I need help in calculating the total pressure required to move droplets in a micro channel network with constrictions.
I am moving 100 droplets in a micro-channel which also has 100 constrictions. Now as far as hydrodynamic resistance goes its calculated straightforward and the resistance of the entire channel will add up while calculating total pressure drop.
this resistances will be in series for series connection and parallel for parallel micro channel connection just like ohm's law and Kirchhoff's law analysis in electrical equivalent.
but when the droplet has to pass a constriction, it has to overcome additional laplace pressure given by Δp=2ϒ*[1/Wchan-1/Wconst], where Wchan is channel width and Wconst is constriction width, assuming that height of both channel and constriction is same. ϒ is the surface tension.
so what is the total pressure required to overcome this laplace pressure for all hundred droplets if they are connected in series and parallel as shown in diagram? all the droplets will reach the constriction at the same time
for eg. if laplace pressure difference calculated at one constriction is 4 mbar, then for 100 droplets in series will it be 400 mbar ? and for 100 droplets in parallel will it remain 4 mbar?
When coupled in series, the pressure drop is indeed additive. When you apply 400mbars you can be sure that all drops pass.
When coupled in parallel, the idea that they all should pass the constrictions at the same time seems unrealistic; if one drop passes the constriction, the flow will short-circuit at that point and the applied pressure at all other points will be modified depending on details in the flow geometry. If you apply 4mbars you can be sure that at least one drop passes, but what happens next is unknown.
Kind regards
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