Integrated Droplet Routing and Defect Tolerance in the Synthesis of Digital Microfluidic Biochips
Numerical study of the microdroplet actuation switching frequency in digital microfluidic biochips
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Transcript of Numerical study of the microdroplet actuation switching frequency in digital microfluidic biochips
RESEARCH PAPER
Numerical study of the microdroplet actuation switchingfrequency in digital microfluidic biochips
Ali Ahmadi • Kurt D. Devlin • Mina Hoorfar
Received: 29 June 2011 / Accepted: 15 August 2011 / Published online: 26 August 2011
� Springer-Verlag 2011
Abstract In this article, an electrohydrodynamic approach
is used to study the microdroplet actuation in contemporary
digital microfluidic biochips. The model is employed to
analyze the microdroplet motion, and investigate the
effects of the key parameters on the devices performance.
The modeling results are compared to the experimental
observations, and it is shown that the model provides an
accurate representation of digital microfluidic transport. An
extensive parametric variation is used to derive the maxi-
mum actuation switching frequency for ranges of the
microdroplet size, gap spacing between the top and bottom
plates and electrode pitch size. As a result, scalability of
the devices is investigated, and it is shown that the
microdroplet transfer rates change inversely with the sys-
tem size, and microdroplet average velocity is nearly the
same for different system scales. As a result of this study,
an adjustable force-based actuation switching frequency
implementation is proposed, and it is shown that faster
microdroplet motion is obtained by in situ adjusting of the
switching frequency. Finally, it has been observed that
fastest microdroplet motion, despite similar studies con-
ducted in the literature, is not achieved via actuating the
next electrode as soon as the microdroplet touches it.
Indeed, the switching frequency spectrum is dependent on
the physical and geometrical properties of the system.
Keywords Digital microfluidic � Microdroplet �Electrocapillary � Switching frequency
1 Introduction
Digital microfluidics is a new technology for generating
discrete microdroplet motion on arrays of electrodes (Pol-
lack et al. 2000, 2002; Lee et al. 2002; Moon et al. 2002;
Cho et al. 2003; Urbanski et al. 2006; Cooney et al. 2006;
Fair 2007; Fouillet et al. 2008; Brassard et al. 2008;
Abdelgawad and Wheeler 2008; Abdelgawad and Wheeler
2009; Fan et al. 2009). These devices are highly scalable
and reconfigurable, and allow for the efficient control
required for chemical and biological applications
(Srinivasan et al. 2004; Wheeler et al. 2005; Chang et al.
2006; Moon et al. 2006; Fair et al. 2007; Nichols and
Gardeniers 2007; Miller and Wheeler 2008; Sista et al.
2008; Jebrail and Wheeler 2009; Luk and Wheeler 2009;
Hua et al. 2010; Malic et al. 2010). As a result, these
devices are capable of performing high throughput analy-
sis, and their reconfigurability reduces both cost and weight
(Su et al. 2006; Fair 2007). A Schematic of a covered
digital microfluidic system is shown in Fig. 1.
Effective control of digital microfluidic devices can only
be achieved by having a deep understanding of the
microdroplet operational dynamics in the system. Without
an accurate prediction of the system kinetics, the system
will not operate at full throughput, and in certain cases, no
fluid transport will be achieved (Arzpeyma et al. 2008).
Therefore, a thorough understanding of the system kinetics
and determining the key parameters in the device perfor-
mance optimization are crucial tasks in the design, control,
and fabrication processes. Accurate models ultimately
allow us to find these key parameters and relate them to the
device throughput.
Geometrical and physical properties of the system and
the actuation switching frequency are the most important
key parameters influencing the throughput of the system,
A. Ahmadi � K. D. Devlin � M. Hoorfar (&)
School of Engineering, The University of British Columbia,
Vancouver, Canada
e-mail: [email protected]
123
Microfluid Nanofluid (2012) 12:295–305
DOI 10.1007/s10404-011-0872-8
and most of the recent studies have focused on investi-
gating and characterizing each effect individually
(Arzpeyma et al. 2008; Bhattacharjee and Najjaran 2010;
Bahadur and Garimella 2006). For instance, Fair (2010)
developed a hydrodynamic scaling model of droplet actu-
ation in a digital microfluidic systems. The proposed ana-
lytical model included the effects of the contact angle
hysteresis, drag from the filler fluid, drag from the solid
walls, and change in the actuation force while a droplet
traverses a neighboring electrode. It was determined that
reliable operation of digital microfluidic is possible as long
as the device is operated within the limits of the Lippmann-
Young equation. Bahadur and Garimella (2006) developed
a model based on the minimization of the system energy,
and predicted the overall performance of the device. They
investigated the origins and the fundamental physics
behind the microdroplet actuation, and used a parametric
variation to find the conditions which maximize the driving
force. In their analytical approach, the size of the micro-
droplet, however, is restricted to the electrode size.
