NIST Special Publication 260-184

Method for Measuring the Volume of 

Nominally 100 μm Diameter Spherical 

Water-in-Oil Emulsion Droplets

John A. Dagata

Natalia Farkas

John A. Kramar

This publication is available free of charge from:

http://dx.doi.org/10.6028/NIST.SP.260-184

NIST Special Publication 260-184

Method for Measuring the Volume of 

Nominally 100 μm Diameter Spherical 

Water-in-Oil Emulsion Droplets

John A. Dagata

Natalia Farkas

John A. Kramar

Engineering Physics Division

Physical Measurement Laboratory

This publication is available free of charge from:

http://dx.doi.org/10.6028/NIST.SP. 260-184

February 2016

U.S. Department of Commerce

Penny Pritzker, Secretary

National Institute of Standards and Technology

Willie May, Under Secretary of Commerce for Standards and Technology and Director
Certain commercial entities, equipment, or materials may be identified in this

document in order to describe an experimental procedure or concept adequately.

Such identification is not intended to imply recommendation or endorsement by the

National Institute of Standards and Technology, nor is it intended to imply that the

entities, materials, or equipment are necessarily the best available for the purpose.

National Institute of Standards and Technology Special Publication 260-184 

Natl. Inst. Stand. Technol. Spec. Publ. 260-184, 23 pages (February 2016) 

CODEN: NSPUE2

This publication is available free of charge from: 

http://dx.doi.org/10.6028/NIST.SP.260-184
ii 

ABSTRACT

This report describes an equivalent-volume measurement method using optical microscopy for 

estimating the mean volume of nominally 100 μm diameter spherical droplets. The droplets are the 

aqueous phase of proprietary water-in-oil emulsions used in a commercial droplet digital polymerase 

chain reaction DNA quantitation system. This method is based on the transition of spherical droplets 

to polygonal structures at constant volume. Close-packed spherical emulsion droplets confined 

within a microfluidic channel transform into a space-filling polygonal lattice as the oil phase 

evaporates. The microfluidic channel height determines the resulting lattice dimensions such that the 

mean droplet volume is traceable to the unit of length. 

KEYWORDS

Droplet digital polymerase chain reaction (ddPCR) 

Droplet volume 

Optical microscopy

Plateau border channels

Princen’s model 

Water-in-oil emulsions
iii

TABLE OF CONTENTS

Abstract................................................................................................................................................ ii

Keywords............................................................................................................................................. ii

Table of Contents ............................................................................................................................... iii

List of Tables...................................................................................................................................... iv

List of Figures..................................................................................................................................... iv

Introduction ......................................................................................................................................... 1

Measurand ......................................................................................................................................... 1

Dilute method ................................................................................................................................... 1

Concentrated method ........................................................................................................................ 1

Calibration ........................................................................................................................................... 3

Calibration of pixel size .................................................................................................................... 3

Dimensional conformance of the Ibidi microfluidic channels by white-light interferometry .......... 4

Channel-to-channel variation ........................................................................................................ 5

Top and bottom surface variation ................................................................................................. 5

Traceable optical measurement of the microfluidic channel height ................................................. 6

Membrane deformation ................................................................................................................. 7

Measurement assurance .................................................................................................................... 8

Measurement ....................................................................................................................................... 9

Measurement of spherical droplets under dilute conditions ............................................................. 9

Measurement of the hexagonal unit cell under concentrated conditions ........................................ 10

Determination of the volume fraction ............................................................................................. 12

Assumption of constant droplet volume ......................................................................................... 14

The unit cell as a quasi-equilibrium structure ................................................................................. 14

Uncertainty analysis.......................................................................................................................... 16

Dilute method ................................................................................................................................. 16

Concentrated method ...................................................................................................................... 17

Type A: Sample emulsion preparation ........................................................................................ 17

Type A: Manufacturing ............................................................................................................... 17

Type A: Measurement ................................................................................................................. 17

Type B: Sample size distribution ................................................................................................. 17

Type B: Pixel calibration ............................................................................................................ 17

Type B: Estimation of VVHEX ........................................................................................................ 17

Type B: Manufacturing ............................................................................................................... 18

Type B: Volume fraction ............................................................................................................. 18

Combined Relative Standard Uncertainty .................................................................................. 19

Validation........................................................................................................................................... 21

Comparison of Results from the Dilute and Concentrated Methods .............................................. 21

Comparison with Literature Results ............................................................................................... 21

References .......................................................................................................................................... 22
iv 

LIST OF TABLES

Table 1: NIST polystyrene latex (PSL) sphere SRMs for optical microscope calibration ................... 3

Table 2: Pixel calibration results for optical microscope with three objectives ................................... 3

Table 3: WYKO Step height for Ibidi plates. ....................................................................................... 5

Table 4: 10X optical cross section results for channel height of channels 3 and 4 .............................. 7

Table 5: 5X optical cross section results for step-height (total thickness) ........................................... 7

Table 6: Samples ................................................................................................................................... 9

Table 7: Summary of mean spherical droplet volume as VVSPH = φD·VVHEX measurements ................ 15

Table 8: Uncertainty budget for dilute method of determining mean droplet diameter ..................... 16

Table 9: Uncertainty budget for concentrated method of determining mean droplet diameter .......... 19

Table 10: Comparison of mean emulsion droplet diameter ................................................................ 21

Table 11: Evolution of mean droplet diameter and volume estimates ................................................ 21

LIST OF FIGURES

Figure 1: Emergence of lattice domain structure across a microfluidic plate....................................... 2

Figure 2: Schematic of the Ibidi microfluidic channel plate................................................................. 4

Figure 3: Cross sectional image of the microfluidic channel of nominally 400 μm channel height. ... 6

Figure 4: Optical image and droplet size distribution under dilute conditions. .................................. 10

Figure 5. Evolution of a close-packed droplet lattice in the microfluidic channel. ............................ 10

Figure 6. Interpretation of optical microscope images of the emulsion droplet tessellation. ............. 11

Figure 7. Determination of the volume fraction using Princen’s model ............................................. 13

Figure 8. Measurement of the hexagonal unit cell out under quasi-equilibrium conditions. ............. 13

Figure 9. Relationship between volume fraction and curvature parameter, r/a .................................. 14
1 

INTRODUCTION

We report here two test methods for measuring the volume of emulsion droplets produced by the 

Bio-Rad QX100 digital droplet polymerase chain reaction (ddPCR) system with a DG8 emulsifying 

cartridge [1]. The dispersed aqueous phase of the water-in-oil emulsion consists of spherical droplets 

about 100 μm in diameter within which DNA substrates are condensed along with proprietary PCR 

reagents. Both methods are intended to provide a traceable and statistically meaningful volume 

determination of the droplets in order to certify the DNA concentration, i.e., the initial number of 

copies of a specific DNA target amplified in a PCR reaction. Adequate specification of the test 

material includes the nature of the DNA, the proprietary reagents used in the formulation, and the 

system used to generate the emulsion.

