slip flow on curvved surface
 

Hi i`m trying to model slip flow over a microsphere in a chanell to find it`s drag. for boundary condition on surface of the sphere i have to use UDF. i used a UDF for the chanell wall but i can`t use it for the sphere. to modify shear on the wall i used (mue*du/dy) but for curved surface i can`t use it so i refer to Generalizad Stress tensor and came to this formula but i don`t know how to modify sin(alpha) can anybody help me?

u_slip=(2-sigma/sigma)*kn*D*[sin(2*alpha)*(du_dx+dv_dy)+(du_dy+dv_dx)]

the coordinate system is located @ center of sphere and sin(alpha)can be found from cell coordinates