Giant streaming currents measured in a gold sputtered glass microchannel array

Chemical Physics Letters 646 (2016) 81–86

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Giant streaming currents measured in a gold sputtered glass microchannel array Abraham Mansouri a,∗ , Larry W. Kostiuk b a b

Department of Mechanical Engineering, American University in Dubai, Dubai 28282, United Arab Emirates Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T2G 2G8, Canada

a r t i c l e

i n f o

Article history: Received 25 October 2015 In final form 7 January 2016 Available online 14 January 2016

a b s t r a c t Pressure-driven-flow of a dilute aqueous solution in a microchannel with charged walls generates streaming currents (ionic current) and streaming potentials across the microchannel. While generation of streaming currents can be performed in network of parallel circular microchannels or unstructured porous media, accurate measurements of such currents remain a challenge. In this study a gigantic amount of streaming current was successfully generated and measured using a glass microchannel array with special gold sputtered coatings on both its ends. Streaming current as high as 0.7 mA was obtained with moderate pressure drop (124 kPa) across the glass microchannel array that consists of approximately 11 250 000 parallel microchannels with radii of 2.5 ␮m. Higher streaming currents are also possible to generate (scaled to 142 ␮A/cm2 of frontal area at a flow rate of 12 cm3 /s) with potential applications in surface charge characterizations and electrokinetic power generation. In addition, apparent  potential of glass microchannel array surface was estimated with the aid of streaming current data and Levine–Olivare theories and an apparent  potential of −65 mV (0 M KCl, a = 8) is reported. © 2016 Elsevier B.V. All rights reserved.

1. Introduction The flow of an electrolyte solution in microchannels, membranes, and porous media is strongly affected by the electrical properties at the channel wall-fluid interface. Streaming current and streaming potential phenomena are consequences of such flows. Streaming current and streaming potential phenomena in well-defined single microchannels have been studied comprehensively both experimentally and theoretically [1–7]. Streaming current represents the convective flux of free charge integrated over the whole cross section of the microchannel. It has been shown that in streaming potential, this ionic convective flux causes accumulation and depletion of charges at microchannel entrance and exit [6]. This imbalance of charges at entrance and exit creates a trans-capillary potential, and consequently a conduction current develops in the direction opposite to the streaming current through any available electrical path (i.e. bulk or surface conductance). Eventually when the ionic convective flux cancels out the conduction current, transcapillary potential across the microchannel is called streaming potential. It should be mentioned that while ionic convective flux happens in hydrodynamic time scale

∗ Corresponding author. E-mail address: [email protected] (A. Mansouri). http://dx.doi.org/10.1016/j.cplett.2016.01.012 0009-2614/© 2016 Elsevier B.V. All rights reserved.

(milliseconds), steady state conduction current and streaming potential occurs in diffusion time scale (seconds). In reality, streaming potential can be relatively straightforward to measure, while streaming currents values can be quite difficult and demanding to capture. Streaming current and streaming potential techniques have also been applied to characterize homogeneous and heterogeneous surfaces [7], bio-polymers [1], and self-assembled monolayers [8] to determine their interfacial properties. Characterization of complex porous media, with unstructured pore geometries, such as membranes and packed beds of granular materials are also routinely conducted employing these techniques [9]. There is, however, a fundamental difference between measurements of streaming current across a single microchannel as opposed to porous media, the latter often represented as a bundle of parallel circular microchannels for mathematical modeling [10]. In either case, the measurement of the electric potential or current is performed by conducting probes or electrodes placed in two bulk electrolyte reservoirs located on both sides of the single microchannel or the porous medium. In this context, two critical problems arise when one attempts to scale up the results obtained for single microchannels to the case of an unstructured porous medium. First, the porous medium will have a significantly lower electrical resistance compared to a single microchannel, making it hard to create situations where the conduction current is negligible. Second,

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Figure 2. Schematic of the experimental apparatus. 11 250 000 of parallel microchannels formed a glass microchannel array akin to a porous medium. The microchannel array thickness was 2 mm and the length of the reservoirs was 36 mm.

