Separation Properties in Homogeneous Electric Field

The first FAIMS systems had the planar gap geometry, which remains the simplest to implement. The homogeneity of electric field in isothermal planar gaps greatly simplifies ion dynamics, and we begin its modeling from that regime. 

Putting oscillations due to E i) aside for a moment and considering only the slow net drift along E for near-equilibrium ions (where the difference AEc between applied Eq and Ec of the ion is small), we can modify Equations 4.4 and 4.5 to  

For A c — 0, this reduces to the standard formula for free diffusion in a gap  

As the diffusion along x is longitudinal (4.1.1), presumably one should use Equation 4.10 with Dn for D. Ions found within the oscUlalion amplitude Ad (3.2.2) of an electrode when the motion toward that electrode starts in the F(t) cycle are destroyed within the cycle, i.e., in essence instantly compared to Hence there are virtually no ions within a segment of physical gap width (g) equal to Ad, leading 

The ion transmission s through FAIMS at the peak apex is found by integration of Equation 4.11 overx, which produces simple exponential decay  

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