Measurand

The intended measurand, VV�SPH, is the mean equivalent spherical volume of aqueous emulsion 

droplets, VV�SPH = 4/3·π·R3

, where R = d/2 is the radius and d the diameter of the droplet. Both 

methods use optical microscopy to obtain this mean volume of these nominally 100 μm diameter 

spherical droplets. 

Dilute method

Assuming that the droplet shape is spherical, the radius R, or diameter d, can be estimated directly 

from optical measurements of dilute droplets within a microfluidic channel of an Ibidi #80621 

μ-Slide VI-flat hydrophobic microfluidic plate [2]. Optical microscopy is generally considered an 

appropriate method for determining the mean volume of a spherical droplet existing in an emulsion. 

It seems a simple matter to measure the diameter of (nearly) perfectly spherical droplets in solution 

[3,4,5]. However in the case of this proprietary emulsion, there are concerns that 1) buoyancy of the 

droplets deforms the droplets so that their shape is no longer spherical; 2) there is a lack of optical 

contrast at the boundaries of the droplets due to multiple oil-water interfaces, making edge 

determination highly uncertain; 3) particle-particle contact makes definition of an area-equivalent 

spherical diameter difficult; and 4) individual-particle diameter measurements become time 

consuming for statistically meaningful sampling. Previous work suggests a deviation of 3 % to 4 % 

from sphericity which introduces a large error into uncertainty analysis [5].

Concentrated method

We propose an alternative approach to droplet volume measurements. Close-packed spherical 

emulsion droplets confined within a microfluidic channel transform into a space-filling polygonal 

lattice as the oil phase evaporates. The microfluidic channel height determines the resulting lattice 

dimensions such that the mean droplet volume is traceable to the unit of length. An optical 

micrograph of this lattice structure is presented in Figure 1.

The lattice is further defined as a hexagonal unit cell. Droplet volume is conserved during this shape 

transformation, which we write as VV�SPH = φD·VV�HEX, where the volume of the hexagonal unit cell, 

reduced by the volume fraction of dispersed (aqueous) droplet phase, φD, yields an estimate for the 

mean spherical droplet volume in solution. The latter term accounts for the hexagonal unit cell 

encompassing the total volume of both aqueous and oil phases, i.e., φD + φC = 1, with φC the 

continuous (oil) phase. 
2

Figure 1: Emergence of lattice domain structure across a microfluidic plate.

Channel dimensions (L×W×H) of the Ibidi #80621 μ-Slide VI-flat hydrophobic are nominally 

17 mm × 3.8 mm × 400 μm. The mean diameter of the self-assembled aqueous emulsion droplets is on the 

order of 100 μm.

Calculation of VV�HEX = NL

-1

·h·AA̅

HEX is straightforward and depends on the number of layers, NL, in the 

lattice formed within a microfluidic channel of height, h, and the hexagonal cross- sectional area, 

AA̅

HEX. Under steady-state temperature and pressure conditions, the microfluidic channel height

represents the space between fixed boundaries which uniquely determines the hexagonal unit-cell. 

Thus the mean droplet volume is ultimately traceable to the unit of length by determination of the 

microfluidic channel height.

We are interested in the limit in which φD → 1, i.e., the condition corresponding to almost complete 

draining of the oil phase. The remaining oil phase is present in so-called Plateau borders, the 

collapsed border channels at the edges and interstices of tessellated droplets. Considerable effort has 

been made to characterize geometric and force balance requirements under these conditions for 

foams and emulsions [6,7,8].
3

CALIBRATION

The height of the microfluidic channel, h, is the essential link between the mean droplet volume and 

the standard unit of length. This link is established with NIST standard reference materials to 

calibrate the pixel size of an optical microscope/camera system. This system is used to determine the 

mean channel height and then, in an independent set of measurements, directly obtain the 

dimensions of the hexagonal unit cell. White-light interference microscopy was performed in order 

to validate the quality of the cross-sectional measurements and provide additional geometrical 

information about the channels.

Calibration of pixel size

A Mitutoyo long-working distance reflection optical microscope equipped with a (1600 × 1200)

pixel Pixelink CCD camera was used to establish a mean traceable value of the channel height. Pixel 

calibration for 5X, 10X, and 50X microscope objectives used in this study was performed using 

NIST SRM polystyrene latex (PSL) spheres. Highly ordered 2Dimensional lattices of PSL spheres 

were prepared on mica substrates and line averages of 10 or more spheres were obtained from 

micrographs using ImageJ analysis software [9]. The PSL SRMs are described in Table 1. The pixel 

calibration results are summarized in Table 2.

Table 1: NIST polystyrene latex (PSL) sphere SRMs for optical microscope calibration

SRM Nominal diameter Certified diameter Year issued

1690 1 μm 0.895 ±0.005 μm 1982

1692 3 μm 2.982 ±0.016 μm 1991

Table 2: Pixel calibration results for optical microscope with three objectives

Results of Pixel Size Measurements 

Objective Mean SD CVa

50X 0.0786 μm 0.000236 μm 0.03 %

10X 0.3943 μm 0.000394 μm 0.10 %

5X 0.7877 μm 0.000315 μm 0.04 %

a CV ≡ 100 ∙ SD/Mean

Dimensional analysis was carried out based on pixel counts initially and converted into a reference 

unit of length using the above information before final data processing. Measurement uncertainty 

associated with the calibration spheres is reported in the NIST SRM Certificates of Analysis [10,11]

and is about 0.5 % for both diameter spheres. An estimate of pixel calibration at 10X is obtained by 

recognizing that the mean diameter of one calibration sphere is 10 pixels and an uncertainty arises in 

the two outermost pixels of the imaged spheres on the scale of the calibration standard. Thus the 

uncertainty is (2/10)×(0.5 %) = 0.1 %. This estimate agrees with the measured relative standard 

deviation of a mean pixel with the 10X objective.
4

Dimensional conformance of the Ibidi microfluidic channels by white-light interferometry

Use of a global mean value for the height of the microfluidic channel is based on the assumption that 

local variation in the nominal 400 μm height is insignificant: 1) along the 17 mm length and across 

the 3.8 mm width of a given channel; 2) among the channels of a given plate; and, 3) for all plates 

from the same lot number. Figure 2 provides a schematic of the Ibidi microfluidic plate.

Figure 2: Schematic of the Ibidi microfluidic channel plate.

WYKO interference microscope measurements were made along the left and right channel edges for all six 

channels. Mean total height of the nominally 400 μm channel plus 200 μm thick membrane step height is 

reported. The step height was created by carefully removing the membrane from the channel. Possible 

deformation of the membrane due to filling and evaporation of the emulsion oil phase was also 

investigated.

The WYKO surface profiler [12] is a non-contact optical profiler used to measure surface roughness 

and step height. Vertical scanning interferometry mode was used for the measurements reported 

here. In this technique, unfiltered (white) light is separated by a beam splitter into two paths. 

