To calculate the Flow Rate Ratio (FRR) for a three-inlet microfluidic chip operating under hydrodynamic focusing, you compare the flow rate of the central (sample) stream to the combined flow rates of the two side (sheath or focusing) streams. The typical formula is:

FRR=Qsheath, totalQsampleFRR=QsampleQsheath, total

where Qsheath, total=Qsheath, left+Qsheath, rightQsheath, total=Qsheath, left+Qsheath, right, and QsampleQsample is the flow rate of the central sample inlet. This ratio determines how tightly the sample stream is pinched or focused within the main channel: a higher FRR means a narrower focused sample stream. For example, if both sheath inlets are set to 10 μL/min and the sample inlet is set to 5 μL/min, then FRR = (10 + 10) / 5 = 4. This calculation is fundamental for controlling the width and position of the focused stream in applications like cell sorting, flow cytometry, or nanoparticle synthesis.

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To calculate the Flow Rate Ratio (FRR) in a three-inlet microfluidic chip, you just compare the total flow coming from the side channels (sheath flows) with the flow from the middle channel (sample flow).

For example, if you're using syringe pumps:

• The left sheath inlet is set to 100 µL/min
• The right sheath inlet is set to 100 µL/min
• The middle sample inlet is set to 50 µL/min

Then, you add the two sheath flows (100 + 100 = 200 µL/min) and divide that by the sample flow (50 µL/min).

So in this case, the FRR is 200 divided by 50, which gives 4.

You can use any units (µL/min, mL/min, etc.) as long as they are the same for all inlets.

This ratio helps you control how tightly the sample gets focused in the center of the channel.

Let me know if you'd like help applying this to your own chip or setup