The process of droplet formation in microfluidic channels with a T-junction is based on using two immiscible liquids, one of which is referred to as the continuous phase (in the “main” channel) and the other is known as the disperse phase. The disperse fluid initially flows perpendicular to the continuous flow. When the two liquids meet at the T-junction of the channels, the disperse phase begins to enter the main channel. In the regime where viscous forces are dominated by surface tension forces, the propagation of the disperse phase into the main channel leads to an increased resistance to the flow of the continuous phase, thereby increasing the pressure in the main channel behind the emerging droplet. When the pressure behind the emerging disperse phase becomes high enough, a neck is created. The emerging disperse phase continues to “block” the main channel flow, increasing the pressure, which in turn causes this neck to get smaller, until it becomes unstable and snaps, separating off and forming a droplet. The droplet then travels forward, entrained in the continuous phase flow. Ideally, the process of droplet formation occurs at a high rate, with droplet break-off occurring at regular intervals at the same point in the channel, resulting in repeatable, well-controlled droplet size and spacing.
A study performed by Xi Engineering is shown below using COMSOL Multiphysics, specifically the Laminar Flow and Level Set modules. These modules are highly flexible to allow the user the ability to account for the correct physics needed to model different situations. By obtaining suitable values for the fluid properties and geometric parameters from the literature, we solve the fully coupled non-linear system of equations numerically.
Experimental and theoretical investigations of the most typical lab-on-a-chip channel configurations have shown that when the forces due to viscosity are dominated by those due to surface tension (i.e., small Capillary number), the size of the droplets produced is determined by the continuous and disperse phase flow rates. If we take the two examples shown in Animation 1, we can see that the two immiscible fluids form an interface at the junction of the inlet and main channel.
The stream of the disperse phase (blue) emerges into the main channel, and a droplet begins to grow; the pressure gradient and the flow in the main channel distorts the droplet in the downstream direction. The significant difference between the two results in Animation 1 is that we can see that the positions in the channel at which the droplets form and the droplet distribution across the channel are different. In Animation 1, top, we can see a continuous parallel-flow regime trailing a few initially-formed droplets. By increasing the continuous phase flow rate and keeping the disperse phase flow rate constant, a more regular and repeatable droplet formation with breakoff near the junction occurs (Animation 1, bottom). This change in the fluid distribution across the channel is due to changing the flow rate ratio.
Alternatively, one could reduce the disperse phase flow rate to promote more rapid droplet generation. The disperse phase flow rate must, however, be high enough that it has sufficient driving pressure to be able to emerge into the main channel in the first place – otherwise no droplets form at all! The process of repeated droplet generation is highlighted as well in Animation 2, where we plot an isosurface of the volume fraction of fluid (i.e. the boundary between the phases).
Animation 1: Animations of the volume fraction of two isotropic liquids in a microfluidic channel containing a T-junction and a serpentine curve.
Animation 2: Volume fraction isosurfaces in 3D, showing highly regular droplet break-off and spacing.