Reflected light from a reference mirror recombines with light reflected from the sample surface as a 

calibrated piezoelectric transducer scans the focal point of the microscope, producing a set of 

interference fringes at best focus. Fringe analysis of images collected along a sequence of focal 

points provides the mean height difference of features on the sample surface and average roughness 

of the entire sample or specific sub-regions.

The WYKO microscope was calibrated using an in-house (10.55 ±0.05) μm step-height standard. 

The microscope was used with a 2.5X objective with 0.5 reduction lens, providing a field of view of 

(4.8 × 3.7) mm2 along the X and Y axes, respectively. The CCD camera contained (736 × 480)

pixels. Step heights were collected and the data plane fit and averaged over all pixels.
5

Channel-to-channel variation

The WYKO instrument was used to sample plate-to-plate and channel-to-channel variation of the 

step height, i.e., the sum of the channel height and the membrane thickness, at locations along the 

left and right sides of the channel by gently removing the membrane with tweezers. Images were 

taken along both sides of three channels from two Ibidi #80621 (lot number 140203/2) plates each.

Six locations per channel were measured for a total of N = 36 locations. The mean step height results 

are summarized in Table 3.

Table 3: WYKO Step height for Ibidi plates.

The field of view at each location is 4.8 mm × 3.7 mm

Left-hand side of channel Right-hand side of channel

Plate Channel Locations Mean SD Locations Mean SD

4 1

3

5

3

3

3

592.0 μm

596.2 μm

596.3 μm

1.3 μm

0.5 μm

0.7 μm

3

3

3

601.0 μm

601.2 μm

598.4 μm

0.4 μm

1.0 μm

2.6 μm

5 2

4

6

3

3

3

601.4 μm

599.1 μm

603.5 μm

0.8 μm

0.6 μm

0.3 μm

3

3

3

603.5 μm

601.7 μm

605.7 μm

0.5 μm

0.3 μm

0.3 μm

Subtotals 18 598.1 μm 3.8 μm 18 601.9 μm 2.3 μm

Combined 36 600.0 μm 3.1 μm

The variation from left to right across the width of the channel is only 0.25 % of the channel height. 

However, this small difference between the left- and right-hand side step heights, 598 μm vs. 

602 μm, obscures a systematic channel-to-channel variation across the plate as seen in the histogram 

presented in Figure 2. A rather large left-right discrepancy was obtained routinely for channel #1 and 

an above-average step height was obtained for channel #6. Since channels #3 and #4 exhibited the 

best left-right uniformity, these channels were used for all droplet volume determination based on 

the hexagonal unit cell. However, no statistically significant differences in estimated droplet volume 

were observed when channels #2 and/or #5 were used.

Top and bottom surface variation

A key assumption of the proposed method requires that the top and bottom surfaces of the 

microfluidic channel are fixed boundaries. These boundaries allow the parameters NL, h, and AA̅

HEX of 

the hexagonal unit cell to be defined. In addition to requiring that the left- and right-hand side of the 

channels are sufficiently constant to make the use of a mean channel height possible, variations of 

the local channel height due to surface roughness and flatness of the top and bottom surfaces must be 

investigated. Measurement of the top membrane surface of two channels using the WYKO 

instrument indicated a surface roughness, Rq = 0.27 μm. The flatness across a central 3 mm portion 

of the 3.8 mm wide channel, was < 0.2 μm or essentially unmeasurable.

In order to make WYKO measurements of the bottom channel surface, the membrane was removed 

with tweezers. This surface has occasional tool marks running parallel to the long channel axis, 

though not as obvious as the tool marks observed along the channel side walls shown in Figure 3. 

For the bottom channel surface, Rq = 0.60 μm and the flatness was again too small to estimate. These 

results are for low spatial frequencies only.
6

Figure 3: Cross sectional image of the microfluidic channel of nominally 400 μm channel height.

From top to bottom, dashed yellow lines identify the nominally 200 μm thick membrane with vertical 

crazing, the side of the channel with a identifiable by horizontal tool marks, and finally the base plate 

which is out of focus in this image.

Traceable optical measurement of the microfluidic channel height

The height of the microfluidic channel is the essential link between the mean droplet volume and the 

standard unit of length. Determination of a mean channel height is based on sampling plates from the 

same lot number. For this measurement, the 200 μm thick membrane making up the upper surface of 

the channel was carefully removed with tweezers and each plate was cross sectioned along the long 

axis of every channel to be tested. Both sides of the channel were then imaged edge-on. One such 

image is shown in Figure 3, where the nominally 400 μm channel height can be associated with 

grooved tool marks running horizontally along the side of the channel. The intersection of the 

channel side with the nominally 200 μm thick membrane, at the upper interface, and with the base of 

the plate (identified by an optical sidewall reflection), at the lower surface, are indicated by yellow 

dashed lines in the figure. Crazing of the membrane, perpendicular to the tool marks makes it 

particularly easy to identify the upper interface.

Three Ibidi #80621 (lot number 140203/2) plates were selected and two to four channels per plate 

were evaluated. Images were taken at ten locations along the left- and right-hand sides of each 

channel. Detailed measurement results for the channel height obtained at 10 times (10X)
7

magnification are presented in Table 4. Detailed measurement results for the total thickness obtained 

at 5X magnification are presented in Table 5.

Table 4: 10X optical cross section results for channel height of channels 3 and 4

Results in italics are not included in statistical summaries.

Left-hand side of channel Right-hand side of channel

Plate Channel Locations Mean SD Locations Mean SD

1 1

2

3

4

5

5

5

5

389.4 μm

391.7 μm

392.6 μm

394.7 μm

3.8 μm

1.2 μm

1.0 μm

2.3 μm

5

5

5

5

390.6 μm

393.5 μm

393.1 μm

393.1 μm

3.1 μm

2.3 μm

2.3 μm

1.4 μm

2 2

3

4

5

5

5

389.0 μm

390.6 μm

390.6 μm

6.7 μm

2.5 μm

3.5 μm

3 3

4

5

5

396.1 μm

395.9 μm

0.8 μm

1.2 μm

5

5

395.1 μm

391.2 μm

0.7 μm

2.5 μm

Subtotals 30 393.4 μm 2.3 μm 20 393.1 μm 1.4 μm

Combined 50 393.3 μm 1.9 μm

Table 5: 5X optical cross section results for step-height (total thickness)

Left-hand side of channel Right-hand side of channel

Plate Channel Locations Mean SD Locations Mean SD

1 1

2

3

4

2

5

5

4

598.2 μm

599.4 μm

598.3 μm

597.6 μm

3.9 μm

1.7 μm

0.4 μm

0.8 μm

5

2

4

600.3 μm

600.6 μm

600.0 μm

1.0 μm

1.7 μm

2.1 μm

2 2

3

4

5

4

2

602.2 μm

597.0 μm

599.8 μm

3.8 μm

0.6 μm

0.6 μm

2

5

4

603.7 μm

601.8 μm

597.2 μm

1.7 μm

4.5 μm

1.7 μm

3 3

4

3

2

600.2 μm

601.0 μm

0.8 μm

1.1 μm

1

5

599.4 μm

600.0 μm 0.7 μm

Subtotals 32 599.3 μm 1.6 μm 28 600.4 μm 1.7 μm

Combined 60 599.8 μm 1.7 μm

There are no statistically significant differences in channel height or total thickness between the leftand right-hand sides of the channels. This step-height result agrees well with the WYKO step-height 

measurement, giving confidence to the mean channel height determination.

