Subdynamic asymptotic behavior of microfluidic valves

Abstract

Abstract-Decreasing the Reynolds number of microfluidic no-moving-part flow control valves considerably below the usual operating range leads to a distinct "subdynamic" regime of viscosity-dominated flow, usually entered through a clearly defined transition. In this regime, the dynamic effects on which the operation of large-scale no-moving-part fluidic valves is based, cease to be useful, but fluid may be driven through the valve (and any connected load) by an applied pressure difference, maintained by an external pressure regulator. Reynolds number ceases to characterize the valve operation, but the driving pressure effect is usefully characterized by a newly introduced dimensionless number and it is this parameter which determines the valve behavior. This summary paper presents information about the subdynamic regime using data (otherwise difficult to access) obtained for several recently developed flow control valves. The purely subdynamic regime is an extreme. Most present-day microfluidic valves are operated at higher Re, but the paper shows that the laws governing subdynamic flows provide relations useful as an asymptotic reference.[1017]

Fluidic Valve for Reactor Regeneration Flow Switching

“…where A is cross-section of the nozzle exit, DP is the measured (or computed) pressure drop, b is the nozzle exit annulus width, _ M M is the mass flow rate, and n is fluid viscosity, the result being a product of Euler number and Reynolds number (Tesař, 2003a). This unusual parameter was introduced in the context of very low Reynolds number microfluidics (Tesař, 2001), where it is particularly useful as an asymptotic reference (Tesař, 2003a), reaching a constant asymptotic value in the subdynamic regime limit Re !…”

“…This unusual parameter was introduced in the context of very low Reynolds number microfluidics (Tesař, 2001), where it is particularly useful as an asymptotic reference (Tesař, 2003a), reaching a constant asymptotic value in the subdynamic regime limit Re ! 0.…”