Figure 1. A SEM picture of a glass microchannel array sputtered with gold. It shows an array of single, straight and circular microchannels. The current sample has a pore size of 2.5 ␮m and thickness and effective diameter of 2 mm and 25 mm, respectively with 45% porosity. The inset shows longitudinal cross section of the microchannels. Metal penetration depth inside the microchannel is shown. Bright area indicates the gold deposited area. In the current sample the penetration depth is 0.3–0.7 times of channel diameters on both sides. Penetration depth is negligible compare to the length of array.

the total volumetric fluid flow through a porous medium will be significantly larger than the flow through a single microchannel, thus having a greater probability of disturbing the ‘bulk’ solution nature of the reservoirs. This second issue is particularly important if the reservoirs have insufficient volumes of fluid. A combined effect of these two factors is that measurement of streaming current across a porous medium becomes extremely sensitive to external influences, and the accuracy of such measurements may be affected, for instance, by the nature and surface area of the electrodes, their placement in the reservoirs, the volume of the reservoirs, and the electrical resistance of the external circuit [11]. However, conventional measurements of such processes do not confer much attention to these factors, instead focusing on the unknown pore structures of the porous media to analyze the results. The main objective of the current study is to employ a structured porous medium with a pore radius as small as 2.5 ␮m and with special gold sputtered coatings on both its ends to generate and to measure much larger streaming currents than previously reported values in literature. A complementary objective is to estimate an apparent  potential of glass microchannel surface and test it against the robust theories in the literature. 2. Experimental apparatus The focus of this work involves the flow through a glass microchannel array (GMA) was 2 mm thick and of 25 mm diameter, made of untreated lead silicate glass (45% SiO2 , 55% PbO). SEM micrographs of the porous substrate are shown in Figure 1. The two faces of the disc sputtered with 100 nm thick nichrome-gold coatings, which acted as conducting surfaces. The reason behind choosing gold as acting electrode is that there were technical limitations associated with reliably of coating the GMA faces with other metals, according to the manufacturer of these materials (Photonics, USA). The sputtering process employed to deposit the metal coatings on the glass did not block the microchannel entrance

and exits. However, there was a penetration of the metal to an extent of approximately 2.5 ␮m from both ends into the microchannel. Prior to the experiments, it was ensured that the sputtered layer of gold was continuous through electrical resistance measurements. Furthermore, it was ensured that no electrical connectivity existed between the gold coatings on the two opposing faces of the microchannel array. The purpose of these gold sputtered electrodes was to provide a direct measure of the electrical conditions at the microchannel array entrance and exit. A custom fabricated experimental apparatus, as described in [12] and shown in Figure 2, was employed to characterize the glass microchannel array. In addition, the two reservoirs were fitted with two circular (25 mm diameter) disc shaped Pt black mesh electrodes, which could be placed at specified distances from the two faces of the GMA. The gold conducting surfaces and the Pt disk electrode pairs were individually connected to an ammeter and a voltmeter devices (Keithley), respectively. This four-electrode configuration was employed to show the extent of polarization and the corresponding polarization potentials that exist when the gold electrodes were used to try to measure the streaming currents. A pressure transducers connected across the GMA also recorded the pressure drop between the two reservoirs. All measurement systems were automated using a LabVIEW based data acquisition interface to a PC. The electrolyte solutions were prepared employing fresh DIUF water of 18.2 M cm specific resistivity (MilliQ 5, Millipore, MA). Experiments were performed with DIUF water containing no added electrolyte (henceforth referred to as 0 M KCl, conductivity of 50 ␮S/m) and 10 mM KCl electrolyte solutions. Conductivity of the electrolyte solutions was measured using a conductivity meter (Accumet AR50, Fisher Scientific) prior to the experiments. In this work, all transient experiments were conducted in an alternating flow direction mode using two 3-way valves and a diaphragm pump (Shurflo). During all the experiments only one sample of GMA was used and data acquisition were performed at 10 Hz frequency. We assumed a conservative value of 10−6 M KCl (yielding a of 8 for microchannel radius of 2.5 ␮m) for pure water concentration in our experiments due to exposure of pure water to the air, impurities and possible dissolutions of the glass made apparatus into pure water. This is also evidenced by measurement of conductivity of pure water running in the system (conductivity of 50 ␮S/m), which is an order of magnitude higher than the value claimed by manufacturer of pure water machine (conductivity of 5 ␮S/m). 3. Streaming current theory When electrical double layer thickness (Debye length, −1 ) becomes comparable with the microchannel dimensions, solid–liquid interactions are no longer negligible. Streaming

