© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

9.2.7.1 Pressure Release Pumps

Some form of motive force must be applied to cause fluid to flow through a tube. The simplest possible motive force is pressurization. Consider a valved cylindrical nozzle of radius r_tube and length l_tube attached to a reservoir of volume V_reservoir maintained at a constant pressurization p_reservoir (even while being emptied). When the valve is opened, the fluid vents through the nozzle at a maximum velocity v_max into an external fluid environment having static pressure p_external < p_reservoir, emptying the reservoir in a time t_empty, both given by:

{Eqn. 9.35}

{Eqn. 9.36}

Taking p_external ~ 1 atm, h = 0.6915 x 10^-3 kg/m-sec for water at 310 K, r_tube = 10 nm and l_tube = 100 nm, then holding v_max <~ 10 micron/sec (the velocity of random thermal intracellular hydrodynamic flows; Section 8.5.3.12) for intracellular discharges requires a driving pressure of p_reservoir ~ 0.5 x 10^-3 atm, which takes t_empty ~ 0.3 sec to empty the reservoir at an energy cost (Eqn. 9.27) of P_flow t_empty ~ 55 zJ (~13 kT). As a practical matter, normal variations in physiological pressure due to ~1 Hz heartbeat pulse waves are 0.5-10 x 10^-3 atm in the tissues and veins and up to 50-70 x 10^-3 atm in the aorta (Section 4.9.1.2), so either valve aperture or p_reservoir must be dynamically controlled if a steady exit velocity is required at such low discharge velocities. In addition, a minimum pressurization of ~p_force (Eqn. 9.24) must be used to overcome capillary forces and initiate the flow. Device cooling during rapid gas discharge is described in Section 5.3.3.

Last updated on 20 February 2003