Beating Poisson encapsulation statistics using close-packed ordering

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Entry by Leon Furchtgott, APP 225 Fall 2010.

"Beating Poisson encapsulation statistics using close-packed ordering" Adam R. Abate, Chia-Hung Chen, Jeremy J. Agresti and David A. Weitz, Lab Chip 9 2628-2631 (2009).


This paper describes a new method for efficiently loading drops with discrete objects. The authors use deformable particles that are close packed to insert a controllable number of particles into each drop.


Drops loaded with discrete objects are used extensively in microfluidics experiments. Each drop serves as a picoliter vessel within which reactions can be performed, so using drops in microfluidic devices can be a key component for many high-throughput scientific applications. However all such applications require an efficient way of loading objects into individual drops. This so far has been quite difficult to achieve. Typically people dilute the materials and then encapsulate them into the drops at random. But this is very inefficient, since by Poissonian statistics a large number of drops will be completely empty.

In response to this inefficiency, several groups have attempted to find more efficient encapsulation methods such as using lasers to guide particles into drops or using inertial ordering of particles prior to encapsulation. However these methods are still difficult to use, slow, or not robust.


The authors developed a simple, robust method to load a controllable number of particles into every drop. The authors increase the volume fraction of the particles to the point that they are close-packed and naturally order into a regular spacing, providing a periodic flow of particles. By matching the periodicity of the drop formation to the particle flow, the authors achieve near perfect loading of a prescribed number of particles in each drop. By using slightly deformable particles, they avoid clogging, providing a robust, simple method for controlling particle loading in drops.

Fig. 1. (a) Schematic of encapsulation device. (b) Photomicrograph of particle encapsulation. The particles are injected at high volume fraction, causing them to order. Water is added in the first junction to space the particles prior to encapsulation. Oil is added in the second junction to form drops and encapsulate the particles. The scale bar denotes 50 µm.

The authors use compliant gel particles in these experiments. These prevent clogging of the channels and are useful substrates for biological and chemical applications. Moreover, since they are deformable, they can be packed at near 100 percent volume fraction without clogging. At this high volume fraction, the particles order into a regular spacing, allowing for uniform filling of the drops (Fig 1b). To encapsulate the particles, the authors use a microfluidic device with two cross-channel junctions arranged in series as shown in Fig 1a. In the first junction water is added to space the particles while in the second junction oil is added to encapsulate them.

Fig. 2. (a) Photomicrograph of close-packed gel particles flowing into encapsulation junction. The evenly spaced particles flow at a periodic rate into the encapsulation junction. The scale bar denotes 100 µm. (b) Average grayscale intensity in the box demarcated; each spike corresponds to a particle moving through the box. (c) Power spectrum of the intensity time trace, with a sharp peak at the average frequency of 1.5 kHz. The frequency as a function of time is plotted inset.

The authors demonstrate that the particles flow periodically by monitoring them at the drop-formation junction. 30 µm particles are injected into a drop maker with channels that are 25 µm tall. Since the particles are larger than the channel, they are confined to a monolayer; the close packing causes them to order in a hexagonal array. The author then record movies of the particles flowing in the channel (Fig 2a). They can detect particles passing by looking at spikes in the average grayscale intensity (Fig 2b). These spikes are periodic, and they have a frequency that remains nearly constant of 1.5 kHz (Fig 2c).

Fig. 3. Encapsulation of close-packed particles. Photomicrograph of encapsulation utilizing close-packed ordering and droplet triggering (a), close-packed ordering (b), and in which particles are disordered and encapsulated inefficiently (c). The scale bars denote 75 µm. (d) Probability distributions of the number of particles per drop.

Once the authors are satisfied that the particles are flowing periodically, they adjust the flow of oil in the drop-making junction at the same rate as that of the particles in order to encapsulate the particles. They can adjust either the drop-making periodicity or the particle periodicity. However, even with flow rates optimized, the periodicities can drift over time leading to improper encapsulation. To correct for this they use a trigger mechanism. They use a long thin nozzle to form drops and encapsulate the particles (Fig. 3a). Thus, the particles plug the nozzle when they are in position for encapsulation; this triggers drop formation, thereby allowing it to compensate for drift in the periodicity of the particles, leading to near perfect encapsulation efficiency, as shown by the measurement of the number distribution in Fig. 3d.

To increase the number of particles, the authors use wider nozzles. The trigger mechanism is limited to single-particle loading into drops. Still, even with no triggering, the encapsulation efficiency is very good.


This is a simple, flexible and robust technique for loading particles into drops since it allows the number of particles encapsulated, the size and volume fraction of the drops in which they are encapsulated, and the frequency and flow velocity of the drops each to be controlled independently.

Relation to Soft Matter

This paper gives insight into how simple concepts in soft matter physics including many we have discussed in class can be applied very elegantly to solve tricky technological problems.