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

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

9.2.6 Effervescence and Crystallescence

Diffusion-limited molecular inflow rates to nanodevices have already been discussed in connection with molecular transport (Section 3.2.2), chemical sensors (Section 4.2), chemical power sources (Sections 6.3.4.1 and 6.5.3), and chemical broadcast communication (Section 7.2.1). A related constraint applies when nanodevices attempt to offload endogenously produced or stored molecules into the local environment, whether by nozzled flow, reversible sorting rotors, or by simple bulk venting. If the excretion rate exceeds the solvation capacity of the surrounding solvent, offloaded gases may coalesce into bubbles and effervesce; offloaded solids may crystallize.

The inception of bubbles or crystals is a complex physical process whose detailed description is beyond the scope of this book. However, the diffusion-limited maximum offloading rate may be conservatively estimated by considering a point emission source releasing soluble gas molecules continuously into an aqueous environment at the constant rate 'Q (molecules/sec). Once emitted, molecules with diffusion coefficient D diffuse a distance DX ~ (2 D 'Q^-1)^1/2 (Eqns. 3.1 and 3.5), giving a minimum steady state concentration c_diffuse >~ (3 / 4p) ('Q / 2 D)^3/2 (molecules/m³). As an approximation at pressures <~100 atm for gases that do not chemically unite with the solvent, Henry's law gives the concentration of dissolved gas as c_solvated = K_henry p_gas (molecules/m³), where p_gas is the partial pressure of the solvated gas and K_henry is the Henry's law constant for the gas (Table 9.2). If the ambient concentration of the gas in the solvent is c_ambient, then the minimum offloading rate 'Q_limit necessary to enable the formation of bubbles occurs when c_diffuse >~ (c_solvated - c_ambient), or:

{Eqn. 9.34}

Thus for oxygen dissolving in 0.15 M saline (~human blood plasma), D = 2.0 x 10^-9 m²/sec (Table 3.3), K_henry = 7.4 x 10²³ molecules/m³-atm (Table 9.2), and c_ambient = 3 x 10²² molecules/m³ (venous plasma; Appendix B), we have 'Q_limit > 8 x 10⁷ molecules/sec at p_gas = 1 atm, or 'Q_limit > 2 x 10⁹ molecules/sec at p_gas = 100 atm. Faster offloading rates than 'Q_limit may cause effervescence. For carbon dioxide in saline (ambient arterial plasma concentration), 'Q_limit > 7 x 10⁸ molecules/sec (1 atm) or 1.5 x 10¹⁰ molecules/sec (100 atm). Once a gas bubble is formed and completely blocks a narrow pipe, the pressure required to dislodge it is approximately p_force as given by Eqn. 9.24, ~3 atm for an air bubble caught in a 1 micron wide tube carrying water at 310 K.

Similar considerations apply to solute releases which, if too rapid, may result in crystallization of the solid. In this case, Eqn. 9.34 may be used if c_solvated is taken as the saturation concentration at the appropriate temperature and pressure. For example, a saturated 70% glucose solution has c_solvated = 7.8 x 10²⁷ molecules/m³; taking D = 7.1 x 10^-10 m²/sec and c_ambient = 2.3 x 10²⁴ molecules/m³ (~blood plasma; Appendix B), 'Q_limit > 1.4 x 10¹⁰ molecules/sec.

Gas solubility almost always declines at warmer temperatures because gas-liquid solvation is exothermic, whereas the solubility of most solids (including glucose and most important electrolytes) usually rises at higher temperatures. (See also Section 10.5.3.)

Last updated on 20 February 2003