“…Consequently, the expansion parameters, κ n , have to satisfy the eigenvalue Eq (15) in the limit ρ → ∞, and we find This transcendental equation has to be solved numerically; for large η , the eigenvalues approach infinity with eigenvalue κ 1 ascending the slowest as shown in Fig 2c . The first eigenvalue, κ 1 , can be approximated with Eq (17) as In addition, by solving Eq (9) with Eqs ( 16 ) and ( 1 ), and using analytical techniques from [ 30 ], the dimensionless expansion coefficients, G n , are given as: An expression for G n in terms of trigonometric functions is provided in Eq (28) in Appendix A . Since the eigenvalues κ n depend on the volume fraction η only, the same dependence holds for the expansion coefficients G n and is visualized in Fig 2d .…”