Theoretical investigation of ion transport dynamics in current-time inside nanochannel and microchannel

In this paper, we study the nanochannel material membrane property to model the ion current-time dynamics. Here we consider a symmetric monovalent electrolyte (z^{+ = -}z- = z) like KCl with bulk concentration, c₀ = 0.1 mM, and assume that the concentration of H⁺ and OH^- is much lower compared to the bulk concentration of the ionic species. The nanochannel length (L_nanochannel) is 5μm and height is 30nm per unit width. The applied voltage is 1V. We obtain the surface charge density of the nanochannel material is -1 mC/m² , the counter-ion concentration is c_K⁺= 0.74 mM and co-ion concentration c_Cl^-= 0.06 mM for surface potential = 52 mV from the ion-ion and ion-wall interactions [1]. The mass and charge (m_K⁺, q_K⁺) for the counter-ion and co-ion (m_Cl^-, q_Cl^-) are obtained. The electrokinetic velocity (velocity), acceleration (a) of the ionic species (velocity/time) is calculated. The ionic species position is tracked using a well known velocity-verlet algorithm [2]. The counter-ion current-time model is I_K⁺(t) = ((q_K⁺velocity)/L_nanochannel) + ((m_K⁺a velocity)/Voltage​​​​​​) , co-ion is I_Cl^-(t) = ((q_Cl^-velocity)/L_nanochannel) + ((m_Cl^-a velocity)/Voltage​​​​​​) and the total ionic current-time through the nanochannel is I(t) = I_K⁺(t) + I_Cl^- (t). The obtained current is validated with Ref. [1] for time step 100 ns. We study for microchannel of length = 1 μm and height of the microchannel = 1 μm per unit width. The nanochannel material membrane current-time is GUI applications in nanofluidic calculators and app software.