Flow Around A Corner A particle at (x0,y) will descend at speed U until y=x0. Ignore gravity Then it finds itself in a horizontal fluid flow. Drag force on particle takes more general form: FD = -(v-u)/B Solve for particle trajectory in x and y directions.

Approaching Drift Velocity Here we consider the trajectory of a charged particle in a constant electric field The force on a charged particle is the charge on the particle times the electric field at its location e is the elementary unit of charge, and –e is the charge on a single electron. Assume the aerosol particle has a single extra electron. The electric field is calculated as E = -V, where V is the electric potential (voltage) Parallel plates at different voltages produce a nearly constant field between them. Let V2 > V1. The distance between them is h. Now consider the generalized force equation for the particle, Equations of this form have the solution, Memory of original velocity decays away A “drift velocity” takes over on same timescale

Approaching Drift Velocity Now that we have solved for velocity, we need to integrate to get trajectory Assume particle starts at rest, vD = 1 cm/s, t = 10s z=vDt z zoffset The result is that the particle initially accelerates until it approaches a path parallel to the constant drift path. The offset between these paths asymptotes to