ISTP-16, 2005, PRAGUE 16TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA

1

Abstract This study demonstrated the mechanical-electrokinetic battery by using the commercially available nano-porous membrane. The energy conversion mechanism of the battery was experimentally examined. The experiments show that the battery performance can be efficiently improved by the unipolar characteristic inside the nano sized channel. The best efficiency (0.77 %) is achieved via a 200 nm pore sized alumina membrane with a 2.1 cm diameter and 60 µm thickness. The maximum output energy is 18 µW for a 20 nm pore sized alumina membrane.

1 Introduction The concept of Electrokinetic battery

incorporated with mechanical energy was recently developed , although the essential mechanism has been studied for nearly 40 years1,2,3. Yang et al.4 has developed an electrokinetic battery consisting of an array of microchannels that convert the hydrostatic pressure of a liquid into electrical energy and the performance is improved by increasing the surface charge density based on a mobile-ion-drain method5. The present study aims for performance enhancement through the application of unipolarity of nano channel.

2 Theory For a channel with surface charge on its

surface, the counterions in the electrolyte will accumulate near the surface; the like ions will be electrostatically repelled. The final surface charge is balanced by an equal but opposite region of counterions, the region was known as the diffusion double layer6,7. The characteristic

thickness of the diffusion double layer is the Debye length 1/κ, which is proportional to n-1/2, where n is the electrolyte concentration. The theoretical studies of the pressure driven flow inside this fine surface charged channel can be found in 8,9,10,11,12. The equation of motion for steady flow through a circular tube is9

( ) [ ]ErPraru )()( ψζπµε

µ−−−=

441 22 (1)

where P = pressure gradient = -dp/dx. The first term in Eq. (1) denotes the velocity contributed by pressure, and the second term denotes the electroosmotic flow.

The Current-Density Profile is described by9

[ ] [ ] )()()()()()( rurnrnErnrnmerix −+−+ −++= 0 (2)

The total current may be obtained by integrating of Eq. (2)

∫=+=a

xconvCond drrriIII0

2 )(π (3)

where

∫=a

cond drrrEI0

2 )(coshψπλ (4)

which is the purely conductive contribution to the total current, and is also the leakage current for the battery, and the convective current is given by

NANO FLUIDIC BATTERY Ming-Chang Lu*, Srinath Satyanarayana** Rohit Karnik** Arun Majumdar**

*Industrial Technology Research Institute, Hsinchu, Taiwan

**University of California at Berkeley, California, USA

*Corresponding author: email: MingChangLu@itri.org.tw, phone: 886-3-5915376, fax: 886-3-5820250

Keywords: Mechanical-electrokinetic, unipolar, nano, battery, membrane

Ming-Chang Lu, Srinath Satyanarayana, Rohit Karnik, Arun Majumdar

2

∫=a

conv drrurrI0

2 )()(ρπ (5)

Iconv represents the convective contribution to the total current as well as the streaming current for the battery. The relationship between Electro-osmosis and Streaming Potential can be expressed as9

FIV

PE

PI

s

=

−=

== πλµεζ

400 (6)

where

∫

+∫

−==

dRdR

RdRdRRR

GaaFF

aas 2

00

2 121

κκ ψβψ

κβψκ

)()(cosh

)()(),,(

*

*

(7) where the dimensionless forms of rR κ= ,

21

20

=

kTe

επ

κ 0n8 , kTeas

ζκψψ 0== )( , 2

02

2222

16 eTkµλπ

κεβ =*

are introduced; λ = 2me0n0 is the conductivity of the neutral electrolyte, m is the mobility of cations and anions, here, we assume the same mobility for cations and anions. The energy output can be expressed by

ssout IEP41

= (8)

where Es is the streaming potential, Is is the streaming current; and the energy input for the battery is the pressure difference ∆p times the flow rate V,

VPPin ⋅∆= (9) The energy transfer efficiency is the maximum output energy divided by the input energy,

VP

IEE

ss

eff ⋅∆= 4

1

(10)

