APPLIED PHYSICS LETTERS 95, 013705 共2009兲
Charge-pumping in a synthetic leaf for harvesting energy from
evaporation-driven flows
Ruba T. Borno,1 Joseph D. Steinmeyer,2 and Michel M. Maharbiz3,a兲
1
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan
48109, USA
2
Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139, USA
3
Department of Electrical Engineering and Computer Science, University of California Berkeley, Berkeley,
California 94720, USA
共Received 24 November 2008; accepted 25 May 2009; published online 7 July 2009兲
Inspired by water transport in plants, we present a synthetic, microfabricated “leaf” that can
scavenge electrical power from evaporative flow. Evaporation at the surface of the device produces
flows with velocities up to 1.5 cm/s within etched microchannels. Gas-liquid interfaces within the
channels move across an embedded capacitor at this velocity, generating 250 ms, 10–50 pF transient
changes in capacitance. If connected to a rectified charge-pump circuit, each capacitive transient can
increase the voltage in a 100 ␮F storage capacitor by ⬃2 – 5 ␮V. We provide estimates of power
density, energy density, and scavenging efficiency. © 2009 American Institute of Physics.
关DOI: 10.1063/1.3157144兴
Trees pump water hundreds of feet into the air without
active pumps by maintaining a large negative pressure gradient across their vasculature. When the gas phase around the
plant is at a lower water potential than the saturated soil,
water evaporates from leaves at thousands of microscale
pores.1,2 These pores prevent the water meniscus from receding, thereby forcing water up from the soil through a network
of microvasculature using adhesive-cohesive forces. Typically, the water potential difference between soil and air varies cyclically, generating periods of condensation and evaporation. To date, researchers have published devices, which
use evaporation of water to drive flow in microchannels, but
none have used this concept to generate electrical power.3–5
We posit that the cyclical environmental gradient in water potential can be exploited by synthetic devices to generate useful electrical energy. These gradients occur in many
places including the surface of the skin during perspiration,
near the surface of bodies of water, and at the soil-air interface.
We present a synthetic “leaf” that scavenges and stores
useful electrical power from evaporation-driven flow 关Figs.
1共a兲 and 1共b兲兴. In each device a central microfluidic stem
connects a fluid reservoir to a microfluidic network, which
acts as an evaporator. During operation, all channels are
filled with deionized 共DI兲 water. The stem is embedded with
slugs of a mobile nonaqueous phase; we used gas bubbles as
the mobile phase to demonstrate the proof of concept. Pairs
of Ti/Pt plates embedded in the stem 关Figs. 1共a兲 and 1共b兲兴 act
as parallel plate capacitors. Each pair of capacitor plates is
connected to a rectifying charge pump circuit similar to that
used in vibration scavenging work 共Cvar in Fig. 2兲.7–9
During operation, dielectric slugs transit between the capacitor plates at the speed of the evaporation-induced flow
关Fig. 1共d兲兴. Figure R1 共EPAPS兲6 presents fluid velocities in
the stem for evaporators with different diameter pores. The
maximum fluid velocity measured at STP, with no illuminaa兲
Electronic mail: maharbiz@eecs.berkeley.edu.
0003-6951/2009/95共1兲/013705/3/$25.00
tion, was 1.5 cm/s 共6 ␮m pores兲. Each dielectric slug generates a capacitance change for both leading 共−dC / dt兲 and
trailing edges 共−dC / dt兲, as it transits between the plates 关Fig.
