Fluid Dynamics Seminar

Mon., Dec. 2, 2013, 2:30 PM
Cullimore, Room 611
New Jersey Institute of Technology


Eshelby's solution and Stokes flow

Liping Liu


Math, Mech. & Aero. Engr., Rutgers University



The closed-form solution concerning an ellipsoidal inhomogeneity in an infinite elastic body, namely, the Eshelby's solution, is well-known among the community of solid mechanics and has been applied to many important materials models including fracture mechanics, composite materials and solid-to-solid phase transition. However, there are very few applications of Eshelby's solution in the context of fluid mechanics. We observe that the Stokes flow is governed by the same equation as for a linear elastic body, and henceforth the analysis and phenomenological material models based on the Eshelby solution can be directly applied to calculate, e.g., effective viscous and viscoelastic properties of suspensions. We also observe that the Eshelby's solution, from a mathematical viewpoint, is essentially a closed-form solution in potential theory. Along this line, we propose two generalizations of ellipsoidal domains and discuss about their potential applications in solid and fluid mechanics.