Membrane deformation

The mean membrane thickness of the microfluidic channel can be estimated from cross-sectional 

optical and WYKO results given in the above Tables: 206.5 ±2.0 μm. Because the membrane is 

relatively thin and composed of a relatively soft plastic material, it is prudent to determine the 

deformation induced during filling and drying of concentrated emulsion. The intact membrane 

covering two separate channels, one a #3 channel and the other a #4 channel, was imaged using the 

WYKO instrument. The surface roughness, Rq, and flatness across the central 3 mm portion of the 
8

3.8-mm wide membrane were determined. Channels were then filled with emulsion solution and 

allowed to sit at ambient temperature and pressure for two hours before the parameters were again 

measured. A slight distortion of the membrane developed. For the two cases, membrane flatness 

before filling was not measurable above the surface roughness. After filling, one side of the 

membrane was raised relative to other by δ ≈ 0.25 μm in one case and δ ≈ 0.5 μm in the other. This 

is illustrated in Figure 2. Data along either edge of the cross section is artificially distorted by the

plane fitting algorithm.

Measurement assurance

The instruments used in this study are located in laboratories that are temperature and humidity 

controlled with long-term conditions maintained at 23 ±1 o

C and 28 ±8 % relative humidity. These 

conditions are monitored on a daily basis and measurements are not performed if conditions are 

outside these limits. This usually only occurs during annual site-wide maintenance events. Once the 

room environment has returned to these normal operating conditions, a period of 3 days is given 

before measurements are resumed.

For the measuring instruments covered in this document, validation of instrument performance 

within specified operational guidelines is carried out by performing a series of test measurements 

using a series of well-established certified reference materials produced, procured, and maintained 

by NIST staff.

The mean pixel size of the Mitutoyo optical microscope was checked just prior to recording of 

measurements using an in-house magnification standard which had previously been calibrated 

against the NIST PSL SRMs 1690 and 1692. Often the calibration was checked again at the end of 

the measurements. A control chart of these measurements is maintained in the laboratory housing the 

microscope.

Traceability is established through the use of calibration artifacts. Each instrument is therefore 

considered to be covered by “calibrate on use” requirements, i.e., each daily period a measurement 

process is executed.
9

MEASUREMENT

Emulsions were freshly prepared using a Bio-Rad QX100 droplet digital polymerase chain reaction 

(ddPCR) system and DG8 cartridge according to the manufacturer’s specifications using its 

proprietary materials and measured on the same day. [1] Ibidi #80621 μ-Slide VI-flat hydrophobic 

microfluidic plates [2] from the same lot number were used for all droplet measurements.

Samples are given a unique sequence to identify the source, the origin of the DNA, the proprietary 

reagent used to generate the emulsion (see below), and a preparation date (e.g., 02/04/2015). Two 

types of DNA sample, human genomic [13] and a bacterial artificial chromosome containing 

cytomegalovirus (CMV) DNA [14], were formulated using one of two proprietary “mastermix”

reagents: “Bio-Rad ddPCR Supermix for Probes” [15] and “ddPCR Supermix for Probes (no 

dUTP)” [16]. We refer to these mastermixes containing, or not containing, deoxyuridine 

triphosphate, as “with dUTP” and “no dUTP”.

These mastermixes may have different chemical composition and physical properties that may affect 

the mean droplet size produced within the emulsifying cartridge. The continuous (oil) phase 

consisted of proprietary QX100 droplet generator oil available from the manufacturer. Table 6 lists 

the materials used to characterize the droplet volume measurement methods described in this report.

Table 6: Samples

TEST ID Sample ID Date DNA Mastermix

2013 645-1-12/19/2014 12/19/2014 Human genomic with dUTP

2013 645-1-03/17/2015 03/17/2015 Human genomic with dUTP

2013 645-1-03/20/2015 03/20/2015 Human genomic with dUTP

2013 645-2-02/04/2015 02/04/2015 Human genomic no dUTP

2013 645-2-02/10/2015 02/10/2015 Human genomic no dUTP

2013 645-2-02/12/2015 02/12/2015 Human genomic no dUTP

2014 645-3-02/24/2015 02/24/2015 CMV with dUTP

2014 645-3-02/27/2015 02/27/2015 CMV with dUTP

2014 645-3-03/03/2015 03/03/2015 CMV with dUTP

2014 645-4-03/11/2015 03/11/2015 CMV no dUTP

2014 645-4-03/12/2015 03/12/2015 CMV no dUTP

Measurement of spherical droplets under dilute conditions

Previous estimates of the mean droplet volume were obtained from optical measurements of droplet 

diameter of highly dilute, 2D droplet arrays [3,4,5]. For this measurement, the emulsion must be 

diluted carefully with the oil phase to avoid coalescence of the droplets. We follow the procedure 

given in the literature by carrying out dilution within the microfluidic channel. First, 40-μL of 

oil-only solvent is introduced into a channel port followed by gentle injection of a small volume of 

the emulsion mixture. Rafting into 2D close-packed arrays occurs spontaneously or with slight 

agitation of the plate. Optical images were taken with the 10X microscope objective. An example of 

a highly dilute droplet array is shown in Figure 4a. As the volume of injected emulsion is increased, 

denser packing occurs and eventually multiple layers of a 3D lattice can be observed. Analysis of 

these optical images relies on a cross-sectional measurement for isolated droplets or at higher 
10

concentration, a line average approach consisting of ten or more droplets for 2D and 3D arrays may 

be used.

Figure 4: Optical image and droplet size distribution under dilute conditions.

a) Optical image of emulsion droplets in a microfluidic channel obtained under highly dilute conditions.

b) Particle size distribution of droplet diameter (sample 645-1-12/19/2015) determined by lognormal 

fitting parameters. Mean and SD are linear-space transformations of the lognormal μ and σ parameters.

Measurement of the hexagonal unit cell under concentrated conditions

40-μL of a freshly prepared emulsion solution is injected into a microfluidic channel of an Ibidi 

#80621 μ-Slide VI-flat hydrophobic microfluidic plate [2], leaving the filling ports open to the 

atmosphere. Over a period of a few hours the oil phase drains from the channel and evaporates and 

menisci appear at both open ends of the channel. Surface tension condenses the aqueous droplet-rich 

phase at or near the mid-point of the channel leading to increased crowding of aqueous droplets. The 

transformation of close-packed spherical droplets first into a rhombic dodecahedron unit cell and 

then into a truncated octahedron (or Kelvin cell) is a function of the volume fraction of the dispersed 

phase, φD. This process is illustrated in a top-down view in Figure 5. Figure 1 illustrates domain 

formation across the entire microfluidic channel.

