MICRO AND NANOSCALE SYSTEMS - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 176

Amount of injected substance is determined by the electrophoretic and total
electro-osmotic mobilitiesm.
In the hydrodynamic mode of entry by the pressure difference in the channel
or capillary of circular cross section, the volume of injected probe V c :

Dπ
= h
where D p -pressure differential; d -diameter of the channel; h- viscosity.

4 p dt

V .

c

128 L

2.3 CONTINUUM HYPOTHESIS
In the simulation of processes in micron-sized systems the following basic prin-
ciples are fundamentals:
1) Hypothesis of laminar flow (sometimes is taken for granted when it
comes to microfluidics);
2) Continuum hypothesis (detection limits of applicability);
3) Laws of formation of the velocity profile, mass transfer, the distribution
of electric and thermal fields;
4) Boundary conditions associated with the geometry of structural elements
(walls of channels, mixers zone flows, etc.).
Since we consider the physical and chemical transport processes of matter
and energy, mathematical models, have the form of systems of differential equa-
tions of second order partial derivatives. Methods for solving such equations are
analytical (Fourier and its modifications, such as the method of Greenberg, Galer-
kin, the method of d'Alembert and the Green's functions, the Laplace operator
method, etc.) or numerical (explicit or more effectively, implicit finite difference
schemes).
Laminar flow. ; a condition in which the particle velocity in the liquid flow is
not a random function of time. The small size of the microchannels (typical di-
mensions of 5 to 300 microns) and low surface roughness create good conditions
for the establishment of laminar flow. Traditionally, the image of the nature of the
flow gives the dimensionless characteristic numbers: the Reynolds number and
Darcy's friction factor.
In the motion of fluids in channels the turbulent regime is rarely achieved. At
the same time, the movement of gases is usually turbulent.
Although the liquids are quantized in the length scale of intermolecular dis-
tances (about 0.3 nm to 3 nm in liquids and for gases), they are assumed to be
continuous in most cases. Continuum hypothesis (continuity, continuum) sug-
gests that the macroscopic properties of fluids consisting of molecules, the same
as if the fluid were completely continuous (structurally homogeneous). Physical
characteristics: mass, momentum and energy associated with the volume of fluid
containing a sufficiently large number of molecules must be taken as the sum of
all the relevant characteristics of the molecules.