Mass Transport in Nanoscale Environments

General Problem 2

To formulate the governing laws of transport of mass through nanoscale environments within biological cells.

  • Simplified Problem 5 (SP5): To determine the laws of (diffusional, electro-osmotic, magnetic, other… combined and multiphysical) mass transport in nanopores and nanochannels, as function of the nanoscale geometry, and the chemical/physical properties of the nanopore/nanochannel walls, of the transported species and of the fluid(s) through which transport takes place.
  • Simplified Problem 6 (SP6): Same as SP5, with the addition of time dynamics of chemical transformation such as degradation of the transported species, and their effect on the surfaces of the nanochannels/pores (e.g., changes in charge, thickness, hydrophobicity).
  • Simplified Problem 7 (SP7): Same as SP6, with the addition of phenomena at the nanopore/nanochannel wall that are specific to the molecules/particles of the transported species.
  • Simplified Problem 8 (SP8): To derive the laws of transport at the nanoscale, starting with Brownian motion, employing methods of statistical mechanics, with the addition of constraint conditions.
  • Simplified Problem 9 (SP9): Hypothesis is that the solution of SP8 will also yield Eq. (5). This is an implicit statement for SP9. 

    Ferrari Challenge - Equation 5 - My hypothesis is that the solution of SP8 will also yield Eq. (5).

  • Simplified Problem 10 (SP10): To derive the closed form, exact expression for the strain concentrator tensor, for the general case of a bi (multi)phasic composite with arbitrary anisotropy, orientation distribution, and concentration of the phases.