Particle paths and flow fields in a prototype differential mobility analyzer (DMA) were numerically analyzed solving Navier-Stokes equation, electric field equation and particle motion considering viscous drag force, Coulomb force and polarization force. Analytically predicted particle diameters for the prototype DMA are in good agreement with the measured particle diameters within $pm$1%. And the analytically predicted particle diameters are also in good agreement with numerical results for the prototype DMA.