Bhattacharjee and Najjaran (2010) modeled the digital
microfluidic systems for different microdroplet sizes,
actuation voltages, dielectric thicknesses, and electrode
sizes. However, in their study, electrode shapes were
assumed to have a simple square geometry. Arzpeyma
et al. (2008) developed a numerical model based on cou-
pling the hydrodynamic and electrostatic governing equa-
tions to investigate the optimum actuation condition. They
investigated the effects of the switching frequency on the
microdroplet motion and proposed a position-based
actuation algorithm for achieving higher microdroplet
velocities. They also recognized the limitations of their
model in terms of hysteresis effects. In a recent modeling
effort, SadAbadi et al. (2010) investigated the effects of
electrode switching frequency on the maximum possible
microdroplet velocity. They showed that the best time for
switching/actuating the next electrode is when the micro-
droplet leading edge contacts that electrode, and late or
early actuation will result in discontinuity in the micro-
droplet velocity.
In this study, a novel numerical electrohydrodynamic
approach is employed to model the microdroplet motion,
and investigate the effects of the key parameters on the
device performance. The friction factor (Ren et al. 2002)
and threshold voltage (Pollack et al. 2002) are the only
empirical parameters used in the developed model. The
numerical analysis employed here allows for modeling any
arbitrary system geometry and microdroplet shape. An
extensive parametric variation is used to derive the maxi-
mum actuation switching frequency (MASF) for wide
ranges of the microdroplet size, gap spacing, and electrode
pitch size. This study results in the development of a force-
based adjusting switching frequency algorithm based on
which optimum motion of the microdroplet is obtained.
The result of the new force-based switching frequency
algorithm will be compared to that of the position-based
algorithm. It will be shown that the latter provides slower
microdroplet motion compared to the force-based actuation
algorithm proposed in this article. In the following sec-
tions, the governing equations of microdroplet motion are
introduced, and the results obtained from the model and
proposed algorithm are presented and discussed.
2 Theory and methodology
In this section, microdroplet motion governing equations
and the boundary conditions used for solving these equa-
tions are explained. Details of the numerical scheme are
presented and discussed in Ahmadi et al. (2011).
2.1 Governing equations
To develop an accurate model for the microdroplet
dynamics, the driving and opposing forces must be quan-
tified. The governing transient equation for the microdro-
plet in the direction of the motion can be written as (Ren
et al. 2002)
mdvtransport
dt¼ Fdriving � Fwall � Ffiller � Ftpcl; ð1Þ
where m is the mass of the microdroplet, vtransport is the
microdroplet transport velocity, and Fdriving, Fwall, Ffiller,
top view
side view
AA
xz
xy
Fig. 1 Schematic of a covered digital microfluidic system is shown
296 Microfluid Nanofluid (2012) 12:295–305
123
and Ftpcl are the driving, wall, filler, and three-phase con-
tact line forces, respectively (Ahmadi et al. 2011; Ren et al.
2002; Bahadur and Garimella 2006; Ahmadi et al. 2009;
Buehrle et al. 2003; Baird et al. 2007; Arzpeyma et al.
2008).
The developed numerical scheme uses the finite volume
method (FVM) to solve the Maxwell equation (Buehrle
et al. 2003) in three material regions (dielectric layers,
filler, and microdroplet interior) (Ahmadi et al. 2011)
r � D ¼ r � ð�EÞ ¼ 0; ð2Þ
where D and E are the electric displacement and electric
field vector and e is the permittivity of the medium. The
electrostatic pressure, pel, can be obtained from the electric
field as
pel ¼�jEj2
2: ð3Þ
The driving (electromechanical) force acting on the
microdroplet interface can be calculated by integrating the
electrostatic pressure along the microdroplet–filler
interface as (Ahmadi et al. 2011)
Fdriving ¼Z
peldAinterface; ð4Þ
where dAinterface is the area element along the
microdroplet–filler interface. Calculating the wall and
filler forces, Fwall and Ffiller, involves the solution of
continuity and Navier–Stokes governing equations for the
hydrodynamic pressure. The continuity equation for
incompressible flow is
r � v ¼ 0; ð5Þ
where v is the velocity vector of the fluid particles. The
Navier–Stokes equation for the motion of the fluid is
q½otvþ ðv � rÞv� ¼ �rphyd þ lr2vþ qgþ qfE; ð6Þ
where phyd is the hydrodynamic pressure, q and l are the
fluid density and viscosity, g is the gravitational
acceleration [which can be ignored as the Bond number
is much smaller than 1 (Arzpeyma et al. 2008)], and qf is
the free charge density. The last term of Eq. 6 vanishes as
the Navier–Stokes equation is solved inside the conductive
liquid microdroplet and a dielectric filler fluid. While, both
the velocity and hydrodynamic pressure of the fluid are
unknown, it has been shown (Lomax et al. 2001) that the
continuity equation (5) and Navier–Stokes equation (6) can
be solved simultaneously using the numerical FVM. The
discretized regions of the digital microfluidic system are
shown in Fig. 2. After solving Eqs. 5, 6, the velocity vector
inside the microdroplet is then used to find the shear force
on the wall (Fwall) as
Fwall ¼Z
walls
s dA; ð7Þ
where s is the shear stress. Using the filler hydrodynamic
pressure (which is obtained from the solution of the Eqs. 5,
6) at the microdroplet interface, filler force, Ffiller can be
calculated as
Ffiller ¼Z
phyddAinterface: ð8Þ
The molecular-kinetic theory (Blake and Coninck 2002)
states that attachment or detachment of fluid particles is the
main source of energy dissipation at the moving three-
phase contact line. Although, dynamic of wetting can be
described by the microdroplet velocity and the dynamic
contact angle (Keshavarz-Motamed et al. 2010; Blake and
Coninck 2002), it was shown (Ren et al. 2002; Ahmadi
et al. 2009) that an additional force has to be added to the
dynamic equation of the microdroplet motion. Using the
molecular-kinetic theory, this three-phase contact line
force can be expressed as
Ftpcl ¼ 2Pnvtransport; ð9Þ
where n = 0.04 is the friction factor, P is the perimeter
length of the microdroplet. This linearly dependent friction
force is especially accurate at low and intermediate
velocities (Ren et al. 2002; Ahmadi et al. 2009).
