The dynamics of liquid slugs forced by a syringe pump

Abstract

Microfluidic processes for chemical synthesis have become popular in recent years. The small scale of the chemical reactions promise greater control over reaction conditions and more timely creation of products. The small scale of microfluidics poses its own set of problems, however. At the microscale, the dominant fluid forces are viscous resistance and surface tension. The effects of viscosity and scale reduce the Reynolds number and make mixing difficult. Much work has been done to control mixing at the microscale.

This problem is concerned with a different microfluidic problem: delivering reactants to the site of reaction. A common setup is to attach syringes full of reactant to a reaction chamber by narrow hydrophobic tubing. Using a stepper motor, a controlled dose of liquid may be injected into the tube. The hydrophobosity causes the dose to curve outward on the sides, becoming a "slug" of reactant with air in front and behind. The syringe at the rear is then switched for one full of air, and air pressure is used to drive the slug to the reaction site.

If too much pressure is applied, the slug will arrive with a significant back pressure that will be relieved through bubbling in the reaction site. This causes the formation of a foam and is highly undesirable. We present a simple model based on Boyle’s law for the motion of a slug through a tube. We then extend this model for trains of slugs separated by air bubbles. Last, we consider the case of a flooded reaction site, where the forward air bubble must be pushed through the flooding liquid.

In conclusion, we have determined the dynamics of a single slug moving towards an empty reaction chamber giving the final equilibrium position of the slug. A phase-plane analysis then determined a condition on the size of the slug needed to ensure that it comes to rest without oscillating about the equilibrium position. The effect of a flooded reaction chamber was then considered. In this case it is impossible to avoid bubbling due to the design of the device. We found that it is possible, however, to reduce the bubbling by minimising the back pressure behind the slug. Finally, the dynamics of multiple slugs with or without a flooded reaction chamber has been investigated.