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ISSN Druckformat: 1044-5110
ISSN Online: 1936-2684
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THREE-DIMENSIONAL TEMPORAL INSTABILITY OF NON-NEWTONIAN LIQUID SHEETS
ABSTRAKT
The three-dimensional temporal instability of a non-Newtonian liquid sheet moving in an inviscid gaseous environment is investigated. The corresponding dispersion relations between the growth rate and the wave number of both symmetric and antisymmetric disturbances are derived. The velocity and pressure distributions are presented. The effects of different parameters on the growth rates are explored. The linear stability analysis shows that a sheet of a viscoelastic non-Newtonian fluid has higher growth rates than Newtonian ones for both symmetric and antisymmetric types of two- and three-dimensional disturbances, indicating that such non-Newtonian liquid sheets are more unstable than Newtonian counterparts. It is found that in non-Newtonian liquid sheets the surface tension effects always resist the occurrence and development of two- and three-dimensional instability, while the aerodynamic effects are the source of the onset and growth of the instability. Similar results have been reported for inviscid and Newtonian liquid sheets by many other authors. It is discovered that two-dimensional disturbances dominate the instability of non-Newtonian liquid sheets for both symmetric and antisymmetric disturbances, and the growth rate decreases as the z-direction wave number increases for three-dimensional disturbances. In viscoelastic non-Newtonian fluids, the liquid viscosity tends to stabilize the sheet, whereas the liquid elasticity results in a destabilization. At the surface tension is decreased, the growth rate and the instability range of non-Newtonian liquid sheets increase significantly for both the symmetric and antisymmetric modes. At low liquid Weber number the maximum growth rate of antisymmetric disturbances is larger, whereas the dominant wave number of antisymmetric disturbances is smaller than that of symmetric disturbances. However, at high liquid Weber number the values of the maximum growth rate and the dominant wave number of symmetric and antisymmetric disturbances approach each other asymptotically. In addition, when the z-direction wave number is greater than zero, the values of the maximum growth rate and the dominant wave number of symmetric and antisymmetric disturbances are almost identical Both the disturbance growth rate and the instability range of non-Newtonian liquid sheets increase greatly with the gas-to-liquid density ratio for both the symmetric and antisymmetric modes. The growth rates of symmetric and antisymmetric disturbances decrease with increasing liquid viscosity and with increasing ratio of deformation retardation to stress relaxation time, but increase with the liquid elasticity in a relatively weak manner for two- and three-dimensional instabilities. The instability range does not change with these three parameters.
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Yang Li-jun, Qu Yuan-yuan, Fu Qing-fei, Gu Bin, Wang Feng, Linear Stability Analysis of a Non-Newtonian Liquid Sheet, Journal of Propulsion and Power, 26, 6, 2010. Crossref
-
WAKIMOTO Tatsuro, AZUMA Tsuneo, Instability of Radial Liquid Sheet Flow, JSME International Journal Series B, 47, 1, 2004. Crossref
-
Wang Chen, Yang Li-jun, Xie Luo, Chen Pi-min, Weakly nonlinear instability of planar viscoelastic sheets, Physics of Fluids, 27, 1, 2015. Crossref
-
Yang Li-jun, Xu Bing-rui, Fu Qing-fei, Linear instability analysis of planar non-Newtonian liquid sheets in two gas streams of unequal velocities, Journal of Non-Newtonian Fluid Mechanics, 167-168, 2012. Crossref
-
Thompson Jeffery C., Rothstein Jonathan P., The atomization of viscoelastic fluids in flat-fan and hollow-cone spray nozzles, Journal of Non-Newtonian Fluid Mechanics, 147, 1-2, 2007. Crossref
-
Yang Li-jun, Fu Qing-fei, Qu Yuan-yuan, Gu Bin, Zhang Meng-zheng, Breakup of a power-law liquid sheet formed by an impinging jet injector, International Journal of Multiphase Flow, 39, 2012. Crossref