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83

Figure 3. Qualitative comparison of velocity, free charge density, streaming current and conduction current profiles in a mid-section of a circular microchannel with a = 1, 5 and 25 in a steady state flow condition.

current represents an ionic convective flux; the fluid flow generates a tangential force on the hydrodynamically mobile part of electrical double layer and transports free charges along the flow direction. From a theoretical viewpoint, for a cylindrical microchannel, the total current; Itotal caused by pressure driven flow and induced transcapillary potential can be estimated by summation of streaming (Istr ) and conduction (Icond ) currents (diffusion current has shown to be negligible, [13]). The streaming current is calculated by integration of the product of velocity and free charge density



Istr = 2

a

(r) · u(r) · r · dr

(1)

0

Istr is the streaming current, a is the radius of the pore, (r) is the net  charge density ( = vi ni e), where  is the valence of the ith ionic species, e is the elementary charge and ni is the ionic number concentration of the ith species, and u(r) is the hydrodynamic velocity profile. Eq. (1) shows that the magnitude of charge separation and streaming current can be influenced by altering the velocity profile and double layer thickness. Conduction currents through the fluid are governed by Icond = A ·  · Ez

(2)

where A is the cross section of microchannel and  is the bulk conductance (S/m) and Ez is the electrical field (V/m). At steady state, conduction and streaming currents are equal (a condition of the Smoluchoswki equation). Qualitative comparison of velocity, free charge density, streaming current and conduction current profiles for a microchannel with a = 1 (double layer overlap), 5 and 25 in a steady state flow condition is shown in Figure 3. To obtain these qualitative results Poisson–Nernst–Planck (PNP) system of equations along with Navier–Stokes equations were solved numerically for a finite length circular microchannel [13]. The first row of Figure 3 shows the near parabolic velocity profiles induced by pressure driven flow in the microchannels; zero velocity at the wall (no-slip boundary

condition) and maximum velocity at the center. Depending on the a of the system, the free charge density and the corresponding streaming and conduction current can be limited to the motion of ions next to the microchannel wall or can disturb the flow field significantly. As expected, parabolic velocity profiles are not affected by these variations of a yet free charge density and streaming and conduction current profiles are a function of a. At a = 1, the double layers extend to the core of circular microchannel and the streaming current profile becomes relatively similar to the velocity profile. The last row represents the conduction current profiles. Since electrical resistance of the double layer is relatively lower than bulk electrolyte, a larger portion of conduction currents often migrate through stern and diffuse layers next to the microchannel wall. It is recommended to use streaming current method for  potential calculation since it ignores surface conductance effects and avoid significant flow impedance and electroviscous effect [2].  potential calculations for low a systems performed by streaming potential method, requires surface and bulk conductance data (surface conductance is caused by the excess of ions next to the solid surface). There are two well-known theories for  potential calculation from streaming current method in the literature. Rice [14] and Levine et al. [15] have estimated analytically the correction factors that must be applied to Smoluchwski’s equation when one deals with low and high  potentials, respectively. However in the literature  potential calculations usually are performed by Rice et al. method. It has been reported that their method may be valid for  potentials as high as −100 mV [2]. Since the counter-ions in electric double layer cannot conduct in streaming current mode, deviation of Smoluchwski’s equation in streaming current mode is assumed to be much lower compare to streaming potential mode for a wide range of low a and high  potential calculations. Now let’s estimate the correction factors form both approaches; for a microchannel array or a porous media, streaming current for a laminar (in this study Reynolds number is of order of 0.3), fully developed flow can be obtained from Rice et al. method for