2.2 Boundary conditions
2.2.1 Moving boundary
The boundary condition used for the microdroplet and filler
along the solid surfaces are the no-slip, no-penetration, and
zero pressure gradient condition. The microdroplet–filler
interface is moving with the microdroplet transport veloc-
ity, vtransport, and is implemented by defining fictitious
Cross-section A-AF=p Ael(i,j) (i,j)
(i,j)
Fig. 2 The discretized regions of the digital microfluidic system are
shown. Black circles show the center of each cell and the dashed linesshow the borders of each cell
Microfluid Nanofluid (2012) 12:295–305 297
123
velocities within solid cells adjacent to fluid cells (Buss-
mann et al. 1999). A method based on the fractional vol-
ume of fluid (VOF) method (Afkhami and Bussmann 2008;
Arzpeyma et al. 2008) is used for modeling the moving
boundary of the microdroplet. The main idea for the
implementation is that the microdroplet–filler interface is
moving with the transport velocity of the microdroplet.
Therefore, this volume fraction of the cells must satisfy the
advection equation
½otf þ vtransportoxf � ¼ 0: ð10Þ
The VOF method is based on the averaging phases at the
interface, in which the volume fraction, f, is advected with
the fluid flow. The volume fraction, f, for each cell is
defined as
f ¼ Vliq
Vcell
; ð11Þ
where Vliq and Vcell are the liquid volume and total cell
volume, respectively.
2.2.2 Microdroplet–filler interface
The relation between the electrostatic pressure, hydrody-
namic pressure, and microdroplet surface curvature can be
expressed as (Zeng and Korsmeyer 2004)
½½pel��n� ½½phyd��n ¼ cdfðr � nÞn; ð12Þ
where [[pel]] and [[phyd]] are the respective electrostatic
and hydrodynamic pressure changes across the droplet–
filler interface, respectively,n is the normal unit vector to
the interface, and cdf is the droplet–filler surface tension.
This discontinuity equation can be simplified by noting that
the surface force density of the electric origin must have no
shearing component. The pressure and surface tension
contributions are therefore normal to the interface (Kang
2002; Jones 2005). The curvature of the interface can then
be extracted from Eq. 2 by determining the electrostatic
pressure from the electric potential and field in the system
and by determining the hydrodynamic pressure from
Navier–Stokes and continuity equations inside the micro-
droplet and the filler.
2.2.3 Microdroplet contact angle
It is shown that the contact angle of a moving microdroplet
(dynamic contact angle) differs from its static value (static
contact angle) at equilibrium (Blake and Coninck 2002;
Keshavarz-Motamed et al. 2010). Using Frenkel–Eyring
activated rate theory of transport in liquids (Blake and
Coninck 2002; Keshavarz-Motamed et al. 2010), the static
contact angle, hS, and the dynamic contact angle, hD, can
be related to the microdroplet transport velocity as
cos hS � cos hD ¼vtransportn
cdf
: ð13Þ
2.2.4 Threshold condition
It has been shown before that there exists a threshold force
caused by pinning and hysteresis which prevents droplet
motion before sufficient applied voltage (Gao and
McCarthy 2006). However, implementing the threshold
condition to the proposed algorithm is not a trivial task.
Most of the recent modeling efforts suggest to subtract a
constant threshold force from the driving force (Ren et al.
2002; Kumari et al. 2008; Bahadur and Garimella 2006;
Ahmadi et al. 2009). However, since the threshold force
cannot be greater than the driving force, subtracting a
constant threshold force leads to inaccurate results.
Therefore, in this article the hysteresis condition is
implemented by considering an effective voltage as
Veff ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2
app � V2tr
q; ð14Þ
where Veff and Vtr are the effective and the threshold
voltage, respectively.
3 Results and discussion
The results of the model are presented in this section. First,
to verify the accuracy of the model, the results obtained
from the model are compared to the experimental results.
After the verification, the scalability of digital microfluidic
devices, and the dependency of the MASF on the electrode
pitch size, gap spacing, and droplet radius are investigated.
Finally, an adjustable force-based switching frequency
method is proposed to allow for higher transport velocity.