Figure 5. Evolution of a close-packed droplet lattice in the microfluidic channel. Droplet shape undergoes a spherical-to-polygonal transformation at constant volume as the volume fraction 

of the dispersed (aqueous) phase increases as a result of draining of the continuous (oil) phase. The time 

required to attain collapsed Plateau border channels (volume fraction φ > 96 %) at ambient temperature and 

pressure is approximately 2 hours. This transformation is fully reversible by addition of solvent, i.e., the oil 

phase.

LN(μ = 4.7545, σ = 0.0038)

Mean = 116.11 μm

SD = 0.44 μm

Frequency

a) b)
11

The microfluidic channel height, nominally h = 400 μm, can accommodate a 3D lattice of ≈100 μm

diameter aqueous droplets where the layer number NL is expected to be 4. That four droplets indeed 

occupy alternating lattice positions is verified by changing the focal point of the microscope 

stepwise through the channel (microscope Z axis). A schematic of the tessellating structure is 

presented in side view in Figure 6a. Optical images at the top and bottom of the channel show 

flattened droplets forming a simple hexagonal tiling and three intermediate tessellating regions 

between the four droplet layers which reveal an unambiguous Kelvin-cell projection, Figure 6b.

Figure 6. Interpretation of optical microscope images of the emulsion droplet tessellation.

a) Side-view schematic of 100-μm diameter emulsion droplets forming a stack within a 400-μm 

microfluidic channel height.

b) Focusing through the channel reveals a simple hexagonal pattern at the top and bottom of the channel 

and the alternating tessellation at the three droplet interfaces, thus confirming the four-layer model.

Since NL = 4 and h = 393.3 ±2.1 μm are independently determined, only a measurement of the mean

hexagonal area, AA̅

HEX, is needed in order to estimate the mean hexagonal volume, VV�HEX. The area is 

obtained from a (Z axis) stack of 10X optical images recorded a dozen or more locations along the 

microfluidic channel at which large-scale lattice domains are found. The area of a regular hexagon of 

edge length a can be calculated as AHEX = 3

2 √3 · aa2. However, the lattice cell may be slightly 

distorted and the edge length is then not a reliable parameter. So instead of basing an area 

determination on measurement of individual hexagonal cells, the average area within a given domain 

is obtained by defining a boundary around a set of N hexagons, computing the total area using 

ImageJ [9], and then dividing the total area by N. We refer to this average as AA̅

HEX. Averaging the 

first and fourth layers was found to yield results essentially identical to averaging data for all four

layers; for simplicity we generally report first and fourth layer averaging only. Each area-averaged 

location contains a contiguous set of ≥20 unit cell positions which was delineated and processed in 

ImageJ. At each location, AA̅

HEX was calculated for each group of unit cells. Since a typical volume 

estimate includes at least 3 days × 4 channels × 6 locations × 4 layers × 20 droplets, the total number 

of droplets averaged by this method is ≥ 5,760 droplets.

a) b)
12

Determination of the volume fraction

So far, we have described the calculation of VV�HEX = h·AA̅

HEX/NL. In order to accurately determine the 

quantity of interest, the mean spherical droplet volume in solution or VV�SPH = φD·VV�HEX, we must 

estimate the volume fraction of the aqueous phase within the hexagonal unit cell, φD.

The volume fraction φD can be defined in terms of VPB, the volume of continuous (oil) phase 

remaining trapped at Plateau border channels, the vertices and edges of the hexagonal unit cell. 

Since the volume of the hexagonal unit cell is VV�HEX, φD = (1 – VPB/VV�HEX). The presence of even a 

small amount of continuous (oil) phase can be inferred from the inherent stability of the hexagonal 

lattice structure, as discussed below. Optical images shown in Figure 5, in which oil in Plateau 

borders appears with a dark contrast and water is transparent, indicate that the triangular 

intersections at which four droplets meet decrease in size and contrast as φD → 1. Much theoretical 

and experimental work has gone into establishing a quantitative understanding of how geometric 

transformations are related to the equilibration of droplet forces in compression [6,7,8].

Our estimation of φD relies on the work of Princen [6,7]. A particularly interesting point is that 

Princen derived results for a 2D hexagonal system as well as for a 3D bulk model. Given that NL = 4, 

as indicated in Figure 6a, the 2D model very closely conforms to the geometry of our system. More 

significantly, since the theoretical 2D and 3D volume fractions converge as φD → 1, the actual 

volume fraction is expected to lie somewhere in between. Princen’s 2D model consists of a pair of 

volume-fraction dependent parameters, R/a and r/a where R and r represent a dimensionless droplet 

radius and its curvature during compression into a regular hexagon of edge length a. These quantities 

are defined in Figure 7.

We now use the factor r/a to obtain estimates for φD. The curvature r/a can be scaled to the 

(isosceles) triangle length at the droplet intersection as shown in Figure 7b. Princen’s 2D model, 

however, yields a dimension for an uncollapsed draining channel, where collapse refers to point at 

which the draining forces have squeezed out all but a negligible amount of oil phase from between 

adjacent droplets. This calculation is represented by the trigonal prism shown in Figure 7c and 

therefore overestimates the volume VPB.

However, we require the volume after collapse, i.e., at the quasi-equilibrium condition at which the 

forces due to external pressure and surface energy are balanced. Plateau border channels in this case 

appear as tetrahedra located at the vertices of the truncated octahedral Kelvin cell, Figure 7d. This 

quasi-equilibrium region is illustrated in Figure 8.

For the series of optical micrographs of emulsion draining shown in Figure 5, estimates for volume 

fraction as obtained from r/a are given in Figure 9. Draining of the oil phase is evidently associated 

with structural transitions of the droplets from spherical to polygonal.

Calculating the oil volume at vertices of Kelvin cells and end caps, and given the number of 

vertices/per unit cell, the 2D and 3D Princen models indicate that 96.5 % < φD < 99 %. Our estimate 

for volume fraction of the aqueous phase φD is 98 ±1 %.
13

Figure 7. Determination of the volume fraction using Princen’s model

a) Definition of the parameters in Princen’s 2D model [6].

b) Triangular droplet intersections for a 2D projection.

c) In 2D, the volume of a Plateau border channel VPB = h

4 ·a

2 overestimates the oil phase.

d) In 3D, a collapsed border channel can be represented by VPB = a3/6·√2, the tetrahedral volume.

Figure 8. Measurement of the hexagonal unit cell under quasi-equilibrium conditions.
14

Figure 9. Relationship between volume fraction and curvature parameter, r/a

Assumption of constant droplet volume

Droplet compression at constant volume involves a transition from spherical shape to space-filling 

polygons. The process by which this occurs has long been investigated as a function of increasing 

volume fraction, φ, in terms of geometrical and force equilibration requirements [6,7,8]. The 

measurement process proposed here relies on a mean droplet volume determination from the 

polygonal lattice once the maximum amount of continuous (oil) phase drains from the emulsion at 

ambient conditions; this is referred to as collapse of the Plateau border, which occurs for φ > 96 %. It 

takes about 2 hours to reach this stage under ambient conditions and the lattice remains stable for a 

period of several hours. If this shape transition at constant volume is reversible, then adding solvent 

(oil) to the system during this period should return the droplets to the initial spherical shape and 

diameter.