A. Mansouri, L.W. Kostiuk / Chemical Physics Letters 646 (2016) 81–86

 potentials less than −25 mV; by inserting the velocity profile (obtained from the Navier–Stokes equation) and free charge density profile (obtained from the Poisson–Boltzmann equation), streaming current in a single microchannel can be estimated as Istr =

-4

6.0×10

-4

4.0×10

-4

SC (A)

84

2.0×10 0.0 -4

-2.0×10

−nεAPz f (a)

(3)

-4

-4.0×10

-4

-6.0×10

0

f (a) = 1 −

2I1 (a) aI0 (a)

(4)

and ε is permittivity, is the viscosity, Pz is pressure gradient, n is the number of microchannels, A is cross-sectional area of streaming channel, f is a correction function, −1 is the Debye length and a is the radius of the pore. In the above expression I0 and I1 are, respectively, the zeroth and first order modified Bessel functions of the first kind. For a  1, f(a) = 1; and for low a having Eq. (4),  potential can be calculated. Since high  potentials surfaces (i.e. silicon, glass, polymers etc.) are abundant in nature, Levine et al. extended the work by Rice et al. and estimated the  potential from following equation: Istr =

−nεAPz (1 − G)

s) =



2 (a)

a

R (R) dR

2

s

(6)

0

It is clear that G depends on both a and s contrary to f (a). In above equation s is the non-dimensional  potential and R = r. Due to complexities of non-linear Poisson–Boltzmann equation the approximate solution of this equation is algebraically complex. Olivare et al. presented an approximation of Levine et al. solution using variational principles [16]. Olivare’ approach is simple and compares favorably with Levine et al. theory up to  potential of −150 mV. In order to calculate the streaming current correction factor, (1 − G), function s is replaced by a trial function of the form = s (I0 (px)/I0 (pa)). For p = 1 this approach reduces to the theory of low potential surfaces by Rice et al. and for p > 1 where



p=



exp 0.0412

2 s



(a)

+ 0.698

2 s

2

(7)

the model becomes more efficient for high  potentials surfaces. In Levine–Olivare approach, Smoluchwski  potential is recovered when (1 − G = 1) and a is large. When a decreases  potential varies accordingly and apparent  potential ( a ) is obtained from Smoluchwski  potential through Eq. (8) 1−G =

500 Time

1000

1 0.5 0 -0.5 -1

0

500 Time (mili-second)

1000

Figure 4. Simultaneous measurement of current and voltage by gold and platinum electrodes, across the GMA. An aqueous 0 M KCl electrolyte solution was pumped through the GMA in alternating flow directions. The peak of streaming currents correspond to zero polarization potential values as depicted by circles on the figure.

(5)

where G which is now function of both non-dimensional surface potential and a in its normalized form is given by: G = G(a,

Polarization Potential ( (V)

where f(a) is:

a 

(8)

In current experiments, the exact number of the microchannels was obtained from manufacturer’s specifications and verified experimentally. For  potential calculations, we have employed following parameters for our calculations: ε = 78.5 × 8.854 × 10−12 C/V/m, n = 11 250 000, P = 124 kPa, a = 8, flow rate = 0.000012 m3 /s, and = 8.9 × 10−4 kg/m s. 4. Results and discussions 4.1. Giant streaming current generation Pressure driven flow of a conducting fluid through a porous medium generates streaming currents. Experimental studies in literature typically report very low-streaming currents (pA to nA)