3.1 Verification
It is required to evaluate the accuracy of the model in terms
of both displacement and velocity of the microdroplet.
Thus, the modeling results are compared and verified with
previous experimental observations. The experimental
setup introduced by Pollack et al. (2002) is used here. The
system consists of an 800 nm thick film of parylene C
which provides insulation over the control electrodes. Both
top and bottom plates have a 60-nm thick top-coating of
Teflon AF 1600. The filler fluid is 1 cSt silicon oil.
Dynamics of a 900 nl microdroplet of 0.1 M KCl solution
with a diameter of D = 1.9 mm moving between two
plates with a gap spacing of H = 0.3 mm and an electrode
pitch size of L = 1.5 mm is modeled.
The displacement and velocity obtained from the model
are shown in Fig. 3a,b, and compared to the experimental
298 Microfluid Nanofluid (2012) 12:295–305
123
observations. The modeling results are in excellent agree-
ment with the experimental data and the expected trend;
the rising edge of both the model and experimental results
for displacement (in Fig. 3a) are nearly the same; however,
the experimental results indicate that the microdroplet does
not complete the transport over the electrode. This
incomplete transport [as reported in Pollack et al. (2002)] is
contributed to insufficient voltage. Figure 3b shows a sharp
peak around the maximum driving force originated from
the sudden change in the rate of the increasing wetted area.
The difference between the experimental and modeling
values at the beginning of its motion is attributed to the
hysteresis effects in the system (Pollack et al. 2002).
Accurate models ultimately allow us to optimize the mi-
crodroplet motion over multiple electrodes. To maximize
the system throughput, the model must be capable of
predicting the actuating frequencies which deliver appro-
priately timed voltages to the underlying electrodes. It is
important to optimize the switching frequencies for the
desired microdroplet average velocity. The relationship
between these frequencies and the average velocity is
studied in this subsection.
Figure 4 shows the arrival time for the microdroplet
leading edge at various positions (i.e., displacements)
across the three-electrode structure. Results are shown for
four switching frequencies (2.5, 5, 10, and 15 Hz) and an
applied voltage of 26 V. The optimal case for transport
occurs with a switching frequency of approximately 13 Hz.
It is apparent from this figure that increasing frequency
leads to shorter arrival times at the end of the third elec-
trode: the 2.5 Hz case has an arrival time of 0.91 s; the
5 Hz case has an arrival time of 0.48 s; the 10 Hz case has
an arrival time of 0.24 s. However, as it can be seen in
Fig. 5, this trend does not apply to the 15 Hz case (which is
above the 13 Hz), as the microdroplet does not successfully
complete its transport over each individual electrode. Such
a phenomenon has been observed before (Pollack et al.
2002; Arzpeyma et al. 2008); there exists a maximum
actuation switching frequency (MASF) for the applied
voltages. This point is apparent from Fig. 6, which show
the maximum switching frequencies over a range of volt-
ages for model results. The results from the proposed
electrohydrodynamic model are compared to the experi-
mental observations (Pollack et al. 2002), and the results
obtained from the explicit electrostatic and hydrodynamic
modeling approach (Ahmadi et al. 2009) for oil and air
systems. It is clear that the model accurately calculates the
MASF over the range of the applied voltages reported in
the experimental results, and successfully predicts the
hysteresis conditions. The verified model can now be used
to obtain the optimum operational conditions to maximize
the device efficiency.
3.2 Effects of the microdroplet size
In this section, the effects of the microdroplet size on the
microdroplet electrohydrodynamics and the MASF is
studied. The microdroplet motion is modeled for its
transport over three electrodes (with an electrode pitch of
L = 1.5 mm and gap spacing of H = 0.3 mm). The
selected applied voltage is 35 V, which is between the
upper and lower values of the voltages (13 and 40 V) used
for the calculation of MASF (see Fig. 6). The numerical
MASF value calculated for this selected voltage (35 V) is
in good agreement with the experimental value. An arbi-
trary switching frequency of 15 Hz is used. Microdroplets
with three different diameters of 1.6, 2.25, and 3 mm are
modeled. The results of the model are presented in terms of
the microdroplet displacement and driving and opposing
forces during its motion. Figure 7 presents the behavior of
the microdroplet (with different sizes) under the same
actuation conditions. The leading edge position of the
microdroplet is shown as a function of time in Fig. 7a. The
difference in the initial positions is due to the fact that the
microdroplet center is aligned with the center of the initial
electrode. This is the most common initial position for a
(a) (b)Fig. 3 The a displacement and
b velocity are compared to the
experimental results (Pollack
et al. 2002). The applied voltage
is 26 V, and the results are
shown for a transition of the
microdroplet over one
electrode. Dynamics of a 900 nl
microdroplet of 0.1 M KCl
solution with a diameter of
D = 1.9 mm moving between
two plates with a gap spacing of
H = 0.3 mm and an electrode
pitch size of L = 1.5 mm is
modeled
Microfluid Nanofluid (2012) 12:295–305 299
123
stationary microdroplet as it self-centers itself with the
initial electrode after dispensing (Fair 2007). As it can be
seen in Fig. 7a, the smallest microdroplet reaches the last
electrode in the shortest time. However, since the same
switching frequency (i.e., 15 Hz) is used, the average
transport velocity is the same for all of the microdroplet
sizes. The driving force for each microdroplet is shown
Fig. 7b with respect to the leading edge position. The
driving forces acting on the larger microdroplets are bigger.