-
Tong Ming-Xi, Yang Li-Jun, Fu Qing-Fei, Thermocapillar instability of a two-dimensional viscoelastic planar liquid sheet in surrounding gas, Physics of Fluids, 26, 3, 2014. Crossref
-
Liu Lujia, Liu Yingjie, Lu Lipeng, Atomization mechanism of a charged viscoelastic liquid sheet, Chinese Journal of Aeronautics, 28, 2, 2015. Crossref
-
Xie Luo, Yang Li-Jun, Fu Qing-Fei, Qin Li-Zi, Effects of unrelaxed stress tension on the weakly nonlinear instability of viscoelastic sheets, Physics of Fluids, 28, 10, 2016. Crossref
-
Deng Han-Yu, Zhuo Chang-fei, Feng Feng, A simplified linear model and breakup characteristics of power-law sheet formed by a doublet impinging injector, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 232, 6, 2018. Crossref
-
Guo Jin-Peng, Wang Yi-Bo, Bai Fu-Qiang, Zhang Fan, Du Qing, Effects of Asymmetric Gas Distribution on the Instability of a Plane Power-Law Liquid Jet, Energies, 11, 7, 2018. Crossref
-
Tong Ming-Xi, Yang Li-Jun, Fu Qing-Fei, Mo Chao-Jie, Effect of Gas/Liquid Shearing on the Viscoelastic Instability of a Planar Sheet, Journal of Fluids Engineering, 139, 4, 2017. Crossref
-
Xie Luo, Yang Li-Jun, Wang Jun-jie, Qin Li-zi, Weakly nonlinear instability of viscoelastic planar sheets with initial varicose disturbances, Aerospace Science and Technology, 79, 2018. Crossref
-
Madlener Klaus, Ciezki Helmut, von Kampen Jens, Heislbetz Bernhard, Feinauer Albert, Characterization of Various Properties of Gel Fuels with Regard to Propulsion Application, 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2008. Crossref
-
Heislbetz Bernhard, Madlener Klaus, Ciezki Helmut, Breakup Characteristics of a Newtonian Liquid Sheet Formed by a Doublet Impinging Jet Injector, 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2007. Crossref
-
Jia Bo-qi, Xie Luo, Yang Li-jun, Fu Qing-fei, Cui Xiao, Linear instability of viscoelastic planar liquid sheets in the presence of gas velocity oscillations, Journal of Non-Newtonian Fluid Mechanics, 273, 2019. Crossref
-
Xu Bingrui, Deng Daosheng, Linear analysis of dewetting instability in multilayer planar sheets for composite nanostructures, Physical Review Fluids, 5, 8, 2020. Crossref
-
Jia Bo-qi, Xie Luo, Yang Li-jun, Fu Qing-fei, Cui Xiao, Energy budget of a viscoelastic planar liquid sheet in the presence of gas velocity oscillations, Physics of Fluids, 32, 8, 2020. Crossref
-
Rathfon Jeremy M., Grolman Joshua M., Crosby Alfred J., Tew Gregory N., Formation of Oriented, Suspended Fibers by Melting Free Standing Polystyrene Thin Films, Macromolecules, 42, 17, 2009. Crossref
-
Dasgupta Debayan, Sharma Saurabh, Nath Sujit, Bhanja Dipankar, Linear Stability Analysis of Viscoelastic Liquid Sheet in Presence of Moving Gas Medium, in Recent Advances in Mechanical Engineering, 2021. Crossref
-
Patrascu Claudiu, Balan Corneliu, Planar liquid sheets surrounded by another immiscible liquid at low capillary Reynolds numbers, Physics of Fluids, 33, 11, 2021. Crossref
-
Dasgupta Debayan, Sharma Saurabh, Nath Sujit, Bhanja Dipankar, Effects of elasticity number and time constant ratio on breakup and droplet formation of viscoelastic planar liquid sheet co-flowing with gases of equal velocities, Journal of Fluid Mechanics, 920, 2021. Crossref
-
Duan Runze, Chen Zhiying, Liu Liansheng, Effect of velocity profile on instability of the viscoelastic liquid sheet, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 229, 11, 2015. Crossref
-
Yang Lijun, Du Minglong, Fu Qingfei, Stability of an annular power-law liquid sheet, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 229, 15, 2015. Crossref
-
El-Sayed Mohamed Fahmy, Alanzi Agaeb Mahal, Electrohydrodynamic Liquid Sheet Instability of Moving Viscoelastic Couple-Stress Dielectric Fluid Surrounded by an Inviscid Gas through Porous Medium, Fluids, 7, 7, 2022. Crossref
-
Niu Lu, Deng Xiangdong, Instability of Viscoelastic Liquid Sheets in a Transverse Electric Field, Mathematics, 10, 19, 2022. Crossref