, 1–7 (2012). https://doi.org/10.1016/j.ijnonlinmec.2012.02.008
Dávalos-Orozco, L.A.: Nonlinear instability of a thin film flowing down a smoothly deformed thick wall of finite thermal conductivity. Interfacial Phenomena and Heat Transfer 2, 55–74 (2014). https://doi.org/10.1615/InterfacPhenomHeatTransfer.2014010400
Dávalos-Orozco, L.A.: Non-linear instability of a thin film flowing down a cooled wavy thick wall of finite thermal conductivity. Phys. Lett. 379, 962–967 (2015). https://doi.org/10.1016/j.physleta.2015.01.018
Dávalos-Orozco, L.A.: Thermal Marangoni instability of a thin film flowing down a thick wall deformed in the backside. Phys. Fluids 28(054103), 1–12 (2016). https://doi.org/10.1063/1.4948253
Dávalos-Orozco, L. A.: Sideband thermocapillary instability of a thin film coating the outside of a thick walled cylinder with finite thermal conductivity in the absence of gravity. Interfacial Phenomena and Heat Transfer 5, 287–298 (2017). https://doi.org/10.1615/InterfacPhenomHeatTransfer.2018024903
Dávalos-Orozco, L.A.: Sideband thermocapillary instability of a thin film flowing down the inside of a thick walled cylinder with finite thermal conductivity. Interfacial Phenomena and Heat Transfer 6, 239–251 (2018). https://doi.org/10.1615/InterfacPhenomHeatTransfer.2019029854
Dávalos-Orozco, L.A.: Sideband thermocapillary instability of a thin film flowing down the outside of a thick walled cylinder with finite thermal conductivity. Int. J. Non-Linear Mech. 109, 15–23 (2019). https://doi.org/10.1016/j.ijnonlinmec.2018.10.015
Dávalos-Orozco, L. A., Ruiz-Chavarría, G.: Hydrodynamic instability of a fluid layer flowing down a rotating cylinder. Phys. Fluids A 5, 2390–2404 (1993). https://doi.org/10.1063/1.858753
Dávalos-Orozco, L.A., You, X.: Three-dimensional instability of a liquid layer flowing down a heated vertical cylinder. Physics Fluids 12, 2198–2209 (2000). https://doi.org/10.1063/1.1286594
Dijkstra, H.A.: The coupling of marangoni and capillary instabilities in an annular thread of liquid. J. Colloid Interface Sci. 136, 151–159 (1990). https://doi.org/10.1016/0021-9797(90)90085-3
Ding, Z.Y., Liu, Z., Liu, R., Yang, C.: Breakup of ultra-thin liquid films on vertical fiber enhanced by Marangoni effect. Chem. Eng. Sci. 199, 342–348 (2019). https://doi.org/10.1016/j.ces.2018.12.058
Duan, L.-S., Duan, L., Jiang, H., Kang, Q.: Oscillation transition routes of Buoyant-thermocapillary convection in annular liquid layers. Microgravity Sci. Technol 30, 565–876 (2018). https://doi.org/10.1007/s12217-018-9638-1
Frenkel, A.L., Babchin, A.J., Levich, B.G., Shlang, T., Sivashinsky, G.I.: Annular flows can keep unstable films from breakup: Nonlinear saturation of capillary instability. J. Colloid Interface Sci. 115, 225–233 (1987). https://doi.org/10.1016/0021-9797(87)90027-0
Frenkel, A.L.: On evolution equations for thin films flowing down solid surfaces. Phys. Fluids A 5, 2342–2347 (1993). https://doi.org/10.1063/1.858895
Ghosh, A., Bandyopadhyay, D., Sharma, A.: Micro-patterning of coatings on a fiber surface exploiting the contact instabilities of thin viscoelastic films. Phys. Fluids 30(114101), 1–18 (2018). https://doi.org/10.1063/1.5053797
