(*Constants required*)
a = 8.2314*10^-7; omega = 3.0318*10^7; Do2 = 2*10^-9; po = 106; ro = 235*10^-6; micron = 1*10^-6; qm = 10^-4; mic = 1*10^-6; De = 5.5*10^-11;  con = (a*omega)/(6*Do2); rl = Sqrt[(6*Do2*po)/(omega*a)];

(*Functions that are pre-defined*)
 rn = Piecewise[{{0, ro <=  rl}, {ro*(0.5 - Cos[(ArcCos[1 - (2*rl*rl)/(ro^2)] - 2*Pi)/3]), ro  > rl}}];

p[r_] = Piecewise[{{po + con*(r^2 - ro^2 + 2*(rn^3)*(1/r - 1/ro)), r > rn} , {0 , r <= rn}}];

q[r_] = qm*((kme/(kme + p[r]))*(p[r]/(kmn + p[r]))  + (kmn/(kmn + p[r]))*j);


(*Coupled Equations to be solved*)
  eqnDe = D[Ef1[r, t], t] -  De*(D[Ef1[r, t], r, r] + (2/r)*(D[Ef1[r, t], r])) + q[r]*Ef1[r, t];

eqnBo = D[Eb1[r, t], t] - (Ef1[r, t])*q[r];


(*Parametric solution for unknowns kme, kmn, j and eo*)
x = ParametricNDSolve[{eqnBo == 0, Eb1[r, 0] == 0, eqnDe == 0,
Ef1[r, 0] == 0, Derivative[1, 0][Ef1][rn, t] == 0,
Ef1[ro, t] == eo},  Eb1, {r, rn, ro}, {t, 0, 14400}, {kme, kmn, j, eo}];

Ebound[r_] =
  Piecewise[{{Eb1[rn, 14400] /. x, r < rn}, {Eb1[r, 14400] /. x,
 r >= rn}}];

x = ParametricNDSolveValue[{eqnBo == 0, Eb1[r, 0] == 0, eqnDe == 0,
    Ef1[r, 0] == 0, Derivative[1, 0][Ef1][rn, t] == 0,
    Ef1[ro, t] == eo},
   Eb1, {r, rn, ro}, {t, 0, 14400}, {kme, kmn, j, eo}];

Ebound[r_] :=
  Piecewise[{{x[rn, 14400, 1, 1], r < rn}, {x[r, 14400, 1, 1],
     r >= rn}}];

Ebound[1]