Answered by Shaykh Hamza Karamali, SunniPath Academy Teacher
If I need to apply medicine to my face that must remain on for the entire day, what is the proper way for me to make wudu? Making wudu washes this medicine off
In the Name of Allah, Most Merciful and Compassionate
If making wudu would cause you (a) loss of life, or (b) loss of limb, or (c) a worsening in your sickness, or (d) a longer recovery time from your sickness, or (e) an excessive blemishing mark on your face, then it would be permissible for you to make tayammum instead of washing the part of your face that you cannot wash.
You would do this by starting your wudu as normal by washing your hands up to your wrists and then at the point when you wash your face, you would do a tayammum on your hands and face with earth. After that, you would wash everything possible of your face and then continue your wudu normally to the end.
When making tayammum, the earth must be able to reach all parts of your face and hands. If this is not possible because of one of the five excuses listed above, you should do whatever you can and perform your prayers, but you will have to repeat all these prayers when you recover from your illness or injury (since you were unable to properly perform both wudu and tayammum).
(al-Minhaj al-Qawim + al-Hawashi al-Madaniyya, 1.184-186)
And Allah knows best.
Hamza.