On the pressure and stress singularities induced by steady flows of a pair of nonmiscible, incompressible, viscous fluids contacting a wall with slip
Tóm tắt
An earlier asymptotic analysis identified the flow-induced power and log singularities present when two nonmiscible, incompressible, viscous fluids contact a wall with no slip permitted. Here a parallel asymptotic analysis identifies such singularities in pressures and stresses when slip is admitted. While the singularity exponents for the two types of contact conditions are similar, the angles of interface impingement that have either power or log singularities are usually quite distinct.
Tài liệu tham khảo
Sinclair, G.B.: On ensuring structural integrity for configurations with stress singularities: a review. Fatigue Fract. Eng. Mat. Struct. 39, 523–535 (2016)
Zhou, Z., Xu, W., Leung, A.Y.T., et al.: A study of stress singularities arising at the multi-material interface in a V-notched bending plate. Eng. Fract. Mech. 180, 179–194 (2017)
Federov, A.Y., Matveenko, V.P.: Investigation of stress behavior in the vicinity of singular points of elastic bodies made of functionally graded materials. J. Appl. Mech. 85, 061008 (2018)
Karoui, A., Arfaoui, M., Trifa, M., et al.: The singular elastostatic fields at the notch-tip of a compressible Ciarlet-Greymonat material. Eng. Fract. Mech. 199, 392–409 (2018)
Grine, F., Trifa, M., Arfaoui, M., et al.: The anti-plane shear elasto-static fields near a crack terminating at an isotropic hyperelastic bi-material interface. Math. Mech. Solids 24, 2914–2930 (2019)
Korepanova, T., Matveenko, V.P., Shardakov, I.: Construction of analytical eigensolutions for isotropic conical bodies and their application for estimation of stresses singularity. Frat. Integr. Strut. 13, 225–242 (2019)
Karoui, A., Trifa, M., Arfaoui, M., et al.: A plane strain analysis of the elastostatic fields near the notch-tip of a Blatz-Ko material. Theor. Appl. Fract. Mech. 103, 102309 (2019)
Kondrat’ev, V.A.: Asymptotic solution of the Navier-Stokes equations near the angular point of the boundary. J. Appl. Math. Mech. 31, 125–129 (1967)
Blum, H., Rannacher, R.: On the boundary value problem of the biharmonic operator on domains with angular corners. Math. Meth. Appl. Sci. 2, 556–581 (1980)
Rayleigh, L.: Scientific papers VI, pp. 18–21. Cambridge University Press, Cambridge (1920)
Dean, W.R., Montagnon, P.E.: On the steady motion of viscous liquid in a corner. Proc. Camb. Phil. Soc. 45, 389–394 (1949)
Moffatt, H.K.: Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 1–18 (1964)
Liu, C.H., Joseph, D.D.: Stokes flow in wedge-shaped trenches. J. Fluid Mech. 80, 443–463 (1977)
Moffatt, H.K.: The asymptotic behavior of solutions of the Navier-Stokes equations near sharp corners. In: Proceedings of symposium on approximation methods for Navier-Stokes problems, Paderborn, Germany, 371–380. Springer Verlag, Berlin (1979)
Sinclair, G.B., Chi, X., Shih, T.I.-P.: On the pressure and stress singularities induced by steady flows of incompressible viscous fluids. Acta. Mech. Sin. 25, 451–462 (2009)
Nitsche, L.C., Parthasarathi, P.: Stokes flow singularity at the junction between impermeable and porous walls. J. Fluid Mech. 713, 183–215 (2012)
Nitsche, L.C., Bernal, B.A.: Stokes flow singularity at a corner joining solid and porous walls at an arbitrary angle. J. Eng. Math. 108, 1–23 (2018)
Sinclair, G.B.: On the pressure and stress singularities induced by steady flows of a pair of nonmiscible, incompressible, viscous fluids in contact with a wall. Acta. Mech. Sin. 26, 669–673 (2010)
Rao, I.J., Rajagopal, K.R.: The effect of the slip boundary condition on the flow of fluids in a channel. Acta Mech. 135, 113–126 (1999)
Dempsey, J.P., Sinclair, G.B.: On the singular behavior at the vertex of a bi-material wedge. J. Elast. 11, 317–327 (1981)