# Microfluidic Resistance

## How to calculate Microfluidic flow resistance?

Microfluidic flows are characterized by the prevalence of the viscous effects compared to inertia. From a physics point of view, this behavior is pointed out by a low Reynolds number indicating laminar flow. It leads to a drastic simplification of the complex Navier-Stokes equations describing fluid displacement. Thus, a very simple equation linking:

• Mean flow-rate Q
• Pressure drop (change in P)
• Microfluidic resistance R

Just like the electrical potential drop dV is proportional to intensity A, fluid pressure drop dP is proportional to the mean flow rate Q. In both cases, a resistance R can be defined as the proportional coefficient.

This analogy points out that the microfluidic resistance quantifies an energy drop along the microfluidic channels. As in an electrical network, equivalent microfluidic resistances can be calculated to simplify modeling of complex microfluidic devices or Lab-On-Chip with multiple parallel and/or series channels.

## Resistance formula

The microfluidic resistance can be calculated for microfluidic channels with simple or common cross section, such as circular or rectangular shapes. For these shapes, the formula directly links microfluidic resistivity with:

• Channel geometry.
• Fluid characteristics

## 2 kinds of microfluidic resistance

In a microfluidic set-up, two kinds of flow resistances can be distinguished, depending on the impact they have on the experiment:

### External flow resistances

This is induced by the tubing and fittings used to connect the microchip to the flow control system (pressure pump, syringe pump, etc.). By applying the electrical analogy, this kind of resistance may become an easy and powerful solution to enhance or adjust the performance of flow control systems.

### Internal flow resistances

This results from the microchip design. Internal flow resistance management may be used such as a passive flow control system: in many applications, microfluidic circuits are designed to create dedicated functionalities such as gradient generator, droplet merging and splitting, passive valves, cell trapping, and so on.