Net fluid flow and non-Newtonian effect in induced-charge electro-osmosis of polyelectrolyte solutions

This paper reports an interesting net fluid flow in the induced-charge electro-osmosis (ICEO) of poly(sodium 4-styrenesulfonate) (NaPSS) solutions measured through microparticle image velocimetry ($\mu \mathrm{PIV}$). The net fluid flow is attributed to the significantly unequal cations and poly-anions of NaPSS. Owing to the phase delay effect of ions, different flow patterns appear with the alternating electric field. The inflow velocity and outflow velocity are found to be unequal and their relative magnitude shows a dependence on the electric field strength. The ICEO velocity is positively correlated with the NaPSS concentration. As NaPSS introduces the non-Newtonian effect, the well-known quadratic relationship between ICEO velocity and electric field strength in Newtonian fluids breaks. The ICEO velocity varies differently with the electric field strength as the NaPSS concentration changes. These new findings can contribute to the understanding of ICEO of complex fluids, e.g., biofluids.

Figure 1

Experimental setup. The PDMS-glass microchannel was fabricated by soft lithography with the dimensions 0.7 mm (height) $\times$ 10 mm (width) $\times$ 40 mm (length). A gold-coated stainless steel cylinder of radius $R=175\mu \mathrm{m}$ was positioned in the middle of the microchannel. The ICEO was generated by the AC electric fields applied through the two platinum (Pt) electrodes, captured using a high-speed CCD camera (Vision Research V611) connected to an inverted optical microscope (Leica DM ILM), and processed by the DaVis 8.0 (LaVision) software.

Figure 2

(a) ICEO flow fields at different times. (b)–(e) Variations of the difference of velocity angle ${\theta }_d$ and velocity magnitude $u$ with time. ICEO flow fields of the (f) NaCl and (g) NaPSS solutions at $t+1$ and $t+5$ s (indicated by streamlines). The difference of velocity angle is defined as ${\theta }_d=arctan\frac{u_y}{u_x}-{\theta }_{\mathrm{theor}}$, where $arctan\frac{u_y}{u_x}$ and ${\theta }_{\mathrm{theor}}$ are the experimental and theoretical [Eq. (1)] velocity angles, respectively, which indicate the velocity direction. The squares and circles represent the inflow ($\theta =\pm \pi$) and outflow ($\theta =\pm \pi /2$), respectively. The velocities in (b)–(e) are collected from two fixed points in the inflow ($\theta =\pm \pi$) and outflow ($\theta =\pm \pi /2$) directions. To not lose the generality, the specific positions of the two points are randomly chosen. The concentrations of NaCl and NaPSS solutions are $0.5\times {10}^{-3}$ mol/L and $2.5\times {10}^{-3}$ monomol/L, respectively. The electric field strength and frequency are $E=450{\mathrm{V}}_{\mathrm{p}-\mathrm{p}}$/cm and $f=2.0$ kHz, respectively. Please also see Video S1 in the Supplemental Material [33].

Figure 3

Schematic illustration of the different flow patterns in the ICEO of NaPSS solutions.

Figure 4

(a) Variation of the absolute value of velocity angle difference $|{\theta }_d|$ with the velocity magnitude $u$. (b) Variation of $u$ along the $r$ direction. The squares and circles represent the inflow ($\theta =\pm \pi$) and outflow ($\theta =\pm \pi /2$), respectively. The curves in (b) are scaled from Eq. (1). The velocities in (a) are randomly picked so as not to lose the generality. The concentrations of NaCl and NaPSS solutions are $0.5\times {10}^{-3}$ mol/L and $2.5\times {10}^{-3}$ monomol/L, respectively. The electric field strength and frequency are $E=450{\mathrm{V}}_{\mathrm{p}-\mathrm{p}}$/cm and $f=2.0$ kHz, respectively.

Figure 5

(a) and (c) Variations of the maximum inflow velocity $u_{\max ,\mathrm{in}}$ with the electric field strength $E$ at different electric field frequencies $f$ and different NaPSS concentrations $c$, respectively. (b) and (d) Variations of the inflow-outflow velocity ratio $u_{\mathrm{i},\mathrm{o}}$ with $E$ at different $f$ and $c$, respectively, where $u_{\mathrm{i},\mathrm{o}}=u_{\max ,\mathrm{in}}/u_{\max ,\mathrm{out}}$. (e) and (f) Variations of the maximum velocity $u_{\max }$ with the second and third power of electric field strength, respectively, of the $c=1\times {10}^{-3}$ mol/L KCl solutions containing 1 vol% PDADMAC, 0.5 vol% NaPVSA, and 1 vol% PEG, respectively, at the electric field frequency $f=500$ Hz [24]. Inset of (a): Variation of $u_{\max ,\mathrm{in}}$ with $f$ at $E=625{\mathrm{V}}_{\mathrm{p}-\mathrm{p}}$/cm. The solid curve in (a) is fitted at $f=1.5$ kHz. The NaPSS concentration is $c=2\times {10}^{-3}$ monomol/L in (a) and (b); the electric field frequency is $f=2.0$ kHz in (c) and (d). The symbol ${\chi }^2$ indicates the fitting goodness.

Figure 6

(a) Variation of the maximum velocity $u_{\max }$ with the NaPSS concentration $c$ at different electric field strengths $E$, and the NaCl concentration $c$ at $E=400{\mathrm{V}}_{\mathrm{p}-\mathrm{p}}$/cm [16]. (b) Variation of $u_{\max }$ with the volumetric concentration of different polymers $c_v$ in the $c=1\times {10}^{-3}$ mol/L KCl solutions [24]. The electric field frequency $f=2.0$ and 1.5 kHz respectively in (a) and (b).