Quantitative Analysis of the Volume Difference of Microdroplets in Vertical Contact Control

We can control the concentration of chemicals in microdroplets by using vertical contact control of droplets. When a microdroplet contacts an opposite microdroplet, chemicals diffuse between the droplets. Then, the coalescent droplet is separated into two microdroplets. Contact control is attractive for use in biochemical applications because it realizes three-dimensional microfluidic systems. However, in vertical contact control, gravity causes a volume difference of the microdroplets, ΔV, after separation. To solve the problem of gravity, we analyze ΔV quantitatively. In experiments, we measure the relationship between ΔV and the size of microdroplets, R. As a result, we find that ΔV increases proportionally to $R^5$, which agrees with a simple theoretical model based on the balance between gravity and surface tension. Our model suggests that ΔV of the microdroplets after vertical contact control can be predicted quantitatively with the material parameters of the density and surface tension of the liquid.

Figure 1

Fabrication process for the wetting pattern substrate.

Figure 2

Microdroplets throughout contact control. Microscopy images of (a) initial hemispherical microdroplets before the contact process, (b) coalescent droplet, (c) double-cone-shaped coalescent droplet immediately before separation, and (d) hemispherical droplets after the separation process. Scale bar indicates 1 mm.

Figure 3

(a) Schematic image of microdroplet formed on the upper substrate. We fit the water-air interface as a circular dotted line. We define the radius of the circular fitting line as the radius of the microdroplet, r, which is larger than the radius of the wetting pattern, R. Height of the droplet formed on the upper (lower) substrate is smaller (larger) than r. (b) Microscopic image of the microdroplet formed on the upper substrate through contact control. Scale bar indicates 1 mm.

Figure 4

ΔV after the separation process. Dashed line is the best-fit curve obtained using the power function, Eq. (2).

Figure 5

Schematic geometry of our model.