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

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

9.2.7.7 Containerized Flow

Once a block of fluid has passed into the interior of a nanodevice, it may be containerized or divergently subdivided and then transported at velocities far higher than diffusive flow (Eqn. 3.1) or Poiseuille flow (Eqn. 9.25) would otherwise permit. The velocities available in containerized flows are largely independent of fluid viscosity and total transport time (unlike diffusive flow), and are nearly independent of fluid pressure and flow channel length (unlike Poiseuille flow).

For easy comparison, consider a disk-shaped container of radius r_block and thickness h_block with useful fractional storage volume f_block (to account for container wall thickness and mechanism overhead). After loading with fluid, the container is transported through a channel of radius r_tube ~ r_block and length l_tube at a velocity v_block, giving a volumetric flow rate of 'V_block = p r_tube² f_block v_block (m³/sec) which is superior to the Poiseuille flow rate in a pressurized tube of equivalent size when:

{Eqn. 9.42}

Containerized transport thus may be preferred to Poiseuille flow in narrow, long transport channels, or in cases where fluid pressure is relatively low or fluid viscosity is relatively high, or where containers can be very thin-walled (e.g., high f_block) such as when strong diamondoid containers are used. For example, a containerized transport channel carrying water at 310 K with r_tube = 10 nm, l_tube = 1 micron, Dp = 1 atm, and f_block = 0.9 produces volume flow rates superior to Poiseuille flow if container transport velocity v_block > 0.002 m/sec. Container/channel sliding interfaces moving up to 1 m/sec have low frictional losses,¹⁰ and speeds up to ~100 m/sec can probably be tolerated in internal mechanisms if flow speed (entirely inside nanodevices) is a more important design criterion than minimizing power dissipation in a particular application. An additional consideration is that subdividing a volume of fluid into many smaller blocks of fluid allows these smaller blocks to be transported independently through numerous spatially independent channels of much smaller bore, greatly increasing the number of flow design options and greatly increasing the relative advantage over Poiseuille flow through channels of similar size.

Last updated on 20 February 2003