3 Experimental Setup

To demonstrate the mechanical electrokinetic battery, we have constructed a power generation device, as illustrated in Fig. 1. The constant flow rate syringe pump (SP200i, WPI Inc.) was used in the battery as a power generation device. The syringe then connected with a flow through pressure sensor (26PCFFU5G, Honeywell) and a filter holder. Inside the filter holder is the alumina membrane obtained from the Whatman Inc., with silver mesh on both sides of the membrane. The diameter of the alumina membrane is 21 mm and the thickness of the membrane is 60 µm. Two different pore sizes, 20 or 200 nm, membranes were studied in our experiment. The pore density of 20 nm pore diameter membrane is 1011/cm2 and it for the 200 nm pore diameter membrane is 109/cm2. The up-view and cross-sectional view of the SEM pictures for the 20 nm membrane was shown in the Fig. 2. The SEM picture for 200 nm membrane is shown in Fig. 3. The silver mesh, as shown in Fig. 4, was made by evaporating 700 nm thick layer silver on the stainless steel mesh (TWP Inc.) with wire diameter 20 µm and spacing 25 µm. The power supply (6286A DC Power Supply, HP) was used as the power source of the pressure sensor. The pressure sensor converted its piezoelectric signal to the voltage signal which indicated its output signal in the multi-meter (KEITHLEY 2000 Multimeter). The other multi-meter (Agilent 34401A Digit Multimeter) records the voltage and current signal from the battery by connecting two Ag-AgCl wires on the silver mesh located on the both sides of the membrane. The testing liquid used in the experiments are the DI water and the KCl aqueous with different concentrations (10-7 M to 0.1 M).

In addition to the alumina membrane, the silica layer13 and amino silane layer14 are also coated on the surface of the alumina membrane. The coated membrane would change its positive surface charge to negative surface charge on the surface and resulted in reversed polarity of the battery and the membrane coating the amino silane on its surface may increase the positive surface charge density on its surface.

NANO FLUIDIC BATTERY

3

4 Experimental Results

4.1 Streaming Potential: The streaming potential of the 20, 200 nm

alumina membranes and 20 nm membranes with amino silane coating under 2 ml/min flow rate for different KCl electrolyte concentrations are shown in Fig. 5. These three membranes all show the same trend that streaming potential decreases as KCl electrolyte concentration is increased, but when the concentration is lowered to the critical concentration, it reaches the saturated value.

These phenomena can be attributed to three effects. Firstly, as the concentration is increased, the Debye length and the excess counterions inside the diffusion double layer are decreased. Secondly, by increasing the electrolyte concentration will result in higher electrolyte conduction, thereby also increasing the leakage current (conduction current). Thirdly, for channel with same size and surface charge density, the higher concentration results in lower zeta potential and hence the lower streaming potential and current.

In addition, if the bulk electrolyte concentration is lower than the critical concentration, the counterion concentration will be restricted by the surface charge density that balance the surface charge accordingly subject to satisfy the system neutrality requirement (ncounterion=2σ/r), thus the counterion concentration becomes constant and be determined by the surface charge density only. This phenomenon is called the unipolar solution. It implies that the Debye length is larger than the channel width, resulting in the unipolar flow. Therefore, the transport phenomenon is dominated by the counterions as the bulk concentration is lower than the critical concentration. The unipolar phenomenon has already been studied by Stein et al.15, they observed that the conductance approaches saturated as the bulk concentration is lower than the critical unipolar concentration. Because the Debye length is of the order of 1~100 nm, we can get the unipolar solution by nano-scale channel for improving performance efficiently.

Since the pressure difference for 200 nm membrane is lower than that for 20 nm membrance under the same flow rate, the streaming potential of 200 nm membrane with porosity (109/cm2) is lower than that of the 20 nm membrane (porosity 1011/cm2) (Fig. 5). The membrane coated with amino silane has lower streaming potential when the channel becomes unipolar. This phenomenon can be explained by

the Smoluchowski7 result,)(

r

pVsλλη

ες2

0 +⋅

⋅∆⋅=∆ ,

which indicated that when channel is unipolar, the surface conductivity λs is a dominating term and therefore, increasing the surface charge density (for example, by coating amino silane on the membrane) will increase the surface conductivity, and thus results in a lower streaming potential.

