I have a fluid mechanics questions. Suppose that we a submillimeter needle that is already inserted in the soft tissue. water can run through this needle if the pump is on. suppose we turn the pump on. Waterjet with initial velocity of v0 starts to cut a channel in soft tissue. There is also backflow as this cuts the tissue (backflow from the same cut channel). my question is what happen to the velocity of the waterjet when it hits tissue and goes through backflow. Is it time dependent? Is it depth dependent? Experiments showed that it is velocity dependent since the depth of cut reached from 0 to say 4 mm in 30 second and after that it increases with the order of like 0.01 mm. So it got me thinking that velocity is depth and time dependent. My pump provided volumetric flow rate Q ml/min so the average velocity of waterjet at the nozzle is v = Q/A.
I have developed a mechanics based model for waterjet based on tissue properties and waterjet needle properties including velocity of waterjet. However for Q = 50 ml/min and 0.32 mm needle the velocity is approx. 10 m/s. including this velocity in model predicts a depth of cut in the order of meter which it should be in the order of mm. How can I include the effect of depth and time in my velocity. Any help is greatly appreciated.
Please also see the attached cartoon for a simple demonstration.
Some comments that may help solve your problem:
1. The water jet will leave the tip of the syringe with a velocity equal to Q/A where Q is the flow rate and A is the area of the flow cross section of the syringe tip.
2. The velocity of the jet of the point of impact is zero due to the no slip condition. The fluid decelerates significantly in the vicinity of the impact. Ideally you would like that all the momentum of the jet at the exit of tip is fully converted in a impact force that cuts the tissue. You want that the fluid only decelerates in the vicinity of the impact.
3. Most likely, you have a jet immersed in water, so the jet momentum dissipates before the impact due to viscous dissipation. The dissipation will depend on the depth of the hole (the amount of water the jet needs to go through). Since depth is time dependent the velocity will be depth and time dependent.
4. If you want to improve the system you need to operate the jet immersed in air, which has a lower viscosity. So the backflow water needs to be drained efficiently.
Following with great interest....
Thank you so much for sharing this article.
Regards,
Emad
Dear Mahdieh Babaiasl
The infiltration process in the tissue is a time dependent process. Su, you should make a transient model for the calculation.
What software you use?
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