1共e兲兴. This change arises because the plates have a much
larger capacitance when water-filled than dielectric-filled due
to the formation of the well known double layer effect
共⬃0.1– 1 pF/ m2兲.10 This double-layer capacitance is
strongly frequency dependent below ⬃1 MHz since it arises
from the movement of solvated ions and water molecules
near the electrode surfaces in response to an applied field.9
For the circuit in Fig. 2, this dependence implies that the
effective value of the water-filled capacitance will vary depending on the speed of the transition. At 1.5 cm/s, rise and
fall times for capacitance changes ranged from 200–250 ms,
corresponding to a 4–5 Hz bandwidth. As our equipment
共HP 4428A LCR兲 was incapable of direct measurements of
reactances at ⬍20 Hz, ⌬C measurements were taken at various frequencies as a bubble transited and extrapolated to dc
关Fig. R2 共EPAPS兲;6 Figure 1共d兲 shows ⌬C = 8 – 10 pF for a
single bubble taken at 1 MHz兴. At 5 Hz, the expected ⌬C is
⬃40 pF 共Fig. R2, red circle兲.6
Because Q = CV for any capacitor, a change in capacitance 共dC / dt兲 must result in a current 共i.e., dQ / dt兲 if V cannot vary 共EPAPS兲.6 A current flowing out of the capacitor
represents energy transferred to an external circuit. In order
to directly measure the current extracted with each bubble,
one stem capacitor was wired in parallel with a surface
mount capacitor 共1 ␮F兲 and an ammeter was placed between the two components. Both capacitors were then precharged to 2 V. At 1.5 cm/s flow, the leading edge of the
bubble produced a 40 pA current 共␴ = 20.12 pA, N = 10兲 into
the surface mount technology 共SMT兲 capacitor, which
flowed back into the stem capacitor on the trailing edge. This
continued as long as there were bubbles in the channel. As
expected, the current at each transition was proportional to
dC / dt, which was proportional to fluid velocity 共not shown兲.
If the embedded capacitor is connected to a rectifying
circuit 共Cvar in Fig. 2兲, current can only flow into the external
95, 013705-1
© 2009 American Institute of Physics
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
013705-2
Appl. Phys. Lett. 95, 013705 共2009兲
Borno, Steinmeyer, and Maharbiz
FIG. 1. 共Color online兲 Synthetic leaf design, operation, and fabrication. 共a兲 Conceptual illustration and 共b兲 top view; scale bar is 3 mm. 共c兲 Cross-section. See
EPAPS 共Ref. 6兲 for fabrication details, 共d兲 a bubble transiting between the capacitor plates, and e兲 measured ⌬C vs time for the bubble in 共b兲.
circuit 共barring leakage, discussed below兲. Each leading
bubble edge generates a current spike into the external circuit, which is used to pump up the voltage on a storage
capacitor 共Cstore, Fig. 2兲, harvesting a portion of the mechanical energy of the fluid flow. See EPAPS6 for a description of
circuit operation and simulation results.
To demonstrate this concept, the water reservoir was replaced with tubing loaded with alternating sections of water
and air bubbles to provide a very large number of sequential
interfaces 共⬎100兲. A syringe pump drove the bubble train
into the device at a flow rate of 100 ␮L / min. Cvar and Cinit
were precharged to ⫺5 V and voltage source was disconnected. While the bubbles transited through the stem, Vout
was measured 关Fig. 3共a兲兴 and video of the bubbles traversing
was synchronized with Vout. In the absence of bubble motion
共regions 1 and 3兲, Vout decays slowly due to the finite input
impedance of the voltmeter 共Agilent 34401A, 10 G⍀兲. During bubble motion 共region 2兲, each leading bubble edge results in an increase in output voltage 共⌬Vout兲 of approximately 2 – 5 ␮V 关Fig. 3共a兲, inset兴. It is important to note that
this circuit works in the face of leakage parasitics in all the
SMT components 共Rparallel = 10 G⍀兲. Good agreement is
seen between a Cadence Spectre transient simulation of the
circuit using the manufacturer’s component models 共red line,
Fig. 3兲 and the measured results 共blue line, Fig. 3兲.
Given the data above, we can determine the constraints
on energy density, power density, and efficiency for this class
of device. The speed of the fluid flow is a function of the
pressure difference between the reservoir and the evaporator
and the fluidic resistance of the microchannel. Since the radius of the reservoir is large 共⬎1 mm兲, the pressure across
the microchannel is dominated by the surface tension-based
pressure drop at the evaporator, which scales with the radius
of the pores,4
␺capillary =
− 2␥ cos ␪
,
d
microchannels will stop if a counterpressure equal to ␺capillary
is applied. Thus, ␺capillary represents the extractable volumetric energy density per pore. In our system, an electrostatic
force arises against the entry of a dielectric slug within the
embedded capacitor due to the difference in dielectric constants between the water and slug; this results in measurable
reduction in velocity when the bubble enters the plates 共data
not shown兲.11 The larger ␺capillary, the larger the electrostatic
pressure required to stop the flow. Thus, more energy can be
extracted. However, as the pore size decreases, the absolute
evaporation rate at each pore decreases. For example, at
20 ° C, 50% relative humidity, liquid in a 6 nm pore is in
equilibrium with the vapor phase and no net evaporation
occurs.12 Thus, energy scavenging from evaporation-driven
flow necessitates a tradeoff between energy density and
power density for a given design.
