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vt = v − (v · n) n , (82)
vn =(v · n) n . (83)
The lack of mass transfer implies
ρ1 v1,n = j D 1,n , ρc,1 v1,n = j D c,1,n ,
ρ2 v2,n = j D 2,n , ρc,2 v2,n = j D c,2,n . (84)
Because j D 1,n and j D 2,n are relativistically small quantities, so are v1,n and v2,n,
hence also j D c,1,n and j D c,2,n.
Three more boundary conditions follow from the conservation of momentum,
one per component. In comparison to the conservation of energy, however,
there is a complication arising from the possibility of an isotropic surface
pressure[13],
Π tot
ij ≡ Πij − Π D ij − αsf (δij − ninj) δ(|r − rsf|), (85)
where αsf is the surface energy density of [13]. After some algebra, we obtain
where
∆(Πnn − Π D
1
nn) =αsf
R1
+ 1
,
R2
(86)
∆(Πt,i − Π D t,i) t1,i = −t1 ·∇αsf , (87)
∆(Πt,i − Π D t,i) t2,i = −t2 ·∇αsf
Πt,i =Πlj nj (δil − ni nl) ,
(88)
Π D t,i =Π D lj nj (δil − ni nl) , (89)
R1, R2 denote the curvature radii, and t1, t2 the attendant principle directions.
The radii are positive if they point into region 1, and the bulge is toward region
2.
From the Maxwell equations, we deduce the boundary conditions,
∆(Bn + B D n )=0, (90)
∆(Et + E D t )=0, (91)
∆(Dn + D D n )=−σsf , (92)
∆(Ht + H D t )=n × jel,sf/c , (93)
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