The Microfluidic Blood Cell Counter · AI Generator #GEN-8AA46D19
Physics · fluid-mechanics
Problem
Modern medical devices use microfluidic channels to count blood cells by measuring pressure changes as cells pass through narrow constrictions. Consider a simplified model of such a device:
A horizontal microfluidic channel has a wide section of cross-sectional area A1=400μm2 connected to a narrow constriction of area A2=100μm2. Blood plasma (viscosity η=1.2×10−3Pa⋅s, density ρ=1025kg/m3) flows through the channel at a steady volumetric flow rate Q=2.0×10−15m3/s.
When a spherical red blood cell of diameter d=7.0μm enters the constriction, it completely blocks the narrow section, forcing all fluid to flow around it through an effective annular area. The cell moves through the constriction with the same speed as the fluid would have in that section without obstruction.
During the time the cell blocks the constriction, what is the pressure difference between the wide section and the exit of the constriction? Assume the channel length from wide section to constriction exit is L=50μm, and treat the flow as laminar with the cell creating a uniform annular flow region.
Note: For laminar flow through a channel, the pressure drop follows ΔP=πd432ηLQ for circular cross-sections of diameter d.