TY - JOUR
T1 - Hydrodynamic boundary conditions from kinetic theory
AU - Protopopescu, V.
AU - Keyes, T.
PY - 1983/4/25
Y1 - 1983/4/25
N2 - A simple tagged particle kinetic equation is studied in the presence of a wall, where the boundary conditions may be reflecting, absorbing, or a mixture thereof. A diffusion equation is derived from the kinetic equation via the scaling, t→ t ε{lunate}2, x→ x ε{lunate}, ε{lunate}→0. To O(ε{lunate}0), the boundary conditions on the diffusion equation are found to be Neumann for pure reflection and Dirichlet if any absorption is present. To O(ε{lunate}), a mixed or "radiative" boundary condition is obtained, which may be interpreted in terms of a Dirichlet condition at an extrapolated length, O(ε{lunate}), inside the wall.
AB - A simple tagged particle kinetic equation is studied in the presence of a wall, where the boundary conditions may be reflecting, absorbing, or a mixture thereof. A diffusion equation is derived from the kinetic equation via the scaling, t→ t ε{lunate}2, x→ x ε{lunate}, ε{lunate}→0. To O(ε{lunate}0), the boundary conditions on the diffusion equation are found to be Neumann for pure reflection and Dirichlet if any absorption is present. To O(ε{lunate}), a mixed or "radiative" boundary condition is obtained, which may be interpreted in terms of a Dirichlet condition at an extrapolated length, O(ε{lunate}), inside the wall.
UR - http://www.scopus.com/inward/record.url?scp=4243271452&partnerID=8YFLogxK
U2 - 10.1016/0375-9601(83)90817-4
DO - 10.1016/0375-9601(83)90817-4
M3 - Article
AN - SCOPUS:4243271452
SN - 0375-9601
VL - 95
SP - 139
EP - 142
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 3-4
ER -