and difficulties associated with accurate measurements. Due to electrode polarization and reservoir electrical resistance, it has been shown that only the peak current detected by gold electrode may represent the theoretical streaming current values [12,17]. Figure 4 depicts streaming currents and polarization potentials measured in the four-electrode configuration for 0 M KCl. In these experiments, the flow direction was altered every two and half seconds. A maximum current of 700 ␮A was recorded immediately after the flow reversal (the subsequent decay in current was attributed to the moderate polarization of the gold electrodes), whereas the maximum polarization potential (1.06 V, still less than streaming potential) was recorded immediately before changing the flow direction and had appeared to reach a steady state value. In a typical streaming potential measurement since no current passes through the electrodes, streaming potentials are higher than the polarization potentials. When an electrode is immersed in an electrolyte solution,  potential develops at the electrode-electrolyte interface. In order to neutralize the excess charges, the counterions in the medium adsorb to the electrode surface forming a double layer. The electrode impedance caused by the unwanted accumulation of the ions on the electrode surface, attenuates the measured electrical properties. This phenomenon is referred to electrode polarization. In streaming current measurement, a charge transfer reaction (reduction–oxidation) occurs between the electrolyte and the electrodes. In an ideal system, the reduction–oxidation reactions at the electrode will be fast enough that no charge will accumulate at the electrodes. However, if the ionic flux toward the electrodes is not balanced by electric flow through the short circuit wire i.e. due to low electrodes surface area or electrode material, then charges will accumulate causing a nonsteady state where the streaming current will decay with time, as shown in Figure 4. Typically, for a concentrated electrolyte solution capacitive-resistive behavior is observed at polarizable electrodes in steaming current measurements, in case of 0 M KCl, however the double layer thickness becomes maximize to the extent that capacitive behavior (exponential decay of current) is not observed [18]. In the current experiments streaming current decays from 700 ␮A at peak and forms a steady plateau at 640 ␮A. For a highly concentrated electrolyte solution the decay can approach zero current in a very short time [12,17,18]. The generated steaming current can be scaled to 142 ␮A/cm2 of frontal area of glass microchannel array at a flow rate of 12 cm3 /s. To generate streaming currents as high as 1 A one needs a similar disk of glass microchannel array with

A. Mansouri, L.W. Kostiuk / Chemical Physics Letters 646 (2016) 81–86

The glass surface may not become heavily deprotonated if the electrolyte solution becomes acidic (concentration of positive ions are greater than negative ions). At low a, inside a glass microchannel pH shift and charge regulation occur thus the glass surface tends to donate less protons. Such charge regulation at glass surface results in a lower surface charge i.e. lower  potentials at the surface. To test Rice et al. theory, the other correction factor was read from Figure 5 (f = 0.77), which results an apparent  potential of −60 mV. It’s clear that both theories predictions are acceptable however Levine–Olivare approach, as expected, shows a better agreement. It is also evident that Rice et al. theory may be apply for high  potentials surfaces.

1

0.8

1−G

Rice et al

0.6

Levine−Olivares ψ =6 s

Levine−Olivares ψ =4 s

Levine−Olivares ψ =2 s

0.4

85

5. Conclusions

0.2

1

10

κa

100

1,000

Figure 5. Plot of (1 − G) as a function of a for both theories of Rice et al. and Levine–Olivare et al. At s = 1 Levine–Olivare et al. theory reduces to Rice et al. theory.

Table 1 Smoluchowski and apparent  potentials of glass microchannel array with pore radius of 2.5 ␮m. The Smoluchowski -potential comes from a separate large a measurement, while the final column uses experimental data collected here and Eq. (3) to estimate the -potential. Smoluchowski  potential

Apparent  potential Levine–Olivare theory (1 − G = 0.81)

Apparent  potential Rice et al. theory (f = 0.77)

