Electroosmotic Flow Hysteresis for Fluids with Dissimilar pH and Ionic Species

Abstract

Electroosmotic flow (EOF) involving displacement of multiple fluids is employed in micro-/nanofluidic applications. There are existing investigations on EOF hysteresis, i.e., flow direction-dependent behavior. However, none so far have studied the solution pair system of dissimilar ionic species with substantial pH difference. They exhibit complicated hysteretic phenomena. In this study, we investigate the EOF of sodium bicarbonate (NaHCO₃, alkaline) and sodium chloride (NaCl, slightly acidic) solution pair via current monitoring technique. A developed slip velocity model with a modified wall condition is implemented with finite element simulations. Quantitative agreements between experimental and simulation results are obtained. Concentration evolutions of NaHCO₃-NaCl follow the dissimilar anion species system. When NaCl displaces NaHCO₃, EOF reduces due to the displacement of NaHCO₃ with high pH (high absolute zeta potential). Consequently, NaCl is not fully displaced into the microchannel. When NaHCO₃ displaces NaCl, NaHCO₃ cannot displace into the microchannel as NaCl with low pH (low absolute zeta potential) produces slow EOF. These behaviors are independent of the applied electric field. However, complete displacement tends to be achieved by lowering the NaCl concentration, i.e., increasing its zeta potential. In contrast, the NaHCO₃ concentration has little impact on the displacement process. These findings enhance the understanding of EOF involving solutions with dissimilar pH and ion species.

Keywords: current monitoring method; electrokinetic phenomena; electroosmotic flow hysteresis; micro-/nanofluidics; numerical simulation.

Figure 1

(a) Schematic for current-time monitoring setup, with (b) actual experimental setup.

Figure 2

Current-time response for 0.475 mM NaHCO₃ (95% concentration of the measurement solution) displacing 0.5 mM NaHCO₃ (measurement solution).

Figure 3

Domain for numerical simulation (not drawn to scale).

Figure 4

Electroosmotic displacement flow of the 0.5 mM NaCl–NaHCO₃ solution pair at the applied electric field of 125 V·cm⁻¹, whereby numerical simulation and experimental results are compared. Normalized currents and times are calculated with I* = (I − I⁰_NaHCO3)/(I⁰_NaCl − I⁰_NaHCO3) and T* = T/T^SS_{NaCl → NaHCO3} respectively, where initial currents of solutions are represented by I⁰ with NaHCO₃ and NaCl subscripts respectively, and time to reach steady-state current for NaCl → NaHCO₃ (arrow indicates EOF direction) is represented by T^SS_{NaCl → NaHCO3}.

Figure 5

Numerically simulated ion concentrations along microchannel for 0.5 mM NaCl → 0.5 mM NaHCO₃ (the arrow indicates EOF direction) in (a) Phase 1 T* = 0, (b) Phase 1 T* = 0.136, (c) Phase 1 T* = 0.227 and (d) Phase 2 T* = 1. Normalized time T* = T/T^SS_{NaCl → NaHCO3}, where T^SS_{NaCl → NaHCO3} is time to reach steady-state current for NaCl → NaHCO₃. Normalized X* = X/L, where X is axial coordinate and L microchannel length.

Figure 6

Numerically simulated ion concentrations along the microchannel when 0.5 mM NaHCO₃ → 0.5 mM NaCl (arrow indicates EOF direction) in (a) Phase 1 T* = 0, (b) Phase 1 T* = 0.227, (c) Phase 1 T* = 0.455 and (d) Phase 2 T* = 1. Normalized time T* = T/T^SS_{NaCl → NaHCO3}, where T^SS_{NaCl → NaHCO3} is time to reach steady-state current for NaCl → NaHCO₃. Normalized X* = X/L, where X is axial coordinate and L microchannel length.

Figure 7

Numerically simulated normalized velocity V* and pressure P along normalized radial r* for normalized X* = 0.25, 0.5 and 0.75 of 0.5 mM NaCl → 0.5 mM NaHCO₃ (arrow indicates EOF direction) in (a) Phase 1 T* = 0, (b) Phase 1 T* = 0.136, (c) Phase 1 T* = 0.227 and (d) Phase 2 T* = 1. Normalized V* = (V − V_Avg)/V_Avg. Average velocity V_Avg = Q/A_L = Q/(πR²), where Q is flow rate obtained by integrating radial velocity over microchannel cross sectional area A_L, and R is channel radius. Normalized r* = r/R. Normalized time T* = T/T^SS_{NaCl → NaHCO3}, where T^SS_{NaCl → NaHCO3} is time to reach steady-state current for NaCl → NaHCO₃. Normalized X*= X/L, where X is axial coordinate and L channel length.

Figure 8

Numerically simulated normalized velocity V* and pressure P along normalized radial r* for normalized X* = 0.25, 0.5 and 0.75 of 0.5 mM NaHCO₃ → 0.5 mM NaCl (arrow indicates EOF direction) in (a) Phase 1 T* = 0, (b) Phase 1 T* = 0.227, (c) Phase 1 T* = 0.455 and (d) Phase 2 T* = 1. Normalized V* = (V − V_Avg)/V_Avg. Average velocity V_Avg = Q/A_L = Q/(πR²), where Q is flow rate obtained by integrating radial velocity over microchannel cross sectional area A_L, and R is channel radius. Normalized r* = r/R. Normalized time T* = T/T^SS_{NaCl → NaHCO3}, where T^SS_{NaCl → NaHCO3} is time to reach steady-state current for NaCl → NaHCO₃. Normalized X*= X/L, where X is axial coordinate and L channel length.

Figure 9

Electroosmotic displacement flow of the 1mM NaCl–NaHCO₃ solution pair at applied electric field of (a) 125 V·cm⁻¹ and (b) 187.5 V·cm⁻¹, whereby numerical simulation and experimental results are compared. Normalized currents and times are calculated with I* = (I − I⁰_NaHCO3)/(I⁰_NaCl − I⁰_NaHCO3) and T* = T/T^SS_{NaCl → NaHCO3} respectively, where initial currents of solutions are represented by I⁰ with NaHCO₃ and NaCl subscripts respectively, and the time to reach steady-state current for NaCl → NaHCO₃ (arrow indicates EOF direction) is represented by T^SS_{NaCl → NaHCO3}.

Figure 10

Experimental observations of varying NaHCO₃ concentration, i.e., 0.5 mM, 3 mM and 5 mM, with the NaCl concentration fixed at 0.5 mM and an electric field of 125 V·cm⁻¹. (a) NaCl → NaHCO₃ (arrow indicates EOF direction), and (b) NaHCO₃ → NaCl.

Figure 11

Experimental observations of varying NaCl concentration, i.e., 0.1 mM, 0.5 mM and 1 mM, with the NaHCO₃ concentration fixed at 3 mM and an electric field of 125 V·cm⁻¹. (a) NaCl → NaHCO₃ (arrow indicates EOF direction), and (b) NaHCO₃ → NaCl.