Table 1.

Using the resistive pulse signal, common equations for calculating particle size, shape, charge, and concentration from the resistive pulse frequency, magnitude, and duration.

Nomenclature
A	Cross sectional area of a pore	f⊥	Shape factor for spheroid with longest dimension perpendicular to pore wall	ve	Electrosmotic velocity
C	Particle concentration	fΠ	Shape factor for spheroid with longest dimension parallel to pore wall	vp	Fluid velocity
				vs	Object velocity through pore
D	Pore diameter	R	Resistance	vμ	Electrophoretic velocity
Ds	Small pore opening diameter in a conical pore	ΔR	Change in resistance	μ	Electrophoretic mobility
Dl	Large pore opening diameter in a conical pore	L	Pore length	Δt	Pulse duration, translocation time
d	particle diameter	Lc	Effective resistive pore length	V	Pore volume
EM	Electric potential	J	Event frequency	v	Particle volume
f	Shape factor	ρ	Solution resistivity	z	Direction along pore length axis

Measured variable		Equation Conditions/References
	Eq. 1	$R=\rho {\displaystyle \underset{L}{\overset{0}{\int }}\frac{\mathit{\text{dz}}}{A(z)}}$
		Resistance in a pore [65]
Resistance R	Eq. 2	$R=\frac{4L_c\rho }{\pi D^2}$
		For a cylindrical pore [6] Lc = L + 0.8Di
	Eq. 3	$R=\frac{4L_c\rho }{\pi D_s{D}_L}$
		Total resistance in a conical pore. Replacing DL and L with Dz and z, the diameter of the pore at a distance z from the small opening can be used to calculate the resistance gradient profile [76].
	Eq. 4	$\frac{\mathrm{\Delta }R}{R}=f\frac{v}{V}S(d/D)$
		A general expression resistance change to particle and pore volume fraction [6, 65, 68]. For spherical particle (f =3/2) and d << D (S = 1) this becomes Maxwell’s theory.
	Eq. 5	$\frac{\mathrm{\Delta }R}{R}=\frac{d^3}{D^2{L}_c}S(d/D)$
		The general expression in terms of a cylindrical pore containing a spherical particle. Combining (1) and (4).
Pulse Magnitude $\frac{\mathbf{\Delta }R}{R}$	Eq. 6	f is particle shape factor [49, 54, 68]   f = 3/ 2   For spherical particles [65]   f = f⊥ + (fΠ − f⊥)cos2 α
		For non-spherical oblate and prolate spheroids as they tumble through a pore [49, 54, 68].
	Eq. 7	$S(d/D)={\left[1-0.8{(d/D)}^3\right]}^{-1}$
		An empirical correction factor developed to describe the non-linear trend between v and V [69, 70, 77].
Pulse Frequency	Eq. 8	$J=\frac{\pi v_s{D}^2}{4}C$
		Nernst-Planck equation relating event frequency to dispersion concentration in a cylindrical pore [20]. The formula includes velocity contributions from electrophoretic and electroosmotic flow, diffusion and external pressure.
Pulse Duration Δt	Eq. 9	$\frac{1}{\mathrm{\Delta }t}\propto f(v_{\mu })+f(v_p)+f(v_e)$
		Particle velocity through a cylindrical pore is a combination of electrokinetic and fluid flow forces [52, 78]. Diffusion velocity is considered negligible in a pore. The combined velocities are inversely proportion to the pulse duration.
	Eq. 10	$\mu =\frac{L_c^2}{E_M\mathrm{\Delta }t}$
		Particle Charge (electrophoretic mobility) measurements can be made when vp and ve are negligible [50, 78].

ⁱL_c = L+0.8D in all following formulas (with exception of conical pore, Eq. 3). This takes into account the residual electric field outside the pore openings.