Microfluidic Flow Restrictors
A little bit of theory
The flow rate in every fluidic system can be computed with the following equation:
Where: ∆P is the pressure difference between the inlet and the outlet of the system, Q is the flow rate throughout the system, Rh is the fluidic resistance of the system.
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This equation is analog to the one that applies for electronic systems
Calculations for the equivalent resistance with resistors in series or in parallel apply similarly for fluidics and electronics. Kirchhoff’s law for circuit calculations is also similar in both domains.
Inadequate resistance leads to poor flow control
Let’s take the example of a microfluidic chip with channels that are 500 µm wide, 70 µm high and 2 cm long. The fluidic resistance is quite small and implies an approximate pressure of 1 mbar for a flow rate of 5 µL/min. A user wanting to control the flow rate with an OB1 200 mbar and a flow-sensor MFS 2 will meet several difficulties:
- The resolution of 0.1 mbar of the OB1 200 mbar will only allow steps of 0.5 µL/min. The precision of the flow sensor becomes inadequate
- Flow rate instabilities may appear due to its sensitivity to small pressure variations
- The flow sensor will saturate at low pressure/high flow rate, leaving the major part of the pressure range unusable. The performance regarding the usable pressure range will be degraded.
Adding flow restrictors enables to reach the best performances
Regarding the former example, it is easy to match the instrument performances to the setup by adding a flow restrictor in series with the microfluidic chip.
Increasing the resistance of the system enables decreasing its sensitivity; hence increasing its stability.
Nevertheless, the maximum reachable flow rate becomes smaller, which sometimes can be a limitation for flushing the system.
Description and setup
Flow restrictors consist of capillaries with different diameters. Their resistance depends on their inner diameter (ID), their length and the viscosity of the liquid that flows through them.
The flow restrictor should be connected directly on the reservoir. Due to the connector size, the restrictor must be longer than 10 cm. If it is long enough, the flow restrictor can be directly connected to the flow sensor or other instrument. Otherwise, it can be connected to an intermediate capillary adapted junction (see picture).
Selecting your flow restrictor
Standard resistance values
The following table gives the resistance of different flow restrictors for different liquids.
Note that these values are given for a 1 cm-long flow restrictor. Since the resistance is proportional to the capillary length, you can easily adjust the length to reach the desired fluidic resistance.
With water, a flow restrictor with an ID of 64 µm and a length of 10 cm will give a resistance of 38 mbar/(µL/min). A pressure drop of 38 mbar across the restrictor will result in a flow rate of 1 µL/min.
The best flow control…
To reach the best flow control, the maximum pressure of your OB1 must match the maximum flow rate of your flow sensor, e.g. an OB1 200 mbar for a 7 µL/min flow sensor gives an ideal resistance of 28 mbar/(µL/min).
…VS the maximum reachable flow rate
In the former example, the user cannot flush the system with a flow rate higher than 7 µL/min, which can be limiting for transient phases. If the user wants to reach a max flow rate of 20 µL/min, a resistance of 10 mbar/(µL/min) is more adapted.
In order to find the best compromise, Elveflow recommends starting with a resistance which is equal to 25% of the OB1 range divided by the desired flow rate.
For an OB1 200 mbar and a desired flow rate of 5 µl/min, use a resistance of 50/5=10 mbar/(µL/min).
Available Plug-&-Play Solutions
Elveflow also offers a broad range of flow resistances kits that are easy and quick to connect and offer excellent chemical compatibility :
- • KFR 1: Kit Flow Resistance 1
- • KFR 2: Kit Flow Resistance 2
- • KFR 3: Kit Flow Resistance 3
- • KFR 4: Kit Flow Resistance 4
- • KFR 5: Kit Flow Resistance 5
- • KFR 6: Kit Flow Resistance 6
- • KFR 7: Kit Flow Resistance 7
Installation could not be easier, since these kits contains enough tubing to make about three to fifteen flow resistances, along with all necessary fittings, and a microfluidic tubing cutter.
The following table indicates the tubing length and flow resitance kit reference to be used based on the typical working pressure and the Elveflow flow sensor used.
Important Note : This table is not intended to provide absolute values for a particular setup and should only be seen as a beginners guide. The microfluidic resistance should be refined based on each setup characteristics. The particular conditions of your use and application of our products are beyond our control. Only a test in the specific conditions of your application will determine the appropriateness of a flow resistance size, which remains a hypothesis among other parameters (e.g. biophysical model chosen, length of fluidic channel, pressure source, chip height, etc …).
To go even further in understanding the hydraulic resistance in microchannels, we highly recommend the following article :
Reexamination of Hagen-Poiseuille flow: Shape dependence of the hydraulic resistance in microchannels – NA Mortensen, F Okkels, H Bruus – Physical Review E 71 (5), 057301.
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