Given the pore size and velocities measured in this work,
we can estimate the maximum power density of our device
by considering a minimum-sized slug of liquid 共two menisci
facing each other兲. A minimum-sized slug moving at 1.5
cm/s has 1.2 pJ of kinetic energy and dimensions of 500 ␮m
wide, 75 ␮m high, and 150 ␮m long 共measured curvature
of meniscus, not shown兲. The maximum volumetric power
density of this device can be calculated by envisioning a
channel composed of trains of minimally sized slugs moving
over arrays of metal plates, which are one meniscus wide;
this scenario maximizes the interfacial area transiting over
plates at any given time.
共1兲
where ␥ is liquid surface tension, ␪ is the liquid-solid contact
angle, and d is the pore diameter. Liquid flow inside the
FIG. 2. Scavenging circuit.
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
013705-3
Appl. Phys. Lett. 95, 013705 共2009兲
Borno, Steinmeyer, and Maharbiz
FIG. 3. 共Color online兲 Measured 共blue兲 and simulated 共red兲 共a兲 voltage, 共b兲
energy of Cstore. The slopes of the three zones are −0.34, 1.8, and
−0.6 ␮V / s.
⌬E = 1.2 ⫻ 10−12 J
Pmax =
t=
⌬E 1.2 ⫻ 10−12 J
= 60 pW
=
0.02 s
t
1
300 ␮m
= 20 ms
1.5 ⫻ 10−2 m/s
N=
1 cm3
= 88 900
300 ␮m ⫻ 500 ␮m ⫻ 75 ␮m
p = 88 900 ⫻ 60 pW = 5
␮W
cm3
loss in zone 3 is due to component leakage and half is due to
the voltmeter 共since both have leakage resistances of
⬃10 G⍀兲. Given this, the leakage rate is 14.3% of the scavenging rate 关Fig. 3共a兲兴. More importantly, while leakage on
Cstore dissipates stored energy, leakage on Cinit eventually
prevents the circuit from operating. Thus, a stand-alone device would require a backup battery to periodically refresh
Cstore, a common feature in many ultralow power, long lifetime devices. Ultralow power electronics for periodic refreshing a precharge condition are a topic of ongoing
investigation.14,15 For our device, the consumption of the
overhead electronics would need to be less than 1 ␮J per
refresh cycle in order to break even if Cstore = 20 nF. For
comparison, a single 0.25 ␮m metal oxide semiconductor
field effect transistor 共MOSFET兲 running at 5 V would consume ⬃0.5⫻ Cgate V2 = 62.5 fJ.16
In conclusion, we presented a proof-of-concept system
for energy scavenging from evaporation-driven motion. Several improvements are needed. First, the bubbles need to be
replaced with an entrapped, nonvolatile dielectric phase 共e.g.,
beads or etched components兲. Further, the pore size of the
evaporator and the fluidic resistance matching between
evaporator and main channel need to be optimized; parameters were set by commercially available ceramic disks and
any improvement will immediately increase power density.
Lastly, microfabricated condensers need to be added to collect water droplets during the condensation cycle.
共2兲
where d is the length and v is the velocity of each slug, Pmax
is the maximum power extractable from one slug, N is the
number of slugs in 1 cm3, and p is the maximum power
density per cm3. Adding the ceramic evaporator volume
共1.414 cm3兲 drops power density to 2 ␮W / cm3. This compares well with vibration scavenging efforts9,13 given that the
existing device can be significantly optimized 共see below兲.
The harvesting efficiency is limited by the circuit’s resistive parasitics. During operation 关Fig. 3共a兲, zone 2兴, Vout
increases with each transition, demonstrating that the harvesting exceeds the loss due to leakage in the entire circuit.
To estimate leakage loss, we assume half of the −0.6 ␮V / s
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Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp