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Sensors and Actuators A 152 (2009) 13–20

Contents lists available at ScienceDirect

Sensors and Actuators A: Physical

journa l homepage: www.e lsev ier .com/ locate /sna

n situ digital microfluidic conductance sampling

acqueline Nichols, Ali Ahmadi, Mina Hoorfar, Homayoun Najjaran, Jonathan F. Holzman ∗

chool of Engineering, University of British Columbia Okanagan, Kelowna, British Columbia, Canada V1V 1V7

r t i c l e i n f o

rticle history:eceived 17 November 2008eceived in revised form 24 January 2009ccepted 5 March 2009

a b s t r a c t

A digital microfluidic device architecture as well as a droplet position measurement algorithm based onin situ conductance sampling is presented. The system is implemented into a digital microfluidic mul-tiplexer configuration, and it is shown to be an effective probe for the spatial distribution of conductivefluids in the structure. The conductance levels between differential combinations of perpendicular lower

vailable online 31 March 2009

eywords:igital microfluidicsonductance samplingicrodrop

plate electrical address lines (x-channels) and upper plate electrical address lines (y-channels) are probedwithin the device, and a MATLAB-based algorithm is executed to extract the size and locations of micro-drops within the system. Modeled results are compared to experimental measurements for the samplingalgorithm and multiplexer device layout.

© 2009 Elsevier B.V. All rights reserved.

lectrowettingctuation

. Introduction

Contemporary laboratory processes have been revolutionizedver the past decade through the introduction of integratedicrofluidic control structures. Microfluidic systems offer new

apabilities for high-throughput screening, interrogation, filtering,nd sorting in a variety of applied biological and chemical fields1–4]. Given the diversity of these applications, a great deal of atten-ion has been focused recently on digital microfluidic architecturesue to their inherent scalability and reconfigurability [5,6]. Theseigital control structures induce discrete droplet motion on arraysf addressable electrodes and can be adapted via programming tovariety of processes.

Numerous phenomenological techniques exist for inducinguid actuation, and techniques based on electroosmosis [7,8],lectrowetting [9–15], dielectrophoresis [16–18], thermocapillaryumping [19,20], and photochemical actuation [21] have alleen successfully demonstrated. The direct electrical actuationechanisms listed here [7–15] are particularly intriguing since

uch processes can be implemented in digital architectures withnderlying square electrode grids providing the digital actua-ion control structure. However, these single-layered techniquesecome increasingly challenging when implemented in complex

wo-dimensional digital systems. Small device dimensions hinderhe required sampling process, because feedback for integratedontrol is typically implemented by way of an optical microscopebove the single-layered electrode grid. Moreover, large numbers of

∗ Corresponding author. Tel.: +1 250 807 8798; fax: +1 250 807 9850.E-mail address: jonathan.holzman@ubc.ca (J.F. Holzman).

924-4247/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.sna.2009.03.013

digital channels lead to structural addressability issues as it is nec-essary to pattern electrical bias lines to each square electrode in thetwo-dimensional grid without crossing, overlapping, or electricalshorting of each other.

With the above digital microfluidic control challenges in mind,spatial conductance sampling is introduced in this work. Conduc-tance sampling provides an inherently sensitive probe to the spatialdistribution of conductive fluids in digital structures as its sen-sitivity is set by the local conductance-per-unit-area. Localizedconduction and measurement sensitivity both increase drasticallyas the ion concentration increases, as changes in conductivitybetween fluidic states can range by as much as six orders of mag-nitude (typically varying for fluids from � = 10−5 S/m to � = 10 S/m[22,23]). This dynamic range dominates over that of other sam-pling processes (capacitance sampling for example [24,25]) as ionicconduction avoids dielectric saturation.

Conductivity sampling has proven to be a particularly usefultool in the characterization and measurement of isolated elec-trolytic solutions [26,27]. The technique introduced in this researchis equally important for probing the spatial distribution of flu-ids in a digital microfluidic structure. The key design issue forthe proposed system relates to the achievable spatial resolu-tion, since the conductance state under investigation is inherentlyfrequency-independent, and multi-frequency sampling algorithmsfor probing scales below the structural dimensions are not possi-ble [5,25,28–31]. With this in mind, a digital multiplexer structure

[32–34] is investigated here. The multiplexer structure incorpo-rates two overlapping and mutually perpendicular linear electrodearrays between which lies the microfluidic control plane. Dif-ferential signals are acquired between the m underlying rowelectrodes (x-electrodes) and overlying n column electrodes (y-

14 J. Nichols et al. / Sensors and Actuators A 152 (2009) 13–20

Nomenclature

(x0,y0) unitless coordinate on the grid� finite conductance of the electrolyted vertical distance between x- and y-electrodesgx dimensionless and normalized summed conduc-

tances in the x directiongy dimensionless and normalized summed conduc-

tances in the y directiongt total dimensionless and normalized summed con-

ductancesm number of electrodes in the x directionn number of electrodes in the y directionp periodic centre-to-centre pitchr0 unitless radius of the microdropw conductive electrode widthAt total microdrop area covering the regions of over-

lapped electrodesGmin negligible conductanceGmax maximum possible conductanceGt total conductance associated with the microdropGx sum of conductances in x directionGxy measured two-dimensional discrete conductance

distributionGy sum of conductances in y directionLx overlap length between the microdrop and the

respective x-electrode

eot(mtiemamn

2

2

mtcmmoyassvlici

and these conductance values can be used to map out the profile of

Ly overlap length between the microdrop and therespective y-electrode

lectrodes). Such a configuration provides a greatly simplified levelf addressability (with only m + n signal inputs) when comparedo standard single-layered two-dimensional electrode matriceswith m × n signal inputs). Furthermore, such a system can be

ore easily scaled down to small electrode widths as the needo independently address numerous individual electrode elementsn the two-dimensional grid without crossing, overlapping, orlectrical shorting does not apply. A theoretical model for theicrodrop-conductance within such a system is presented here,

nd a MATLAB-based sampling algorithm is applied to a digitalicrofluidic multiplexer prototype to verify the proposed tech-

ique.

. Conductance sampling system

.1. Sampling algorithm

As the underlying fluid dynamics and motion within digitalicrofluidic multiplexers have been analyzed elsewhere [34], it is

he intent here to analyze the capability of these electrical/fluidontrol structures for sampling of the spatial state of internalicrodrops. A SolidWorks schematic of such a digital microfluidicultiplexer is shown in Fig. 1(a) and (b). The structure is comprised

f an underlying x-channel linear electrode array and an overlying-channel linear electrode array. The orientations of these arraysre made to be perpendicular, such that (with electrowetting-basedystems, for example) x-channel voltages can create net surface ten-ions on droplets perpendicular to the x-electrodes, and y-channeloltages can create net surface tensions on droplets perpendicu-

ar to the y-electrodes. The conductive electrodes are fabricated onnsulating substrates and have a width (w) and a periodic centre-to-entre pitch (p) as shown in the figure. This bi-layer configurations shown magnified in Fig. 1(b).

Fig. 1. SolidWorks schematic views of a portion of the proposed digital microfluidicmultiplexer design are shown with an (a) orthographic projection and (b) magnifiedisometric view.

The multiplexer gap between the electrode arrays forms theregion in which microdrop sampling, actuation, and control canbe carried out. The spatially dependent differential conductanceassociated with arbitrary fluid distributions are measured using thelinear electrode arrays, as the regions of overlap between x- and y-electrodes without electrolyte will exhibit negligible conductancewith

Gmin = 0, (1)

whereas, the regions of overlap between x- and y-electrodes withelectrolyte will exhibit higher levels of conductance. The maximumpossible conductance,

Gmax = �w2

d, (2)

is obtained when the fluid fully covers the w2 area of intersectingxy electrodes. An arbitrary xy multiplexer location will have a con-ductance varying between these minimum and maximum values,

the microdrop.For digital microdrop routing algorithms it is necessary to

have an effective means of extracting both droplet positions andsizes. Such a system is demonstrated here by way of a numerical

d Actuators A 152 (2009) 13–20 15

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J. Nichols et al. / Sensors an

rea-weighting algorithm using circular microdrop profiles. Thisimplified system can be characterized by a total of 3N parametersor a system of N microdrops. The algorithm takes as its input the

easured two-dimensional discrete conductance distribution Gxy

nd computes an output consisting of each microdrop’s: (i) cen-re (x0,y0) location and (ii) radius r0. These quantities are definedere as unitless values on the grid having been normalized withespect to the electrode pitch p. A numerical series sum over all y-hannels is executed for each x-electrode conductance, producing ane-dimensional array of the total conductance of each x-channel,

x =n∑

y=1

Gxy = �w

d· Lx = Gmax · Lx

w. (3)

Similarly, a numerical series sum over all x-channels is carriedut for each y-channel conductance, producing a one-dimensionalrray of y-channel summed conductances,

y =m∑

x=1

Gxy = �w

d· Ly = Gmax · Ly

w. (4)

The total conductance associated with the microdrop is given by

t =m∑

x=1

Gx =n∑

y=1

Gy = Gmax · At

w2. (5)

In these expressions, Lx and Ly, when multiplied by w, give thereas of overlap between the microdrop and the respective x- or-electrode, and At is the total microdrop area covering the regionsf overlapped electrodes. The numerical execution is simplified byntroducing dimensionless and normalized summed conductancesefined for each circular microdrop as

x = Gx

Gmax, (6)

y = Gy

Gmax, (7)

nd

t = Gt

Gmax. (8)

Having collected the discrete two-dimensional grid of differ-ntial conductances Gxy and calculated the normalized summedonductances gx, gy, and gt from this grid, the numerical algorithms completed with the computation of the microdrop centre andadius from

0 =m∑

x=1

x · gx

gt, (9)

0 =n∑

y=1

y · gy

gt, (10)

nd

0 =√

1�

· gt, (11)

espectively. The centre location is found here from weightedositional averages of the x- and y-channel normalized summedonductances gx and gy, in proportion to the total normalized con-uctance gt, and the radius is calculated from the normalized area

f the circular microdrop. As before, locations are defined in termsf unit-multiples of pitch p with integer positions correspondingo the middle of each respective electrode. With these definitionshe (x0,y0) and r0 results are recorded as generalized and unitlessuantities, as the overlapping electrode area w2 cancels in the gt

Fig. 2. Flowchart for the employed conductance sampling algorithm. The input sam-pled conductance matrix is extracted from the prototype with a high-impedance(greater than 10 M�) DC measurement and processed with the presented MATLAB-based algorithm.

normalization process, and unit-multiples of the pitch p give aneffective conducting area of p2 = 1.

Execution of the algorithm described above may be complicatedby complexity issues relating to the presence of multiple micro-drops in the system. The algorithm described above incorporatesweighted positional averages which, in the presence of multipledrops, will give erroneous intermediate centralized averages. Toovercome this, a pre-processing step is added to the algorithm afterthe collection of the measured two-dimensional conductance gridGxy and before the calculation of conductance sums. In this a prioristep, the nonmonotonic nature of the measured data sets is inves-tigated, and the presence of peaks and troughs in the microfluidicconductance is used as a decisional factor in sectioning the Gxy datainto separate two-dimensional conductance grids. A Gxy grid is cre-ated for each individual microdrop in isolation, and the subsequentalgorithm steps, displayed in Fig. 2, are independently applied toeach of these microdrop Gxy grids. The overall process can be imple-mented with fluid distributions of coalescing microdrops, such asthose of Fig. 3(a), and separate microdrops, such as those of Fig. 3(b).

The operation of the conductance sampling algorithm ispresented in Fig. 3(b) for a hypothetical microfluidic system incor-porating two separate microdrops. The first microdrop has a radiusof r01 = 5 and centre at (x01,y01) = (22,8), while the second microdrophas a radius of r02 = 3 and centre at (x02,y02) = (10,30). A cylindri-cal profile is used to represent the physical microdrop area in themodel, and the theoretical discrete conductance values, Gxy, arecalculated for the two-dimensional grid. Each Gxy value gives aproportional measure for the degree of microdrop area overlapat that position, and the resulting discrete conductance distribu-tion is shown. The two Gxy grids (each associated with one of thetwo microdrops) are then processed by the conductance samplingalgorithm, and the weighted positional averages are calculated.The centres and radii of each microdrop, with (x01,y01) = (22,8) and

r01 = 5 for the first droplet and (x02,y02) = (10,30) and r02 = 3 for thesecond of droplet, are equal to the initial values of these hypothet-ical microdrops (within a 2% accuracy). These theoretical modelresults, shown in Fig. 3(b), are in good agreement with the initialmicrodrop attributes.

16 J. Nichols et al. / Sensors and Actuators A 152 (2009) 13–20

Fig. 3. Theoretical results for hypothetical microdrop fluid profiles with (a) an arbi-trary fluid distribution and (b) two separated microdrops in the digital microfluidicmultiplexer. The results are shown as discrete conductance surface plots.

Fig. 4. Photographs of (a) the bottom (x-channel) electrode layer and (b) a micro-drop on this layer are shown. The electrode layer of the device as shown incorporates40 linear channels and is 16 mm wide. The copper electrodes have a width of

w = 200 �m and a centre-to-centre pitch of p = 400 �m and are patterned (via UVlithographic exposure and FeCl wet etching) on an insulating epoxy substrate. Thetop and bottom layers are positioned with a central gap of d = 150 �m separatingthem.

2.2. Sampling structure

The bottom (x-channel) layer of the constructed digital microflu-

idic multiplexer structure is shown isolated in the photographsof Fig. 4(a) and (b). The structure is comprised of periodic cop-per electrodes with a width of w = 200 �m and a centre-to-centrepitch of p = 400 �m fabricated on an insulating epoxy substrate.

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J. Nichols et al. / Sensors an

he identical top (y-electrode) layer is positioned on top of theottom layer in a perpendicular orientation with a central gap of= 150 �m separating them. The electrode patterns are designed

uch that the copper electrode lines transition easily to the copperontact pads. The copper contact pads are made to be of a suffi-ient length to protrude from the overlapping central multiplexeregion, and electrical contacts are established from each contactad to the electrical sampling system. Conductance sampling is

ig. 5. Experimental results for a single microdrop within the digital microfluidic multipleurface, and (c) extracted microdrop model overhead view. Conductance values are samonductances for the background level are below the measurable limit of the apparatus w

ators A 152 (2009) 13–20 17

carried out through the measurement of conductance at each differ-ential xy channel pair, and the resulting discrete two-dimensionalGxy conductance grid is recorded.

3. Conductance sampling results

The conductance sampling process within the digital microflu-idic multiplexer is tested first for a system with one microdrop.

xer are shown as a (a) discrete conductance surface, (b) extracted microdrop modelpled with a high-impedance probe by way of the electrically contacted bias lines.ith Gmin < 0.1 �S.

1 d Actu

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8 J. Nichols et al. / Sensors an

he microdrop is comprised of an NaCl electrolytic solution with2.8 M electrolyte concentration (with a conductivity measured toe approximately � = 0.2 S/m). The microdrop is dispensed betweenhe perpendicular x- and y-electrode plates, and conductance sam-

ling of the differential Gxy combinations is carried out. The discretexperimental sampling results are shown in Fig. 5(a) as a functionf x- and y-channel indices. The distribution here shows a defini-ive nonmonotonic profile at the location of the microdrop, withonductance values in the two-dimensional array varying from the

ig. 6. Experimental results for two microdrops within the digital microfluidic multiplexurface, and (c) extracted microdrop model overhead view. Conductance values are samonductances for the background level are below the measurable limit of the apparatus w

ators A 152 (2009) 13–20

background minimum value Gmin = 0 (below the 0.1 �S measurablelimit of our apparatus) to the maximum value at the centre of themicrodrop, Gmax = 40 �S. The algorithm introduced in the previoussection is then applied to the discrete sampled values, and the nor-

malized summed conductances are used to extract the location andsize of the microdrop. The results are shown visually in Fig. 5(b)and (c). The measured microdrop is characterized by a location of(x0,y0) = (30.0,26.6) and a radius of r0 = 3.6, and these experimentalresults are in qualitative agreement with overhead observations of

er are shown as a (a) discrete conductance surface, (b) extracted microdrop modelpled with a high-impedance probe by way of the electrically contacted bias lines.ith Gmin < 0.1 �S.

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he investigated microdrop. As described in Section 1, these over-ead measurements are particularly challenging in multi-layeredrchitectures and limited in accuracy due to the presence of theverlying metal electrode array. The conductance sampling processemonstrated here will have an ultimate measurement resolutionhat is set by the transverse dimensions of the multiplexer structurei.e. the electrode width w and pitch p).

A subsequent investigation is carried out with the proposed con-uctance sampling method for a system containing two separateicrodrops. The microdrops are dispensed into the central gap of

he digital microfluidic multiplexer, and electrical sampling is car-ied out to extract the two-dimensional conductance grid Gxy. Theiscrete experimental sampling results are shown in Fig. 6(a)–(c).onmonotonic profiles are again exhibited in the regions of theicrodrops shown here, as the conductance values range frombackground of Gmin = 0 to maximum values of Gmax1 = 34.5 �S

nd Gmax2 = 40.0 �S at the centres of each of the two microdrops.he results are pre-processed and separate sampling algorithmsre carried out for the microdrops to give the resulting locationsnd radii. For the first (lower maximum conductance) microdropcentre location of (x01,y01) = (9.5,10.5) and radius of r01 = 2.4 areetermined, and for the second (higher maximum conductance)icrodrop a centre location of (x02,y02) = (17.4,10.8) and radius of

02 = 2.6 are determined. As was the case for Fig. 5, the experimen-al results here are in qualitative agreement with overhead imagingbservations, though the challenges of imaging through the topetal electrode array (being a major motivation for this work) again

imit the accuracy of these visual observations.

. Conclusion

In this work, a system for in situ conductance sampling wasresented. It was shown that a digital microfluidic multiplexerrchitecture could be implemented with a conductance samplinglgorithm to extract the state of microfluids within the system. Theentres and radii of microdrops were accurately measured fromiscrete conductance states of differential combinations of per-endicular x- and y-channels, and the locations and sizes of theorresponding microdrops were successfully extracted. The ulti-ate resolution for this conductive fluid sampling system is limitedainly by the transverse structural dimensions of the multiplexer

tructure (the electrode width and pitch), and these integrated sys-ems will, therefore, be well-suited to future investigations of digitaluid actuation incorporating microscopic scales and highly parallelrchitectures.

cknowledgements

The authors wish to acknowledge financial support from theatural Sciences and Engineering Research Council of Canada

NSERC) and technical support from Mr. R. LaMountain.

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Biographies

Jacqueline Nichols is currently enrolled in a BASc degree in the School of Engineer-

ing at the University of British Columbia Okanagan.

Ali Ahmadi completed his BSc in mechanical engineering from the University ofTehran in 2004. In 2007, he completed his MSc degree from the same universityafter having researched fluid properties in spray breakup modeling. In September2007, he commenced his PhD degree in the School of Engineering at the University

2 d Actu

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Alberta in 1998, and his PhD in electrical engineering from the University of Alberta

0 J. Nichols et al. / Sensors an

f British Columbia Okanagan. He is currently researching microfluidic dynamics inigital microfluidic devices.

ina Hoorfar graduated from the University of Tehran in 1998. She received herASc and PhD degrees in mechanical engineering from the University of Toronto

n 2001 and 2005, respectively. Currently, she is an assistant professor at School of

ngineering, the University of British Columbia Okanagan. Her research involves theetermination of interfacial properties using digital imaging.

omayoun Najjaran received his MASc and PhD degrees in mechanical engineeringrom the University of Tehran in 1996 and University of Toronto in 2002, respectively.e worked the National Research Council (NRC) Canada 2003 to 2006. Currently, he

ators A 152 (2009) 13–20

is an assistant professor in the School of Engineering at the University of BritishColumbia Okanagan. His expertise includes robotics, mechatronics and control sys-tems.

Jonathan F. Holzman received his BSc in engineering physics from the University of

in 2003. In 2004 and 2005 he worked as a Postdoctoral Research Fellow in the Depart-ment of Information Technology and Electrical Engineering at the Swiss FederalInstitute of Technology (ETH) in Zürich, Switzerland. He is currently an assistant pro-fessor in the School of Engineering at the University of British Columbia Okanaganin Canada.