@Preben Alsholm 

I have tried differnt bounday conditions.

We dont have enough boudary conditins,

for sure h(0)=0 and D(h)(0)=theta, for the third bouyndary condition it is like that at infinity D(D)(h)=1/R, I belive that may be at last several micron is enough for infinity, becaus ethe totoal diameter is less that 100 micron. For the last condition there are different way to give that conditions one of the is that  D(D(H)(-infinity)=0 due to flat surface but i have heard that it dosent work for solution and there are some other complicated conditions. but as long as i have the experimental result so i already have profile so i can give the boundary condition like h(2e-6)=200e-9.

So fo you mean taht i need to increase the infinity size from 2 micron to much more value. how thet have conflit the secend drivation is the curveture but h(2e-6)=200e-9 this value showshight of a point in the profile.

@Preben Alsholm 

Thanks for your response.

The boundary condition are h(0)=0 D(h)(0)=tehta (the contact angle),D(D(h))(infinity)=1/R the curveure of the film goeas to the droplet radious at infinity the physical infinity might be about 2 or 3 micron, and finally from teh experiment i have the graph the value of some point because i have profile of the film for instance h(2e-6)=200e-9.

or something like hat or D(D(H)(-infinity)=0,( the flat curveture ) the - infinfity can be equal to 2e-6.

can you send the maole file also.

@Preben Alsholm 

yes, It is real problem. it is the evaporative contact line problem. 

The conditions is related o the problem, that i might simpify it in this way, but still canot solve it.

@tomleslie 

Thanks for your replay and time

@loramina123 

I also trie this 

calc_contact.mw

Download calc_contact.mw

@tomleslie 

calc_contact.mw

Hi, Thaks for your kind reply, it was usefull, but I still have problem to solve the equation.

Download calc_contact.mw

Download calc_contact.mwcalc_contact.mw

@Preben Alsholm 

Hi , Thanks for your respounse Carol,

You probably did not see the whole answer.

Actually there is Z in the answer and i dont know what is that Z, furthermore for real small value of r i get the coplex answer which is not acceptable.

e := {T = 1/RootOf(-609600000000000000000000000000000000000000000000000000000+(879515018020273730453559011332895956000000000000000000000000000*sqrt(-625000000*r^2+1)-

761682348615485390130551939524898425387968750740910059296172487)*Z^5+(-2959335021226548863761237057896000000000000000000000000000000*sqrt(-625000000*r^2+1)+

2562859306691152293409465394507279449380503585614734443742000)*_Z^3+

182392320000000000000000000000000000000000000000000000000000*_Z^2)^2}