The reversibility of the spherical-to-polyhedral shape transition illustrated in Figure 5 was verified as 

follows. First, the diameter of spherical droplets was measured within the first several minutes of 

channel filling, i.e., prior to the shape transition into a hexagonal unit cell. After hexagonal domains 

had been allowed time to form due to sufficient draining, approximately 2 hours, an additional 

volume of pure oil phase was introduced into the microfluidic channel, restoring droplets to their 

spherical form. Then measurements of the spherical diameter were obtained for these re-solvated 

droplets. No detectible difference in the spherical diameter between initial and re-solvated droplets 

was found.

The unit cell as a quasi-equilibrium structure

The unit cell, the principle measurement model of droplet volume, is actually a metastable structure 

since the emulsion collapses eventually. It is essential therefore to verify that the measured structures 

are in a physically meaningful steady-state (or quasi-equilibrium configuration) between draining 

and coalescence. That this condition is met for the measurement process is illustrated in Figure 8. 

The theoretical volume fraction is estimated from the change in mean droplet volume as a function 
15

of time according to Princen’s model [6,7]. Recording of data commences at about 90 minutes when 

it becomes possible to measure the tessellating layers and end caps. At that time draining has already 

pushed the system toward φD = 0.965. Our measurements begin after 2 hours, i.e., along the flat 

region of the curve and end before the final compression and loss of remaining oil phase that sets in, 

after about 5 hours. During this time the Plateau borders have collapsed and the external pressure is 

insufficient to force additional oil out of the interstitial pockets, at least for an additional few hours.

Measurement results and their standard deviations for the mean spherical volume of emulsion 

droplets are given in Table 7: Summary of mean spherical droplet volume as V�SPH = φD·V�HEX

measurements. The results are broken down according to protocol: mastermix (with dUTP vs. no 

dUTP) and DNA source (human genomic vs. CMV). There are no significant differences in droplet 

volume between the human and viral DNA. However, the volume difference between mastermixes is 

significant.

Table 7: Summary of mean spherical droplet volume as VV�SPH = φD·VV�HEX measurements

Mastermix;DNA Samples

Number platesNumber ChannelsNumber LocationsNumber Droplets

Volume

Mean ±SD, nL

With dUTP;

Human genomic

645-1-12/19/2014

645-1-03/17/2015

645-1-03/20/2015

7 8 59 4720 0.8017 ±0.0037

With dUTP;

CMV

645-3-02/24/2015

645-3-02/27/2015

645-3-03/03/2015

8 12 72 5760 0.8064 ±0.0059

With dUTP 15 20 141 10480 0.8041 ±0.0048

No dUTP;

Human genomic

645-2-02/04/2015

645-2-02/10/2015

645-2-02/12/2015

7 12 72 5760 0.7681 ±0.0074

No dUTP;

CMV

645-4-03/11/2015

645-4-03/12/2015

5 7 14 1120 0.7657 ±0.0032

No dUTP 12 19 86 6880 0.7669 ±0.0053
16

UNCERTAINTY ANALYSIS

Dilute method

Measurement uncertainty in the case of the dilute method was assumed to depend principally on 

pixel calibration and droplet boundary determination, i.e., edge location of the spherical droplet. The 

pixel calibration uncertainty at 10X is 0.1 %. The contribution from edge location was estimated 

from optical image cross sections of apparently contacting spheres as shown in Figure 4a. Analysis 

of the slope of grayscale intensity values indicates that the exact droplet boundary could occur across 

a region of approximately ±4 pixels for each droplet edge, or ±8 pixels per droplet. At 10X each 

pixel corresponds to 0.394 μm, so that the region spans 3.15 μm. For an average droplet this is 

100×3.15 μm/116.1 μm, or 2.7 %.

An estimate of the relative uncertainty arising from the finite width of the droplet size distribution of 

0.38 % was obtained from the lognormal width parameter calculated for data from 866 individual 

droplet measurements summarized in Figure 4b.

Table 8 summarizes the uncertainty budget for this method.

Table 8: Uncertainty budget for dilute method of determining mean droplet diameter

Component x u(x) %u(x)

a Distribution

1 Pixel calibration @ 10X 0.3943 μm 0.0004 μm 0.10 % Uniform

2 Edge location of spherical droplets 116.1 μm 3.15 μm 2.7 % Uniform

3 Droplet size distribution 116.1 μm 0.44 μm 0.38 % Uniform

a %uu(xx) ≡ 100 ∙ uu(xx)/xx

The combined relative standard uncertainty for the dilute method is:

%uudilute = �1

3

��%uu2(xxii)

3

ii=1

= 2.73⁄1.73 = 1.6 %

where u(xi) are normal-distribution standard uncertainties of the components as listed in Table 8 and 

the factor �1⁄3 converts them to represent normal-distribution estimates. [17] Using a coverage 

factor of k = 2, the expanded relative uncertainty is then

%UUkk=2 = 2 ∙ %uudilute = 3.2 % .

Table 10 compares results of the dilute and concentrated methods.

However, estimates based on spherical droplet diameters are sensitive to the dilution environment. 

This introduces considerable uncertainty into the measurement since the draining of the oil phase 

around the droplets affects optical contrast at the droplet periphery as well as leading to nonspherical droplet shapes. These potential sources of variability and bias are not accounted for in the 

above budget.
17

Concentrated method

To estimate an expanded uncertainty for the measurement of the mean spherical volume of emulsion 

droplets for the concentrated method, both Type A and Type B uncertainty components are 

evaluated. Type A components are associated with an analysis of empirical measurement data 

according to statistical means and Type B estimates are concerned with the capability of a proposed 

measurement process to realize an abstract measurand.

Hierarchical ANOVA [18] analysis was performed to discern any significant impact of day-to-day 

sample preparation, manufacture of the microfluidic plates, and, measurement repeatability and 

reproducibility. The resulting Type A estimates are characterized as normal distributions in Table 9. 

The remaining sources of variability and bias are treated as Type B uniform distributions. These 

uncertainty components are described more fully below and are summarized in Table 9.

Type A: Sample emulsion preparation

The emulsion-forming process may be sensitive to a number of physical and chemical variations 

arising from volume and the choice of constituents in the proprietary mixes used in the preparation 

of the emulsion. The ANOVA component for this source of error appears as entry 1 in Table 9.

Type A: Manufacturing

Qualification of the specific lot of plates is treated below as a Type B uncertainty, so we are 

primarily concerned here with identifying potential variations which might lie outside the expected 

tolerances. The ANOVA component for this source of error appears as entry 2 in Table 9. Similarly, 

the traceable determination of the height of the microfluidic channel is also calibrated and 

determined as a separate Type B uncertainty below and is established for the specific lot of plates 

used in these measurements.