On the other hand, the opposing forces (i.e., shear, drag,
and three-phase contact line) increase due to the increased
microdroplet mass and surface area. Therefore, the mi-
crodroplets move slower as their sizes increase. The results
presented reveal the fact that the microdroplet size is
a key parameter in determining the microdroplet
electrohydrodynamics.
To investigate the relation between the microdroplet
size and the MASF, transport of three different microdro-
plet sizes over six electrodes (for the same system as
before) is studied. Figure 8 shows the time required for
completing the transport for three different microdroplet
sizes as a function of the switching frequency. For each
size, as the switching frequency increases the time required
decreases. However, the switching frequency cannot be
increased above a certain frequency which is called the
MASF. Interestingly, the MASF is strongly dependent on
the microdroplet size (see Fig. 8); smaller microdroplets
allow for higher MASF values.
3.3 Effects of system architecture
The system architecture plays a crucial role in microdroplet
dynamics. In essence, structural layers and geometric
parameters of the device have the most important effects on
the microdroplet motion (Ren et al. 2002). In this section,
the effects of the gap spacing and electrode pitch size on
the MASF are individually analyzed, and scalability of
digital microfluidic architectures is investigated. Figure 9
shows the MASF versus microdroplet diameter for three
different gap spacings (i.e., H = 0.6, 0.3, and 0.15 mm).
The electrode pitch size is kept constant as L = 1.5 mm.
The results from Fig. 9 confirm again that as the droplet
diameter increases, the MASF will decrease (given the
constant gap spacing). However, for the same microdroplet
diameter, as the gap spacing decreases, microdroplet
motion becomes slower due to the resulting increase in the
wall force. This is an interesting observation, as it shows
that for pre-fabricated top and bottom plates, faster trans-
port can be achieved simply by controlling the gap spacing
and the microdroplet volume. The effect of the electrode
Fig. 4 The arrival time for the modeled microdroplet leading edge is
shown for various positions (i.e., displacements) across the three-
electrode structure. The applied voltage is 26 V, and the results are
shown for four switching frequencies (2.5, 5, 10, and 15 Hz)
time = 0.4 s time = 0.8 s time = 1.2 stime = 0.0 s
time = 0.2 s time = 0.4 s time = 0.6 stime = 0.0 s
time = 0.1 s time = 0.2 s time = 0.3 stime = 0.0 s
time = 0.07 s time = 0.13 s time = 0.2 stime = 0.0 s
Switching Frequency = 2.5 Hz
Switching Frequency = 5.0 Hz
Switching Frequency = 10.0 Hz
Switching Frequency =15.0 Hz
Fig. 5 The concept of
maximum actuation switching
frequency (MASF) is illustrated
300 Microfluid Nanofluid (2012) 12:295–305
123
pitch size on the MASF is shown in Fig. 10a. The gap
spacing is kept constant as H = 0.3 mm. The results show
that by decreasing the electrode pitch size the system
MASF increases. To determine the effect of the electrode
pitch size on the transport velocity, a similar plot is shown
in Fig. 10b. Interestingly, by decreasing the electrode pitch
size and keeping the gap spacing constant, for the same
diameter-electrode pitch size ratio, higher transport veloc-
ities can be achieved. This increase in the velocity can be
due to the decrease in the shear force because of the
reduced in the wetted area.
It has been shown before that digital microfluidic
structures are highly scalable (Pollack et al. 2002). The
scalable nature of these systems are studied here. Two
system designs are modeled: L = 1.5 mm and H = 0.6
mm; L = 0.75 mm and H = 0.3 mm. The size of the
second design is half of the size of the first design.
Figure 11 shows the MASF of these setups over a range of
microdroplet diameter-electrode pitch size ratios (D/L).
The MASF of the smaller design is larger than that of the
bigger design. However, the transport velocity of both
systems is the same (see Fig. 11b). This is a very important
observation which confirms the scalable nature of digital
microfluidic systems.
3.4 Adjustable force-based switching frequency
implementation
Constant switching frequency implementation is the sim-
plest actuation algorithm. However, by applying a constant
Applied Voltage(V)
MASF (Hz)
10 20 30 400
10
20
30
40
Experimental ResultsExplicit E/H ResutsCoupled EH Results
50 60 70
50
/
Oil Filler Air Filler
Fig. 6 The maximum switching frequencies for the proposed model
are shown for a range of voltages and compared to the explicit
electrostatic and hydrodynamic modeling (Ahmadi et al. 2009) and
(Pollack et al. 2002) experimental results for oil and air filler systems
Time (s)
Displacement (mm)
0.00 0.05 0.10 0.150
1
2
3
4
5
6D=1.60 mmD=2.25 mmD=3.00 mm
(a)
Displacement (mm)
Force ( N)
0.00 1.00 2.00 3.00 4.000
5
10
15
20
25
30
35
40D=1.60 mmD=2.25 mmD=3.00 mm
µ
(b)
Fig. 7 The effects of the microdroplet size on electrohydrodynamic properties are shown for three different diameters. a The microdroplet
leading edge position is shown as a function of time. b The driving force is shown as a function of the microdroplet leading edge position
Completion time(s)
Frequency (Hz)
0.20 0.25 0.30 0.35 0.40 0.45
10
15
20
25
30D=1.60 mmD=2.25 mmD=3.00 mm
Fig. 8 The time required to complete the transport over six
electrodes is shown as a function of the switching frequency for
microdroplets of three different diameters
Microfluid Nanofluid (2012) 12:295–305 301
123
frequency the device will not operate at its optimum
throughput and maximum transport velocity. In Fig. 12, the
maximum number of electrodes in which the microdroplet
can be transported (before it stops) is shown as a function
of the actuation switching frequency. Depending on the
constant switching frequency, the microdroplet will ulti-
mately stop after completing its transport over a limited
number of electrodes. Adjustable switching frequency
algorithms have been proposed to address this issue
(Arzpeyma et al. 2008; SadAbadi et al. 2010). Arzpeyma
et al. (2008) showed that optimum actuation is achieved
via actuating the next electrode as soon as the microdroplet
touches it. This has been referred to as an adjustable
position-based actuation algorithm. In this article, a new
electrode actuation algorithm is proposed in which actua-
tion is based on finding the maximum force acting on the
microdroplet (i.e., adjustable force-based actuation). As it
can be seen in Fig. 13, the proposed algorithm is based on a
feedback control submodule which monitors the micro-
droplet location. After sensing the microdroplet position,
the algorithm considers two potential actuation scenarios ,
as it is demonstrated in Fig. 14. After calculating the
driving force using the electrohydrodynamic model for
each scenario, the proposed algorithm chooses the opti-
mum actuation scheme which leads to higher velocity. This
performance of the proposed algorithm was examined with
respect to the other methods available (i.e., constant fre-
quency, adjustable position-based frequency). Figure 15
presents the results of this comparison. In essence, it shows
the time required to complete transport over six electrodes
as a function of the microdroplet leading edge position for
three different algorithms: constant frequency, adjustable
position-based frequency, and adjustable force-base fre-
quency. It is evident from the results that the adjustable
Droplet Diameter (mm)
MASF (Hz)
1.50 2.00 2.50 3.0010
15
20
25
30
35
H=0.6 mmH=0.3 mmH=0.1 5mm
Fig. 9 MASF is shown for three different gap spacings as a function
of microdroplet diameter
D/L
MASF (hz)
1.00 1.50 2.00 2.50 3.000
20
40
60
80
100
120 L=0.375 mmL=0.750 mmL=1.500 mmL=3.000 mm
(a)
D/L
Transport Velocity (mm/s)
1.00 1.50 2.00 2.50 3.0010
20
30
40
50
L=0.375 mmL=0.750 mmL=1.500 mmL=3.000 mm
(b)Fig. 10 The effect of the
electrode length on the MASF
and the microdroplet transport
velocity is shown. a The
increase in the MASF as the
length of the electrode decreases
is shown. b The increase in the
transport velocity due to the
decrease in the wetted surface
area is shown
D/L
MASF (hz)
1.00 1.20 1.40 1.60 1.80 2.000
20
40
60
80L=0.75 mm
L=1.50 mmH=0.60 mm
H=0.30 mm
(a)
D/L
Transport Velocity (mm/s)
1.00 1.20 1.40 1.60 1.80 2.000
20
40
60
L=0.75 mm
L=1.5 mmH=0.30 mm
H=0.60 mm
(b)Fig. 11 a The MASF of two
designs over a range of
microdroplet diameter-electrode
pitch size ratios (D/L) is shown.
b The microdroplet transport
velocity of two designs over a
range of microdroplet diameter-
electrode pitch size ratios
(D/L) is shown
302 Microfluid Nanofluid (2012) 12:295–305
123
force-based frequency results in faster microdroplet
motion. It should be noted that both adjustable position-
based actuation and adjustable force-based actuation will
lead to the same result for the case where the microdroplet
diameter is equal to the adjustable force-based electrode
length. However, as the ratio of the microdroplet diameter
and electrode size increases, the adjustable force-based
algorithm provides much faster motion compared to the
adjustable position-based actuation. The in situ control of
microdroplet motion in digital microfluidic systems is a
crucial task. Depending on the size of the system, the most
suitable switching frequency spectrum has to be found to
achieve the highest transport velocity.
4 Conclusion
In this study, the electrohydrodynamic method is imple-
mented numerically to investigate the effects of system
architecture and microdroplet size on the digital microflu-
idic system dynamics. The proposed methodology provides
a vital tool in the design and control processes, and can be
used for numerous applications including optimum routing
and achieving higher transport velocities. The modeling
results showed that for pre-fabricated top and bottom
plates, faster transport can be achieved simply by con-
trolling the gap spacing and the microdroplet volume. It
was also shown that depending on the constant switching
frequency, the microdroplet will ultimately stop after
completing its transport over a limited number of elec-
trodes. Therefore, a force-based adjustable switching fre-
quency was proposed and implemented. Compared to the
constant frequency and adjustable position-based algo-
rithms, the proposed adjustable forced-based algorithm
provides higher velocities.