4.2 Streaming Current: The streaming current for these three

membranes under 2 mL/min flow rate are plotted in Fig. 6. The streaming current approaches saturation as the bulk concentration is lower than the critical concentration. The reasons for this situation are the same as those in the previous section. The amino silane membrane with higher streaming current can be explained by the increase of surface charge density. The decrease of streaming current for 200 nm membrane is due to the reduction of pressure difference. The amino silane membrane reaches its maximum streaming current at 102.67 µA for DI water. The maximum streaming current is 70.25 µA with 10-6 M KCl electrolyte for 20 nm alumina membrane and 33.75 µA with 10-6 M KCl electrolyte for the 200 nm membrane.

4.3 Streaming Potential and Current for the Membrane with Silica coating:

The streaming potential and streaming current for alumina membrane with silica layer coated is shown in Fig. 7. By using the surface process mentioned in Kovtyukhova et al.13, we successfully transfer the polarity of the membrane. The streaming potential and current show the reversed polarity of the original

Ming-Chang Lu, Srinath Satyanarayana, Rohit Karnik, Arun Majumdar

4

alumina membrane. In additional, the trend of both the streaming potential and current versus concentration are the same as the previous results. The streaming potential and current approaches saturated as the potassium charlotte electrolyte concentration is lower than the 10-5 M. Stream potential and current reach the maximum at -0.163 V and -37.33 µA for the silica membrane with 10-6 M KCl electrolyte.

4.4 Energy Conversion Efficiency and Output Energy:

Figure 8 shows the lower electrolyte concentration with higher efficiency for all the membranes due to the unipolar characteristics. Moreover, efficiency reaches maximum of 0.77 % for the 200 nm pore sized alumina membrane among different membranes. The high efficiency is caused by the unipolar property of the electrolyte, the lower pressure drop and less overlapped diffusion double layer for the 200 nm membrane. However, the lower efficiency by the amino silane membrane is because, although, the increased surface charge promotes streaming current, it also results in lower streaming potential. Therefore, the present study suggests that increasing surface charge density is not absolutely beneficial for efficiency concerns. The energy output is higher for the membranes at lower electrolyte concentration (Fig. 9). The output reaches maximum energy at 18 µW for 10-6 M KCl electrolyte with 20 nm alumina membrane.

5. Conclusion In this study, we have examined the

mechanical electrokinetic battery by using the nano porous membrane. Due to the unipolar characteristic inside the nano channel, the performance of the battery is improved up to the efficiency of 0.77 % by using the 200 nm alumina membrane. But the maximum output energy is 18 µW by using the 20 nm alumina membrane.

Acknowledgments

The authors would like to express the gratitude to the Department of Industrial Technology as well as the Energy Bureau from Minstry of Econmomic affairs, Taiwan for their financial support to our current study.

References [1] J.F. Osterle, Electrokinetic Energy Conversion,

Journal of Applied Mechanics, pp.161–164, 1964. [2] D. Burgreen and F.R. Nakache, Efficiency of

Pumping and Power Generation in Ultrafine Electrokinetic Systems, Journal of Applied Mechanics, pp. 675-670, 1965.

[3] F.A. Morrison, JR. and J. F. Osterle, Electrokinetic Energy Conversion in Ultrafine Capillaries, The Journal of Chemical Physics, Vol. 43, No. 6, pp. 2111-2115, 1965.

[4] Yang J. el al., Electrokinetic microchannel battery by means of electrokinetic and microfluidic phenomena, Journal of Micromechanical and Microengineering, Vol. 13, pp. 963-970, 2003.

[5] Yang J. et al., Electrokinetic power generation via Streaming Potentials in Microchannels: A Mobile-Ion-Drain Method to Increase Streaming Potentials, The 2004 International Conference on MEMS, NANO and Smart Systems, Banff, Alberta-Canada, pp. 675-679, 2004.

[6] J. Israelachvili, Intermolecular and surface forces, 2nd ed, (Academic Press, London, 2003).

