Diffusive spreading of time-dependent pressures in elastic microfluidic devices

Abstract

Here we show that transient flow of Newtonian fluids in viscoelastic PDMS microfluidic channels can be described by a diffusive pressure spreading mechanism analogous to the electric telegrapher's equation. The pressure diffusion constant D_p = 1/R_xC_x of a channel with length l is determined by the hydrodynamic resistance R_x and capacitance C_x per unit length of the channel. l²/D_p sets the timescale for the transmission of pressure steps along the channel and the relaxation after a pressure step in steady state flow. For oscillatory flows, the channel acts as a low-pass filter with a cutoff frequency ω_cutoff = 2πD_pl⁻², so that pressure and flow rate pulses disperse and get smoothed while they travel along the channel. The combination of different microparticle tracking techniques allows the determination of pressure and flow profiles at any point in the channel and excellent agreement with theoretical predictions is obtained.