Apparent  potential Experimental data

−78 mV

−63 mV

−60 mV

−65 mV

radius of approximately 48 cm. This is to the best of our knowledge the highest streaming current reported in the literature through a structured porous medium. It is worth noting that the generated streaming current is 270% higher than previously reported data for a GMA sample with pore radius of 5 ␮m at similar flow conditions [12]. This is mainly due to decrease in microchannel radius (lower a) and increase in number of microchannels per unit surface area. 4.2. Estimation of apparent  potential In this section the focus is now shifted to surface charge characterization and estimation of glass microchannel array  potential. Smoluchowski  potential is defined at large a and typically it is obtained from streaming potential measurements. In this study the estimated value is found to be −78 mV ( s ≈ 3) for the electrolyte solution of 10 mM KCl. This value is in close proximity to the reported glass and silica surface  potentials in the literature [19,20]. Using the Smoluchowski  potential and theory of Levine–Olivare, we can estimate an apparent  potential for 0 M KCl electrolyte solution (at a = 8). According to Figure 5, and with a correction factor of (1 − G) = 0.8124, an apparent  potential of −63 mV was estimated. Apparent  potential can also be estimated with the aid of experimental streaming current data and Eq. (3) (Istr = − nε a APz /␮). As seen in Table 1 the comparison shows an excellent agreement. Apparent  potentials are lower than Smoluchowski  potential due to surface charge regulation phenomena [21]. It is known that when a glass substrate comes into contact with a liquid, the surface silanol groups become highly deprotonated and negatively charged. The number of protons that are donated into electrolyte solution depends heavily on the pH level.

Giant streaming currents were successfully generated and measured employing a gold sputtered glass microchannel array and apparent  potential of a glass microchannel array was estimated using streaming current data and Levine–Olivare theory. Some of the key observations are: a. 0.7 mA of streaming current was generated and recorded successfully employing a four electrode cell and an alternating flow approach (allows to identify the moment in time when the transcapillary potential is zero, so the conduction current is negligible) with great potential for electrokientic power generation application and surface charge characterizations. b. Levine–Olivare theory was tested against Rice et al. theory. The correction factor predicted by Levine–Olivare theory multiplied by Smoluchowski  potential yields an apparent  potential which matches the apparent  potential obtained from experimental data to a great level of accuracy. c. During the steaming current experiments capacitive behavior of gold electrodes was not observed. The reason being (a) the double layer thickness becomes very large at gold-electrolyte interface and (b) gold electrodes polarization are negligible in case of 0 M KCl. Acknowledgements Financial support for this work was provided by the Natural Science and Engineering Research of Canada. The authors are grateful to Photonis USA Inc. for custom fabricating the gold-sputtered glass microchannel array. References [1] C. Werner, H. Körber, R. Zimmermann, S. Dukhin, H.J. Jacobasch, J. Colloid Interface Sci. 208 (1) (1998) 329. [2] D. Erickson, D. Li, C. Werner, J. Colloid Interface Sci. 232 (2000) 186. [3] M. Ueda, Y. Takamura, Y. Horiike, Y. Baba, Jpn. J. Appl. Phys. 41 (2002) 1275. [4] F.H. van der Heyden, D. Stein, C. Dekker, Phys. Rev. Lett. 95 (11) (2005) 116104. [5] A. Mansouri, C. Scheuerman, D.Y. Kwok, L.W. Kostiuk, S. Bhattacharjee, J. Colloid Interface Sci. 292 (2005) 567. [6] J.H. Masliyah, S. Bhattacharjee, Electrokinetic and Colloid Transport Phenomena, John Wiley & Sons, 2006. [7] J. Yang, F. Lu, L.W. Kostiuk, D.Y. Kwok, J. Micromech. Microeng. 13 (6) (2003) 963. [8] R. Schweiss, P.B. Welzel, C. Werner, W. Knoll, Langmuir 17 (14) (2001) 4304. [9] M. Sbai, A. Szymczyk, P. Fievet, A. Sorin, A. Vidonne, S. Pellet-Rostaing, M. Lemaire, Langmuir 19 (21) (2003) 8867. [10] P. Fievet, M. Sbai, A. Szymczyk, J. Membr. Sci. 264 (1) (2005) 1. [11] A. Mansouri, S. Bhattacharjee, L.W. Kostiuk, Lab Chip 12 (20) (2012) 4033. [12] A. Mansouri, L.W. Kostiuk, S. Bhattacharjee, J. Phys. Chem. C 112 (2008) 16192. [13] A. Mansouri, L.W. Kostiuk, S. Bhattacharjee, J. Phys. Chem. B 111 (2007) 12834.

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