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