Numerical analysis of high frequency pulsating flows through a diffuser-nozzle element in valveless acoustic micropumps

Abstract

The concept of a valveless acoustic micropump was investigated. Two-dimensional, time-varying, axisymmetric, incompressible viscous flows through a planar diffuser-nozzle element were analyzed for applications in valveless acoustic micropumps. The diffuser divergence half-angles (h), and the maximum pressure amplitudes (P) were independently varied. The inflow was periodic and the excitation frequency (f) was varied over the range 10 kHz B f B 30 kHz. The net time-averaged volume flux and the rectification capability of the diffuser were found as functions of h, f, and P. The phase difference between pressure and velocity waveforms, the life time and the size of large scale flow recirculation regions inside the microdiffuser, and energy losses were found to be strongly frequency dependent. Keywords Acoustic micropumps Á Acoustic standing waves Á Microdiffuser Á Numerical analysis List of symbols DP Pressure drop (Pa) d Stokes layer thickness (m) g Rectification capability k Acoustic wavelength (m) l Shear viscosity (kg/m s) m Kinematic viscosity (m 2 /s) x Angular frequency (rad/s) q Density (kg/m 3 ) h Diffuser divergence half-angle (°) n d Pressure loss coefficient in the diffuser direction n n Pressure loss coefficient in the nozzle direction D h Hydraulic diameter of the microdiffuser at the inlet (m) f Excitation frequency (Hz) I Flow inductance (kg/m 4 ) I d Flow inductance in the diffuser direction (kg/m 4 ) I n Flow inductance in the nozzle direction (kg/m 4 ) N Cell numbers P Maximum pressure (Pa) p Pressure (Pa) p 0 Static pressure (Pa) Q Volumetric flow rate (m 3 /s) Q net Net flow rate (m 3 /s) R Flow resistance (kg/m 4 s) R d Flow resistance in the diffuser direction (kg/m 4 s) R n Flow resistance in the nozzle direction (kg/m 4 s) Re Reynolds number T Excitation period (s) t Time (s) U Maximum velocity (m/s) u Velocity in x direction (m/s) v Velocity in y direction (m/s) V net Sectional net velocities (m/s) Wo Womersley number x Axial position (m) x max Maximum fluid displacement during one oscillation cycle (m) y Transverse position (m) Z Flow impedance (kg/m 4 s) Z d Flow impedance in the diffuser direction (kg/m 4 s) Z n Flow impedance in the nozzle direction (kg/m 4 s)

Steady and unsteady flow analysis in microdiffusers and micropumps: a critical review

“…Two main types of fixed microvalves have been used in valveless micropumps which are microdiffusers (Stemme and Stemme 1993;Gerlach et al 1995;Olsson et al 1999;Pan et al 2001;Schabmueller et al 2002;Yang et al 2004a;Jeong and Kim 2007;Sun and Yang 2007;Hwang et al 2008;Nabavi and Mongeau 2009) and Tesla microvalves (Forster et al 2001;Feldt and Chew 2002;Morris and Forster 2003). In fixed microvalves wear and fatigue in the valves are eliminated since they have no moving parts.…”

“…Very recently, a new diffuser-based pumping mechanism has been proposed by the author and his co-workers, which is able to pump fluids at both macroscale (valveless standing wave pump) (Nabavi et al 2008a) and microscale (valveless acoustic micropump) (Nabavi and Mongeau 2009). In reciprocating valveless micropumps, a moving diaphragm does pressure work on the working fluid in a periodic manner.…”

“…These studies were performed with water as the working fluid. In Sun and Huang (2006), Wang et al (2007) and Nabavi and Mongeau (2009) single microdiffuser has been investigated, whereas, the total pump has been analyzed in the rest of the studies. Pan et al (2001) suggested an optimal frequency range for reciprocating valveless micropumps based on an analytical model.…”

“…The volume flow rate increased linearly with the voltages from 15 to 40 V at the resonance frequency. Nabavi and Mongeau (2009) simulated the high frequency (10 kHz B f B 30 kHz) pulsating flows through microdiffusers for different divergence angles and maximum pressure amplitudes. This range of frequency is used in valveless acoustic micropump in order to keep the chamber length small (L min = k/4).…”

Microfluidic rectifier based on poly(dimethylsiloxane) membrane and its application to a micropump

“…By contrast, in dynamic microfluidic pumps, a continous energy source is used to exert a steady driving force on the fluid. Nabavi and Mongeau 35 performed a numerical investigation into the effects of the divergence angle and maximum pressure amplitude on the characteristics of high-frequency (10$30 kHz) pulsating flows through a micro-diffuser. Wang et al 36 presented a valveless micropump incorporating a nozzle-shaped actuation chamber, which functioned as both a pumping chamber and a flow rectification structure.…”