Process Intensification: An Overview of Principles and Practice - Process Intensification for Green Chemistry - page 8

Kolgomorovor Batchelor length scale. At themicroscale level, theKolgomorov length scale,
h K (representing smallest scales of turbulence before viscosity effects dominate), and
Batchelor length scale, h B (representing smallest scales of fluctuations prior to molecular

diffusion), are defined as [17-19]:

1 = 4

v 2
e

h K ¼

(1.7)

1 = 4

vD l
e

¼ h K

p

Sc

h B ¼ (1.8)

, for liquids is typically of the order of 10 3 , so that

v
D l

where the Schmidt number, Sc ¼

h B << h K . For aqueous solutions in turbulent regimes, m.

The physical phenomena of the micromixing process include engulfment, deformation
by shear and diffusion of the fine-scale fluid elements. The relevant mixing times
associated with these processes are [5]:

h K is of the order of 10-30 m

0 : 5

v
e

Engulfment

: t e ¼

17 : 2 (1.9)

0 : 5

v
e

Shear deformation and diffusion : t Ds 2 arc sinh ð 0 : 05 Sc Þ (1.10)

More often than not, t D S << t e , resulting in the overall micromixing process being

dictated by the progression of the engulfment phenomenon taking place at the Kolgomorov
length scale.
Although the actual molecular mass transfer process before the reaction is ultimately
achieved by molecular diffusion, enhancing the rates of macro- and mesomixing through
turbulent hydrodynamic conditions enables faster attainment of the fluid state, where
micromixing and therefore molecular diffusion prevail.

1.3.3 Transport Processes

Understanding transport processes is at the heart of PI, as the subject can be defined as a
search for new ways of enhancing or achieving transport of mass, heat or momentum.
Transport processes - heat, mass and momentum transfer - are generally governed by
equations of the same form. They are all flows in response to a 'driving force' - a
temperature difference, a concentration difference and a pressure difference, respectively -
opposed by their respective resistances. Brief overviews of the intensification of mass, heat
and momentum transfer follow.

1.3.3.1 Heat Transfer

Heat transfer - the transport of energy from one region to another, driven by a temperature
difference between the two - is a key consideration in the design of all unit operations. Unit
operations have defined operating temperatures, so the heat flows in and out must be
understood in order to maintain the temperature within a desired range. Reactors, for