  Determining physically admissible boundary conditions for higher moments in
an extended continuum model is recognised as a major obstacle. Boundary
conditions for the regularised 26-moment (R26) equations obtained using
Maxwell's accommodation model do exist in the literature; however, we show in
this article that these boundary conditions violate the second law of
thermodynamics and the Onsager reciprocity relations for certain boundary value
problems, and, hence, are not physically admissible. We further prove that the
linearised R26 (LR26) equations possess a proper $H$-theorem (second-law
inequality) by determining a quadratic form without cross-product terms for the
entropy density. The establishment of the $H$-theorem for the LR26 equations in
turn leads to a complete set of boundary conditions that are physically
admissible for all processes and comply with the Onsager reciprocity relations.
As an application, the problem of a slow rarefied gas flow past a spherical
droplet with and without evaporation is considered and solved analytically. The
results are compared with the numerical solution of the linearised Boltzmann
equation, experimental results from the literature and/or other macroscopic
theories to show that the LR26 theory with the physically admissible boundary
conditions provides an excellent prediction up to Knudsen number $\,\lesssim 1$
and, consequently, provides transpicuous insights into intriguing effects, such
as thermal polarisation. In particular, the analytic results for the drag force
obtained in the present work are in an excellent agreement with experimental
results even for very large values of the Knudsen number.
