Physics question: Let's say we have a large spherical flask with a venting/ negative pressure fan at the neck

the flask is 10,000 liters or larger, and the fan is not high efficiency or sealed well, more like a bathroom fan. You turn on the venting fan at normal atmosphere. The air is clean. Then you introduce smoke for a while near the inside surface of the fan. It of course tries to vent the smoke, but since there in no other inlet of air, eventually the pressure within the flask goes down and the fan is not efficient enough to keep a vaccuum. Does the residual smoke achieve equal distribution within the large flask, or a hemispherical distibution near the fan?