Type A: Measurement

Measurement and analysis of hexagonal unit cells is largely an operator-intensive effort to identify 

locations within a channel with a high degree of lattice perfection. The hexagonal area of individual 

unite cells may be subject to layer-by-layer variations and geometric distortion of polygons. These 

are expected to average out over a large number of unit cells and droplets and use of the ANOVA 

technique is an effort to validate this assumption. The ANOVA component for this source of error 

appears as entry 3 in Table 9.

Type B: Sample size distribution

The sample size distribution produced by the emulsion system is distinct from the day-to-day 

variability of sample preparation which may result from pipetting and so forth. It is considered a 

possible Type B uncertainty. As reported for the dilute method, the standard deviation of the droplet 

size distribution is 0.44 μm, based on the results shown in Figure 4. It appears as entry 4 in Table 9.

Type B: Pixel calibration

This estimate is also carried over from the dilute method and appears as entry 5 in Table 9.

Type B: Estimation of VV�HEX

The measurand VV�SPH = φD·VV�HEX, is an idealized model of the actual measurement data. The 

uncertainty evaluation is presented in two parts. We first evaluate the uncertainty components arising 

from the calculation of VV�HEX = h·AA̅

HEX/NL.
18

The major component of uncertainty due to measurement is the traceable determination of the 

channel height, h, which was found to be about 0.13 %. It appears as entry 6 in Table 9. This 

uncertainty could be reduced if local measurement values were used instead of a single global value. 

However, its contribution is small enough for the intended use. NL = 4 is considered an errorless 

constant as it is always observed for well-formed droplet domains. It appears as entry 7 in Table 9.

For the estimation of an average hexagonal area, we do not use lattice parameters. Compressive 

forces acting on the droplets are not purely isotropic, so that a 3D polygonal lattice is not necessarily 

definable by a single hexagonal edge length a across the domain. Absolute lattice constants can only 

be guaranteed if the droplets are incompressible. For this reason, we do not calculate the area of a 

hexagonal unit cell based on based on AHEX = 

3

2√3 · aa2. Rather, optical images indicate that 

hexagonal domains are distorted by lateral or vertical skewing or subject to shearing along the 

channel boundaries. Therefore, averaging a large number of contiguous unit cells by defining a 

boundary around a set of N hexagons and computing the total area using ImageJ provides a reliable 

estimate of the mean unit-cell area within a given domain. Repeatability of image analysis to 

determine AA̅

HEX in this manner was found to be ± 0.017 %. This contribution appears as entry 8 in 

Table 9.

Type B: Manufacturing

Components of uncertainty arising from channel roughness, form errors, and dimensional 

conformance of the microfluidic channel are evaluated from WYKO and optical measurements of a 

large number of ibidi channel plates from the same lot number.

Channel roughness was determined from the root-mean-square (RMS) surface roughness of the top 

exposed surface of intact membranes and mechanically grooved channels using WYKO analysis 

software. This error was calculated to be about 0.2 % of the channel height measurement, close to 

the resolution limit of the instrument, and appears as entry 9 in Table 9.

Since the channel membrane has a thickness of only about 200 μm, it is possible that channels do not 

possess a uniform rectangular cross section. This may be due to deformation of the membrane during 

manufacturing or arise from compressive forces as the concentrated fluid dries within the channel.

Flatness across empty and filled channels was estimated to be less than 0.2 % based on WYKO data 

as shown on the right hand side of Figure 2, close to the resolution limit of the instrument. It appears 

as entry 10 in Table 9.

Uniformity of the channel cross section was also evaluated in terms of a difference between the left 

and right channel height as shown on the left hand side of Figure 2. Some differences are apparent 

from the total height measured across the ibidi plate. The variations are an aspect of manufacturing 

and, as noted earlier, by avoiding the use of channels 1 and 6, deviations from a rectangular 

geometry are small. This component is estimated by comparing difference between left/right channel 

data presented in Tables 3 to 5 and appears as entry 11 in Table 9.

Type B: Volume fraction

The uncertainty related to the volume fraction, φD, represents the largest uncertainty contribution to 

VV�SPH since it is must be estimated by interpolating between Princen’s 2D and 3D theoretical models. 

Nevertheless, the calculated expanded uncertainty, U, lies within the range required by the intended 

use. It appears as entry 12 in Table 9.
19

Table 9: Uncertainty budget for concentrated method of determining mean droplet diameter

Component x u(x) %u(x)

a Distribution

1 Sample preparation 0.064 % Normal

2 Manufacturing 0.022 % Normal

3 Measurement 0.044 % Normal

4 Droplet size distribution 116.1 μm 0.44 μm 0.38 % Uniform

5 Pixel calibration 0.3943 μm 0.0004 μm 0.10 % Uniform

6 Channel height, h 393.3 μm 2.1 μm 0.13 % Uniform

7 Channel number, NL 4 0 0.0 % Uniform

8 Estimation of AA̅

HEX 0.017 % Uniform

9 Channel roughness 0.02 % Uniform

10 Form errors 0.2 % Uniform

11 Left/Right channel conformance 0.2 % Uniform

12 Volume fraction, φD 0.98 0.01 1 % Normal

a %uu(xx) ≡ 100 ∙ uu(xx)/xx

Combined Relative Standard Uncertainty

The uncertainty estimate for the mean droplet volume can be performed as follows. Note that Type 

A and Type B components are expressed in linear dimensions. This is consistent with the view that 

traceability is fundamentally established through a calibrated measurement of the microfluidic 

channel height. The combined relative standard uncertainty of the Type A components for the 

droplet diameter is:

%uuA(dd) = ��%uu2(xxii)

3

ii=1

= 0.081 %

where u(xi) are normal-distribution standard uncertainties of the components 1 to 3 listed in Table 9. 

The combined relative standard uncertainty of the Type B components is:

%uuB(dd) = �1

3

��uu2(xxii)

11

ii=4

= 0.50

1.73 = 0.29 %

where u(xi) are uniform-distribution relative standard uncertainties of the components 1 to 3 listed in 

Table 9 and the factor �1⁄3 converts them to represent normal-distribution estimates. The complete 

combined relative standard uncertainty of the droplet diameter measurements is then:

%uu(dd) = �uuA

2(dd) + uuB

2(dd) = �0.0812 + 0.292 = 0.30 %.

Assuming a coverage factor of k = 2, an expanded relative uncertainty for the droplet diameter 

estimated in this manner is

%UUkk=2(dd) = 2 ∙ %uu(dd) = 0.60 %
20

which is substantially less than the 3.2 % relative expanded uncertainty calculated for the dilute 

method.

What we desire is the combined uncertainty of the equivalent spherical droplet volume,

VV�

SPH = φDD ∙ VV�HEX,

where

VV�

HEX = �

4

3

� ππ �

dd

2

�

3

= �

ππ

6

� dd3.

A linearized model* for the combined relative uncertainty of VV�

HEX is

uu(VV�

HEX)

VV�

HEX

= 3 ∙

uu(dd)

dd .