[7] P.C. Hiemenz and R. Rajagopalan, Principles of Colloid and Surface Chemistry, 3rd ed, (Marcel Dekker, Inc. New York, 1997)

[8] C.L. Rice and R. Whitehead, Electrokinetic Flow in a Narrow Cylindrical Capillary, The Journal of Physical Chemistry, Vol. 69, No. 11, pp. 4017-4023, 1965.

[9] S. Levine, J.R. Marriott, G. Neale and N. Epstein, Theory of Electrokinetic Flow in Fine Cylindrical Capillaries of High Zeta-Potentials, Journal of Colloid and Interface Science, Vol. 52, No. 1, pp. 136-149, 1975.

[10] S. Levine, J.R. Marriott, and K. Robinson, The theory of electrokinetic flow in a narrow parallel-plate channel, Journal of Chemical Society-Faraday Transcation, Vol. 2, No. 71, pp. 1-11, 1975.

[11] X.Y. Chen, K.C. Toh, J.C. Chai and C. Yang, Developing Pressure-driven Liquid Flow in Microchannels under the Electrokinetic Effect, International Journal of Engineering Science, Vol. 42, pp. 609-622, 2004.

[12] H. Daiguji, P. Yang and A. Majumdar, Ion Transport in Nanofluidic Channel, Nano Letters, Vol. 4, No. 1, pp. 137-142, 2004.

NANO FLUIDIC BATTERY

5

[13] N.I. Kovtyukhova, T.E. Mallouk and T.S. Mayer, Templated Surface Sol-Gel Synthesis of SiO2 Nanotubes and SiO2-Insulated Metal Nanowires, Advanced Materials, Vol. 15, No. 10, pp. 780-785, 2003.

[14] D.G. Kurth and T. Bein, Thin Films of (3-Aminopropyl)triethoxysilane on Aluminum Oxide and Gold Substrates, Langmuir, Vol. 11, pp. 3061-3067, 1995.

[15] D. Stein, M. Krluithof and C. Dekker, Surface-Charge-Governed Ion Transport in Nanofluidic Channels, Physical Review Letters, Vol. 93, No. 3, pp. 035901-1-4, 2004.

Fig. 1. The experimental setup of the nano fluidic battery

(a)

(b)

Fig. 2. The SEM pictures of the 20 nm alumina membrane (a) up view, (b) crossional view

Fig. 3. The SEM pictures of the 200 nm alumina membrane

Fig. 4 Silver mesh (wire diameter 20 µm, spacing 25 µm)

1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1

0.000.020.040.060.080.100.120.140.160.180.200.220.240.260.280.30

Stre

amin

g P

oten

tial (

V)

Concentration (M)

Fig. 5. The streaming potential versus the concentration, (∆) 20 nm pore size alumina membrane, (×) 20 nm pore size alumina membrane with amino silane coating, (O) 200 nm pore size alumina membrane

Ming-Chang Lu, Srinath Satyanarayana, Rohit Karnik, Arun Majumdar

6

1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.105

101520253035404550556065707580

Stre

amin

g C

urre

nt (µ

A)

Concentration (M)

Fig. 6. The streaming current versus the concentration, (∆) 20 nm pore size alumina membrane, (×) 20 nm pore size alumina membrane with amino silane coating, (O) 200 nm pore size alumina membrane

1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1-0.18

-0.16

-0.14

-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

Stre

amin

g P

oten

tial (

V)

Concentratin (M)

-40

-30

-20

-10

0

Stre

amin

g C

urre

nt (µ

A)

Fig. 7. The (O) streaming potential and the ( ) streaming current for alumina membrane with silica layer

1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Effi

cien

cy (%

)Concentration (M)

Fig. 8. The energy conversion efficiency for the battery with different membranes, (∆) 20 nm pore size alumina membrane, (×) 20 nm pore size alumina membrane with amino silane coating, (O) 200 nm pore size alumina membrane, (◊) 20 nm pore size alumina membrane with silica coating

1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1

0

5

10

15

20

Out

put E

nerg

y (W

)

Concentration (M)

Fig. 9. The output energy of the battery with different membranes, (∆) 20 nm pore size alumina membrane, (×) 20 nm pore size alumina membrane with amino silane coating, (O) 200 nm pore size alumina membrane, (◊) 20 nm pore size alumina membrane with silica coating