I wanted to know if positively pressurised spaces would be better at stopping larger particles or smaller particles. Suppose we have a positively pressurised space. If there is an orifice, this causes air to move outwards from the room. This air velocity field is meant to protect contaminants from coming in, but what is the physics of this scenario? Let's assume that the velocity field of air ejected by the positively pressurised space is constant, and in one direction. Now, suppose someone outside the room sneezes, droplets are ejected, and move at some initial velocity in the direction opposite to the velocity field. Are bigger or smaller particles better stopped by such a field? Suppose we have multiple size spheres being ejected at some velocity. Without airflow, we would expect them to all fall down at the same trajectory, regardless of their size or mass. But things change when we push the spheres through a fluid (air). ![[Screenshot 2025-09-01 at 13.18.51.png]] For low Reynolds number flow, we have drag force from the Stokes' law (Stokes 1851), which is meant to model dense spheres in translational motion. We also have gravity and bouyancy. Stokes' law says that $ \mathbf F _{\text { drag }} = - 6 \pi r \mu ( \mathbf v - \mathbf v _ { \text { fluid }} ) $ Where we have - $\mathbf v$ is the velocity of the sphere in question - $r$ is the diameter of the particle - $\mu$ is the dynamic viscosity of the surrounding fluid - $\mathbf v_ {\text{ fluid}}$ is the flow field far away - which in this case is our constant velocity field. Gravitational force is given by $ \mathbf F _ { \text { grav }} = m \mathbf g$ This means that the motion of this particle is given by the differential equation $ \frac{ d \mathbf v } { dt } = \mathbf g - \frac { 6 \pi r \mu } { m } (\mathbf v - \mathbf v _ { \text{ fluid }} ) $ And, we have the initial condition that the particle initial moves at some $\mathbf v _0$ . Simulating this with particles of different sizes, **we find that the drag causes the big particles to settle quicker to the floor, as their downward terminal velocity is higher. But due to inertia, they take longer to switch direction.** ![[Screenshot 2025-09-01 at 15.10.35.png]] Here is the same simulation with air viscocity = 0 (free particle) ![[Screenshot 2025-09-01 at 15.12.25.png]] ## Acknowledgements Thank you to Ben Trettel for valuable discussions.