Given the 0.30 % value for %uu(dd) calculated above and recognizing that

%uu(VV�

HEX) ≡ 100 ∙

uu(VV�HEX)

VV�HEX

and %uu(dd) ≡ 100 ∙

uu(dd)

dd ,

the percent relative standard uncertainty of the volume is

%uu(VV�

HEX) = 3 · %uu(dd) = 3 · 0.30 % = 0.90 %.

From Table 9, the volume fraction is φDD = 0.98 ± 0.01 with a combined relative standard 

uncertainty of %uu(φDD) = 1.0 %, so the linearized model yields

%uu(VV�

SPH) = �%uu2(φDD) + %uu2(VV�HEX) = �1.02 + 0.902 = 1.4 %

for the combined relative standard uncertainty of the spherical volume. Assuming a coverage factor 

of k = 2, an expanded relative uncertainty for the droplet volume measurement is then

%UUkk=2(VV�

SPH) = 2 ∙ %uu(VV�SPH) = 2 ∙ 1.4 % = 2.8 %.

While reflecting the uncertainty component estimates listed in Table 9, this expanded uncertainty 

should be appropriate for droplets formed from both the “with dUTP” and “no UTP” mastermixes.

 

* First-order Taylor series expansion: y = f(x); u(y) = �∑ �

∂∂∂∂

∂∂∂∂�

2

∙ uu2(xx)
21

VALIDATION

Comparison of Results from the Dilute and Concentrated Methods

Table 10 compares estimates of droplet diameter from the dilute and concentrated methods. The 

diameter is obtained directly in the dilute method, whereas the volume is obtained first in the 

concentrated method.

Table 10: Comparison of mean emulsion droplet diameter

All values in μm

Dilute Method Concentrated Method

Mastermix;DNA Sample Value Mean ±SD Value Mean ±SD

With dUTP;

human genomic 

645-1-12/19/2014

645-1-03/17/2015

645-1-03/20/2015

116.1

115.5

116.3

116.0 ±0.4 116.0

115.9

116.1

116.0 ±0.1

With dUTP;

CMV 

645-3-02/24/2015

645-3-02/27/2015

645-3-03/03/2015

115.5

115.9

116.0

115.8 ±0.3 115.6

116.6

116.6

116.3 ±0.6

With dUTP 115.9 ±0.3 116.1 ±0.4

No dUTP;

human genomic

645-2-02/04/2015

645-2-02/10/2015

645-2-02/12/2015

113.7

114.3

114.5

114.2 ±0.4 113.8

114.8

114.6

114.4 ±0.5

No dUTP;

CMV 

645-4-03/11/2015

645-4-03/12/2015

na

114.1

114.1 114.2

114.4

114.3 ±0.1

No dUTP 114.2 ±0.3 114.4 ±0.4

Droplet diameter estimates obtained by dilute and concentrated methods agree reasonably well, 

indicating that the possibly simpler dilute method can be used to establish, or assess, volume and 

DNA concentration. The significant difference between the “with dUTP” and “no dUTP”

mastermixes extends to the dilute method.

Comparison with Literature Results

The present results are validated against previously published work in Table 11.

Table 11: Evolution of mean droplet diameter and volume estimates

Source Date Diameter, μm Volume, nL

Nominal 124.0 1.000

Bio-Rad [1] 2009 120.2 0.910

NMIA [4] 2012 118.4 0.868

IRMM [3] 2015 116.8 0.834

NIST, Dilute method, with dUTP

NIST, Dilute method, no dUTP

2015

2015

115.9

114.2

0.815

0.780

NIST, Concentrated method, with dUTP

NIST, Concentrated method, no dUTP

2015

2015

116.1

114.4

0.804

0.767
22

There is a trend toward lower volume estimates, and therefore higher DNA concentration values, as 

refinements to the emulsifying system and its software occurred. In addition, larger sets of droplet 

measurement data obtained under more controlled conditions have appeared. However, a persistent 

discrepancy between DNA concentration estimates based on ddPCR and other methods remain. This 

has been discussed in the literature recently [see the discussion of Figure 4 of Reference 3]. We 

expect that volume estimates reported in this work will reduce or eliminate this discrepancy.

REFERENCES

[1] Bio-Rad Laboratories Inc., Pleasanton, CA, USA. (http://www.bio-rad.com/en-us/applicationstechnologies/introduction-digital-pcr)

[2] Ibidi LLC, Verona, WI, USA. (http://ibidi.com/xtproducts/en/ibidi-Labware/Channel-Slides/mSlide-VI-Flat)

[3] P. Corbisier et al., DNA copy number concentration measured by digital and digital quantitative 

PCR using certified reference materials, Anal. Bioanal. Chem. 407 1831 (2015).

[4] L. B. Pinheiro et al., Evaluation of a droplet digital polymerase chain reaction format for DNA 

copy number quantification, Anal. Chem. 84 1003 (2012).

[5] S. Bhat et al., Single molecule detection in nanofluidic digital array enables accurate 

measurement of DNA copy number, Anal. Bioanal. Chem. 394 457 (2009).

[6] H. M. Princen, Highly concentrated foams, I. Cylindrical systems, J. Coll. Interface Sci. 71 55 

(1979).

[7] H. M. Princen, M. P. Aronson, and J. C. Moser, Highly concentrated emulsions, II. Real systems, 

J. Coll. Interface Sci. 75 246 (1980).

[8] A. Bhakta and E. Ruckenstein, Decay of standing foams: drainage, coalescence and collapse, 

Adv. Coll. Interface Sci. 70 1 (1997).

[9] ImageJ v1.47, available from the National Institutes of Health. (http://rsbweb.nih.gov/ij/)

[10] SRM 1690 – Nominal One-μm Polystyrene Spheres.

(https://www-s.nist.gov/srmors/certificates/archive/1690.%20Dec%2022,%201982.pdf)

[11] SRM 1692 - Polystyrene Spheres (3 μm Diameter Particle Size).

(https://www-s.nist.gov/srmors/view_cert.cfm?srm=1692)

[12] Paraphrased from: WYKO Surface Profilers Technical Reference Manual, 1998.

[13] SRM 2390 – DNA Profiling Standard.

(https://www-s.nist.gov/srmors/certificates/archive/2390.%20Aug%2010,%201992.pdf)

[14] SRM 2366a - Cytomegalovirus DNA (TowneΔ147 BAC) for DNA Measurements.

(https://www-s.nist.gov/srmors/view_detail.cfm?srm=2366a)

[15] ddPCR Supermix for Probes #186-3010.

(http://www.bio-rad.com/en-us/sku/1863010-ddpcr-supermix-for-probes)

[16] ddPCR Supermix for Probes (no dUTP) #186-3024.

(http://www.bio-rad.com/en-us/product/ddpcr-supermix-for-probes-no-dutp)

[17] JCGM 100:2008 (2008) Guide to the expression of uncertainty in measurement (GUM). Sèvres, 

France. (http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf)
23

[18] G. E. P. Box and G. C. Tiao, Bayesian Inference in Statistical Analysis, John Wiley and Sons, 

Inc., New York (1992), Chapter 5.