Acetone can be used as a type of solvent welding to the edge of the edge of the case, to provide an airtight seal.
WARNING :
Very easy to get this wrong, and irreparably damage the case
! 
Acetone has a very low surface tension, and can easily penetrate a long way inside from the edge, and give a very unsightly result.
Apply the acetone with the tip of an an orange stick in tiny droplets along the edge of the case. Patience essential.
If done successfully, the acetone would have achieved an airtight seal.
Practice beforehand on some other acrylic objects to be joined along the edge, to achieve some skill in the application of the acetone.