Day 23

Pressure Drop in Flowing Fluids

Pressure spreads with speed of sound inside fluids. Hence, for most microfluidic applications this speed is practically infinite (water: ca. 1000m/s). Hence, a pressure change is instantly present over the whole channel system. However, once the fluid moves inside the microfluidic channels, pressure gradients rise due to friction. Consequently, the pressure is not uniform any more. The pressure gradient calculates as:

 p = R * Q

This means, the larger the hydrodynamic resistance is the stronger the pressure differences at a given volume flow results.

If working with pressure sensitive objects as bubbles or extrusion of vesicles and droplets, the local pressure matters. It drives the instability against the resistance of the surface-tension of the fluid-fluid interface. Therefore, it is advisable to keep the supply channels before and after the crossing location as short as possible.

As positive side effects shorter channels also imply less risk of bubbles, a chance to supervise more of the channels with high magnification and the possibility to work with lower pressures. Last, but not least: Faster dynamics of pressure changes can also be achieved in short channel systems as the slew rate of the externally connected pressure controller is limited: The supplied slew rate Δpout / Δt scales down according to the hydrodynamic resistance of the channel system: 

Δpout / Δt = R * Δpin / Δt

since the volume flow is equal due to mass conservation. Only a fraction of the pressure amplitude arrives at the centre of long channels. Therefore follow our KISS-slogan of Microfluidics:

Keep it short and slim!

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