Frequency (Hz)
Number of Electrodes Transported
22.00 24.00 26.00 28.00 30.000
5
10
15
Fig. 12 The maximum number of electrodes which the microdroplet
can be transported is shown as a function of the actuation switching
frequency (before it stops)
Fig. 13 The proposed algorithm is based on a feedback control
submodule which monitors the microdroplet location
Fig. 14 The algorithm considers two potential actuation scenarios.
After calculating the driving force using the electrohydrodynamic
model for each scenario, the proposed algorithm chooses the optimum
actuation scheme which leads to higher velocity
Displacement (mm)
Time (sec)
0.00 2.00 4.00 6.000.00
0.05
0.10
0.15
0.20Constant FrequencyAdjustable Force-based FrequencyAdjustable Position-based Frequency
Fig. 15 The time required to complete the transport over six
electrodes is shown as a function of the microdroplet leading edge
position for three different algorithms: constant frequency, adjustable
position-based frequency, and adjustable force-based frequency
Microfluid Nanofluid (2012) 12:295–305 303
123
References
Abdelgawad M, Wheeler AR (2008) Low-cost, rapid-prototyping of
digital microfluidics devices. Microfluid Nanofluid 4(4):349–355
Abdelgawad M, Wheeler AR (2009) The digital revolution: a new
paradigm for microfluidics. Adv Mater 21(8):920–925
Afkhami S, Bussmann M (2008) Height functions for applying
contact angles to 2D VOF simulations. Int J Numer Methods
Fluids 57(4):453–472
Ahmadi A, Najjaran H, Holzman JF, Hoorfar M (2009) Two-
dimensional flow dynamics in digital microfluidic systems.
J Micromech Microeng 19(6):065003
Ahmadi A, Holzman JF, Najjaran H, Hoorfar M (2011) Electrohy-
drodynamic modeling of microdroplet transient dynamics in
electrocapillary-based digital microfluidic devices. Microfluid
Nanofluid 10(5):1019–1032
Arzpeyma A, Bhaseen S, Dolatabadi A, Wood-Adams P (2008) A
coupled electro-hydrodynamic numerical modeling of droplet
actuation by electrowetting. Colloids Surf A Physicochem Eng
Aspects 323(1–3):28–35
Bahadur V, Garimella SV (2006) An energy-based model for
electrowetting-induced droplet actuation. J Micromech Micro-
eng 16(8):1494–1503
Baird E, Young P, Mohseni K (2007) Electrostatic force calculation
for an EWOD-actuated droplet. Microfluid Nanofluid
3(6):635–644
Bhattacharjee B, Najjaran H (2010) Simulation of droplet position
control in digital microfluidic systems. J Dyn Syst Meas Control
132(1):014501-3
Blake T, Coninck JD (2002) The influence of solid liquid interactions
on dynamic wetting. Adv Colloid Interface Sci 96(1–3):21–36
Brassard D, Malic L, Normandin F, Tabrizian M, Veres T (2008)
Water-oil core–shell droplets for electrowetting-based digital
microfluidic devices. Lab Chip 8(8):1342–1349
Buehrle J, Herminghaus S, Mugele F (2003) Interface profiles near
three-phase contact lines in electric fields. Phys Rev Lett
91(8):086101
Bussmann M, Mostaghimi J, Chandra S (1999) On a three-dimen-
sional volume tracking model of droplet impact. Phys Fluids
11:1406–1417
Chang YH, Lee GB, Huang FC, Chen YY, Lin JL (2006) Integrated
polymerase chain reaction chips utilizing digital microfluidics.
Biomed Microdevices 8(3):215–225
Cho SK, Moon H, Kim CJ (2003) Creating, transporting, cutting, and
merging liquid droplets by electrowetting-based actuation for
digital microfluidic circuits. J Microelectromech Syst
12(1):70–80
Cooney CG, Chen CY, Emerling MR, Nadim A, Sterling JD (2006)
Electrowetting droplet microfluidics on a single planar surface.
Microfluid Nanofluid 2(5):435–446
Fair RB (2007) Digital microfluidics: is a true lab-on-a-chip possible.
Microfluid Nanofluid 3(3):245–281
Fair RB (2010) Scaling fundamentals and applications of digital
microfluidic microsystems. Microfluid Based Microsyst
0:285–304
Fair RB, Khlystov A, Tailor TD, Ivanov V, Evans RD, Griffin PB,
Srinivasan V, Pamula VK, Pollack MG, Zhou J (2007) Chemical
and biological applications of digital-microfluidic devices. IEEE
Des Test Comput 24(1):10–24
Fan SK, Hsieh TH, Lin DY (2009) General digital microfluidic
platform manipulating dielectric and conductive droplets by
dielectrophoresis and electrowetting. Lab Chip 9(9):1236–1242
Fouillet Y, Jary D, Chabrol C, Claustre P, Peponnet C (2008) Digital
microfluidic design and optimization of classic and new fluidic
functions for lab on a chip systems. Microfluid Nanofluid
4(3):159–165
Gao L, McCarthy TJ (2006) Contact angle hysteresis explained.
