Maximum number of microchannels in parallel for a syringe pump

[MSM]

Basically, I want to determine how many microchannels I can have in parallel to drive a fluid (for now assume water),without the syringe pump stalling. Let's say a syringe pump have a maximum linear force of 50 lb_f. and I want to drive the fluid at 60 ml/hr. So if I have 4 parallel channels then the syringe must drive 240 ml/hr. How do I determine the maximum number of channels in parallel before the pump stalls? I can calculate the syringe pressure from the diameter of the syringe and the max linear force.

Here is what I did. Using electrical circuit analogy, we can calculate the hydraulic resistance (R_H) in parallel and we have set flow rate (Q) from the syringe pump. I drew a schematic using a circuit drawing tool for simplicity. For a circular shape channel, the resistance is calculated as follows:

R_H=8μL/(πd⁴ )
Where L is the length of the microchannel
d is the diameter of the microchannel
μ is the dynamic viscosity.

Assume all resistances are equal R_H1 to R_H4.

Now I can calculate the total hydraulic resistance for the parallel channels.
The total flow rate is the sum of all flow rates

then we have
∆P=R_Htotal*Q

I am not sure where to go from here. What if I want to pressurize the system to let's say 50 psi? rather than having the system in atmospheric?

How do I link what I calculated to what I am trying to find? Image attached

Thanks

 

[jrmichler]

If I understand correctly, you want a flow of 60 ml/hr through each microchannel. If we can assume that each microchannel is the same size and length, then the pressure drop through each channel will be the same.

If all of the microchannels are in parallel, then the pressure needed will be the same regardless of the number of channels. The total flow will be 60 ml/hr times the number of channels.

The flow is almost certainly laminar. You can verify that by calculating the Reynolds number (search the term) for your channel at your flow rate. If the Reynolds number is less than 2000, you have laminar flow. In that case, the flow rate will be proportional to pressure. If you double the pressure, the flow rate will double from 60 ml/hr to 120 ml/hr.

If you need calculate the pressure drop for a flow rate, search Moody chart. Note that the total pressure drop includes the pressure drop of the channels from the pump to the microchannels. That pressure drop is added to the pressure drop of the microchannels.

 

[Lnewqban]

A running pump will not be able to supply that small amount of fluid per minute without creating problems of heating, etc.
It seems that you will need to keep a constant upstream pressure at all times, while having a fixed resistance to the tiny flow.

Consider experimentation and a way to modulate that upstream pressure as your best friends in your goal of delivering a precise volume.
Also consider the practical feasibility of drilling those micro channels and ways to keep them unclogged with time of operation.