Geodesic
Non-linear wave propagation in a weakly compressible Kelvin-Voigt liquid containing bubbly clusters
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 1, pp. 171-194

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The effect of bubble-bubble interaction on wave propagation in homogeneous weakly compressible viscoelastic bubbly flow is investigated using the reductive perturbation method. The bubble dynamics equation is derived using the kinetic energy conservation approach. The bubble dynamics and mixture equations are coupled with the equation of state for gas to investigate the shock wave propagation phenomenon in the mixture. A two-dimensional Korteweg-de VriesBurger (KdVB) equation in terms of a pressure profile is derived. It is found that the bubble-bubble interaction has no effect when using the parameters under our consideration.
Keywords: shock wave, Kelvin–Voigt liquid, bubbly liquid, KdVB equation. 
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     author = {Y. B. Chukkol and M. Abdullahi and I. Bello},
     title = {Non-linear wave propagation in a weakly compressible {Kelvin-Voigt} liquid containing bubbly clusters},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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     url = {http://geodesic.mathdoc.fr/item/VUU_2023_33_1_a11/}
}
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Y. B. Chukkol; M. Abdullahi; I. Bello. Non-linear wave propagation in a weakly compressible Kelvin-Voigt liquid containing bubbly clusters. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 1, pp. 171-194. http://geodesic.mathdoc.fr/item/VUU_2023_33_1_a11/