Langmuir 22(14):6234–6237
Hua Z, Rouse JL, Eckhardt AE, Srinivasan V, Pamula VK, Schell
WA, Benton JL, Mitchell TG, Pollack MG (2010) Multiplexed
real-time polymerase chain reaction on a digital microfluidic
platform. Anal Chem 82(6):2310–2316
Jebrail MJ, Wheeler AR (2009) Digital microfluidic method for
protein extraction by precipitation. Anal Chem 81(1):330–335
Jones TB (2005) An electromechanical interpretation of electrowett-
ing. J Micromech Microeng 15(6):1184–1187
Kang KH (2002) How electrostatic fields change contact angle in
electrowetting. Langmuir 18(26):10318–10322
Keshavarz-Motamed Z, Kadem L, Dolatabadi A (2010) Effects of
dynamic contact angle on numerical modeling of electrowetting
in parallel plate microchannels. Microfluid Nanofluid 8(1):47–56
Kumari N, Bahadur V, Garimella SV (2008) Electrical actuation of
dielectric droplets. J Micromech Microeng 18(8):5018
Lee J, Moon H, Fowler J, Schoellhammer T, Kim CJ (2002)
Electrowetting and electrowetting-on-dielectric for microscale
liquid handling. Sens Actuators A Phys 95(2–3):259–268
Lomax H, Pulliam TH, Zingg DW (2001) Fundamentals of compu-
tational fluid dynamics. Springer, Berlin
Luk VN, Wheeler AR (2009) A digital microfluidic approach to
proteomic sample processing. Anal Chem 81(11):4524–4530
Malic L, Brassard D, Veres T, Tabrizian M (2010) Integration and
detection of biochemical assays in digital microfluidic loc
devices. Lab Chip 10(4):418–431
Miller EM, Wheeler AR (2008) A digital microfluidic approach to
homogeneous enzyme assays. Anal Chem 80(5):1614–1619
Moon H, Cho SK, Garrell RL (2002) Low voltage electrowetting-on-
dielectric. J Appl Phys 92(7):4080–4087
Moon H, Wheeler AR, Garrell RL, Loo JA, Kim CJ (2006) An
integrated digital microfluidic chip for multiplexed proteomic
sample preparation and analysis by MALDI-MS. Lab Chip
6(9):1213–1219
Nichols KP, Gardeniers HJGE (2007) A digital microfluidic system
for the investigation of pre-steady-state enzyme kinetics using
rapid quenching with MALDI-TOF mass spectrometry. Anal
Chem 79(22):8699–8704
Pollack MG, Fair RB, Shenderov AD (2000) Electrowetting-based
actuation of liquid droplets for microfluidic applications. Appl
Phys Lett 77(11):1725–1726
Pollack MG, Shenderov AD, Fair RB (2002) Electrowetting-based
actuation of droplets for integrated microfluidics. Lab Chip
2(2):96–101
Ren H, Fair RB, Pollack MG, Shaughnessy EJ (2002) Dynamics of
electro-wetting droplet transport. Sens Actuators B Chem
87(1):201–206
SadAbadi H, Packirisamy M, Dolatabadi A, Wuthrich R (2010)
Effects of electrode switching sequence on EWOD droplet
manipulation: a simulation study. In: Proceedings of the ASME
FEDSM-ICNMM, vol 31212, pp 1–6
Sista R, Hua Z, Thwar P, Sudarsan A, Srinivasan V, Eckhardt A,
Pollack M, Pamula V (2008) Development of a digital micro-
fluidic platform for point of care testing. Lab Chip 8(12):2091
Srinivasan V, Pamula VK, Fair RB (2004) An integrated digital
microfluidic lab-on-a-chip for clinical diagnostics on human
physiological fluids. Lab Chip 4(4):310–315
Su F, Hwang W, Chakrabarty K (2006) Droplet routing in the
synthesis of digital microfluidic biochips. In: Proceedings of the
conference on design, automation and test in Europe: Proceed-
ings, European design and automation association, Munich,
pp 323–328
Urbanski JP, Thies W, Rhodes C, Amarasinghe S, Thorsen T (2006)
Digital microfluidics using soft lithography. Lab Chip
6(1):96–104
304 Microfluid Nanofluid (2012) 12:295–305
123
Wheeler AR, Moon H, Bird CA, Loo RRO, Kim CJ, Loo JA, Garrell
RL (2005) Digital microfluidics with in-line sample purification
for proteomics analyses with MALDI-MS. Anal Chem
77(2):534–540
Zeng J, Korsmeyer T (2004) Principles of droplet electrohydrody-
namics for lab-on-a-chip. Lab Chip 4(4):265–277
Microfluid Nanofluid (2012) 12:295–305 305
123