Hernández-Hernández, I.J., Dávalos-Orozco, L. A.: Competition between stationary and oscillatory viscoelastic thermocapillary convection of a film coating a thick wall. Int. J. Thermal Sci. 89, 164–173 (2015). https://doi.org/10.1016/j.ijthermalsci.2014.11.003
Kolegov, K.S.: Simulation of patterned glass film formation in the evaporating colloidal liquid under IR heating. Microgravity Sci. Technol 30, 113–120 (2018). https://doi.org/10.1007/s12217-017-9587-0
Krishnamoorthy, S., Ramaswamy, B., Joo, S.W.: Spontaneous rupture of thin liquid films due to thermocapillarity: A full-scale direct numerical simulation. Phys. Fluids 7(9), 2291–2293 (1992). https://doi.org/10.1063/1.868478
Liu, R., Ding, Z.J., Zhu, Z.Q.: Thermocapillary effect on the absolute and convective instabilities of film flows down a fibre. Int. J. Heat Mass Transfer 112, 918–925 (2017). https://doi.org/10.1016/j.ijheatmasstransfer.2017.05.030
Liu, R., Ding, Z.J., Chen, X.: The effect of thermocapillarity on the dynamics of an exterior coating film flow down a fibre subject to an axial temperature gradient. Int. J. Heat Mass Transfer 123, 718–727 (2018). https://doi.org/10.1016/j.ijheatmasstransfer.2018.03.023
Mo, D.-M., Ruan D.-F.: Linear-stability analysis of thermocapillary-buoyancy convection in an annular two-layer system with upper rigid wall subjected to a radial temperature gradient. Microgravity Sci. Technol. https://doi.org/10.1007/s12217-019-9692-3 (2019)
Moctezuma-Sánchez, M., Dávalos-Orozco, L. A.: Linear three dimensional instability of viscoelastic fluid layers flowing down cylindrical walls. Microgravity Sci. Technol 20, 161–164 (2008). https://doi.org/10.1063/1.858895
Moctezuma-Sánchez, M., Dávalos-Orozco, L.A.: Azimuthal instability modes in a viscoelastic liquid layer flowing down a heated cylinder. Int. J. Heat Mass Transfer 90, 15–25 (2015). https://doi.org/10.1016/j.ijheatmasstransfer.2015.06.035
Rietz, M., Scheid, B., Gallaire, F., Kofman, N., Kneer, R., Rohlfs, W.: Dynamics of falling films on the outside of a vertical rotating cylinder: Waves, rivulets and dripping transitions. J. Fluid Mech. 832, 189–211 (2017). https://doi.org/10.1017/jfm.2017.657
Ruiz-Chavarría, G., Dávalos-Orozco, L.A.: Stability of a liquid film flowing down a rotating cylinder subject to azimuthal disturbances. J. Phys. II (France) 6, 1219–1227 (1996). https://doi.org/10.1051/jp2:1996126
Ruiz-Chavarría, G., Dávalos-Orozco, L.A.: Azimuthal and streamwise disturbances in a fluid layer flowing down a rotating cylinder. Phys. Fluids 9, 2899–2908 (1997). https://doi.org/10.1063/1.869402
Shlang, T., Sivashinsky, G.I.: Irregular flow of a liquid film down a vertical column. J. Physique 43, 459–466 (1982). https://doi.org/10.1051/jphys:01982004303045900
Tsveloduv, O. Yu., Bocharov, A.A.: Nonstationary periodic spatial waves on the surface of a viscous liquid film falling down a vertical cylinder. Thermophys. Aeromech. 19, 293–306 (2012). https://doi.org/10.1134/S0869864312020126
Tuckerman, L.S., Barkley, D.: Bifurcation analysis of the Eckhaus instability. Physica D 46, 57–86 (1990). https://doi.org/10.1016/0167-2789(90)90113-4
Yu, Z.: Thermocapillary instability of self-rewetting films on vertical fibers. Phys. Fluids 30(082104), 1–10 (2018). https://doi.org/10.1063/1.5043482
