Droplet dispensing in digital microfluidic
Assessment of long-term reproducibility
devices:
Katherine S. Elvira,1 Robin Leatherbarrow,2 Joshua Edel2 and Andrew deMello1
1
Department of Chemistry and Applied Biosciences, Institute for Chemical and
Bioengineering, Wolfgang-Pauli Strasse, ETH Zürich, Zürich, CH 8093, Switzerland
2
Department of Chemistry, Imperial College London, Exhibition Road, South
Kensington, SW7 2AZ, United Kingdom
I. DROPLET VOLUME CALCULATIONS
The droplet volume was calculated as follows:
1) Calculate the inner droplet area
Inner droplet area = total droplet area - observed boundary area/2 - P * single pixel
area/2, where all measurements are determined for each droplet in ImageJ. This
represents the area of the droplet that is full-height. It assumes that a boundary of the
calculated thickness lies at the centre of the observed boundary (the area of the
calculated boundary is P * single pixel area, since this factors the single pixel area, a
band of 1 pixel thickness, by the boundary-thickness-to-pixel-size ratio P). This is
illustrated in Figure 3 (a).
2) Calculate the volume of the curved boundary region
Volume of boundary region = 0.675 * P * single pixel area * spacer thickness.
Figure 3 (b) details the calculation of the cross-sectional area of the curved region.
This is equal to 67.5 % of the total cross-sectional area of the boundary region. The
volume of the boundary region is equal to the plan area of the region multiplied by the
spacer thickness multiplied by this percentage.
3) Calculate the total droplet volume
Total droplet volume = (inner droplet area * spacer thickness + volume of boundary
region) ± total error/2
II. ERROR ANALYSIS
To calculate the error inherent in this method for droplet volume calculation, the
following steps were followed:
1) Calculate the predicted droplet boundary width, b
This will depend on the device spacer (76 or 120 μm) and the contact angle of the
droplet (measured for water on a Teflon surface as 119.5° ± 1.1°). The calculation is
shown diagrammatically in Figure 3 (c) and it assumes a circular section. For the 76
or 120 μm spacers, b is 10.2 and 16.1 μm respectively.
2) Compare b to the known pixel size
The pixel size is determined by using ImageJ to measure the size of an electrode
(known size to be 1 mm) for each experiment. The software counts the number of
1
pixels in that 1 mm line. This allows the ratio of boundary width to pixel size to be
calculated, P = b ⁄ pixel size. In all images, the ratio is between 0.5 and 1.5 and
therefore the droplet boundary should appear in the image as a line 1 pixel in width.
3) Calculate the error in the boundary measurements
Boundary error = observed boundary area - single pixel boundary area. Where both
measurements are determined for each droplet using ImageJ. The single pixel
boundary area is the skeleton area (i.e. the droplet boundary one pixel wide); the
observed boundary area is often wider than one pixel due to shadowing and other
effects.
4) Calculate the pixelation error
Pixelation error = 1 pixel * single pixel boundary area. Due to the pixelation of the
image, there is an error of half a pixel width either side of the observed boundary.
This is equal to the single pixel boundary area (i.e. the perimeter of the droplet times
one pixel wide).
5) Calculate the total error
Total error = (boundary error + pixelation error) * spacer thickness. All other
sources of error (contact angle measurement, spacer thickness, electrode size) have
been discarded as negligible in comparison.
2