Fluid flow and mass transfer

FLUID FLOW
&
MASS TRANSFER
Md. Saiful Islam
BPharm, MSc
North South University
Fb Group: Pharmacy Universe

Definition of Fluid - a substance that has no fixed shape and yields easily to external
pressure; Any substance that does not offer permanent resistance to distortion. Thus,
liquids, gases, and vapours will be included.
A flow can be Laminar, Turbulent or
Transitional in nature. This becomes a very
important classification of flows and is
brought out vividly by the experiment
conducted by Osborne Reynolds in 1883. He
injected a dye into a flowing fluid (water) of
varying velocity and observed its path as it
was carried by the fluid. When the speeds
were small the flow seemed to follow a
straight line path (with a slight blurring due to
dye diffusion). As the flow speed was
increased the dye fluctuates and one observes
intermittent bursts. As the flow speed is
further increased the dye is blurred and
seems to fill the entire pipe.
Definition of Flow - the action of moving along in a steady, continuous stream.

When the velocity of the water is low, the
thread of dye remains undisturbed in the
center of the water stream and moves
steadily along the tube, without mixing. This
condition is known as streamline, viscous, or
laminar flow.
As the velocity is increased to high values
eddies begin to occur in the flow, so that the
dye mixes with the bulk of the water
immediately after leaving the injection
needle. Since this is a state of complete
turbulence, the condition is known as
turbulent flow.
At moderate velocities, a point is reached (the
critical velocity) at which the thread begins to
waver, although no mixing occurs. This is the
phase of transitional force.

As a result of his experiments, Reynolds found
that flow conditions were affected by four
factors:
Diameter of pipe
Velocity of fluid
Density of fluid
Viscosity of fluid
All these factors can be connected into a
particular expression known as Reynolds
Number:
ρud
Re =
µ
Where Re = Reynolds Number; ρ = density of fluid
(kg/m3); u = velocity of fluid (m/s); d = diameter of
pipe (m); µ = viscosity of fluid (kg/ m s)
Significance of Re:
The significance of Reynolds
Number is that it can be used to
predict the character/pattern of
flow in a particular set of
circumstances. In general:
Re < 2000 = Laminar flow
2000 < Re < 4000 = Unstable flow*
Re > 4000 = Turbulent flow
*The flow at this range of Re values
depends on the form of the flow
channel. If there is no disturbance
of any sort the flow pattern may
persist being laminar even at values
exceeding 2000. On the other hand,
if the pipe surface is rough or if
there are bends or other pipe
fitting, flow maybe turbulent at
values less than 4000, possibly
lower even than 2000!

Distribution of Velocities across the tube and the Boundary Layers:
When a fluid flows along a tube, not all parts are moving at the same velocity, so
that, for example, a portion near the wall will not travel at the same velocity as fluid
near the center. The outer ‘layer’ is held back by drag against the wall, while
frictional forces also exist between the various layers (viscosity of the fluid). Thus,
the fluid in the center can move at a the highest velocity, with the frictional forces
causing a continual decrease in the velocity towards the wall, until, ultimately, it
becomes zero at the wall itself. Since Re is proportional to u (velocity), the value of
Re also decreases and hence as the diagram above demonstrates as we approach
near the wall the flow changes from turbulent to transitional to streamline to
ultimately stationary.

Boundary Layer
A layer of more or less stationary fluid (such
as water or air) immediately surrounding an
immersed object in relative motion with the
fluid.

• Mass transfer is the net movement of mass
from one location to another.
• Some common examples of mass transfer
processes are the evaporation of water from a
pond to the atmosphere; the purification of
blood in the kidneys and liver, and the
distillation of alcohol.
• In industrial processes, mass transfer
operations include separation of chemical
components in distillation columns, absorbers
such as scrubbers, adsorbers such as activated
carbon beds, and liquid-liquid extraction.

Solid/Fluid Mass transfer
• The transfer of mass from a
solid to a fluid
• Consider a crystal of a soluble
material immersed in a solvent
in which it is dissolving. The
crystal in this scenario is going
to be surrounded by a
stationary boundary layer of
the solute, with the bulk of the
fluid able to move. Such
movement could be natural
convection (arising from
temperature or density
changes), or forced convection
resulting from agitation.

• Hence, the transport of the molecules of
the dissolving solid will take place in two
stages:
– First, the molecules move through the
boundary layer by molecular diffusion,
with no mechanical mixing or movement.
(comparable to heat transfer by
conduction)
– Secondly, once the material has passed
through the boundary layer, mass transfer
takes place by bulk movement of the
solution, known as eddy diffusion.
(comparable to heat transfer by
convection)
• Since there is no limit to the vigor of the
movement of the bulk of the fluid, the
controlling factor in the rate of solution
of the crystal will be the molecular
diffusion through the boundary layer.

• Mass transfer by molecular diffusion can be represented by
an equation, similar to conduction heat transfer, in which:
W = DA (C1 – C2)θ
L
or, w = DA (C1 – C2)
L
Where, W = weight of solute diffusing;
w = weight of solute diffusing in unit time;
D = diffusion coefficient;
A = area;
θ = time;
C1 = concentration of solute at interface
C2 = concentration of solute in bulk;
L = Film thickness
Diffusion coefficient is a proportionality constant. The higher the value of
diffusion coefficient (of one substance with respect to another), the faster they diffuse into each
other. E.g. Carbon dioxide in air has a diffusion coefficient of 16 mm2/s, and in water its diffusion
coefficient is 0.0016 mm2/s

• A similar equation can be written for vapour:
w = DA (P1 – P2)
L
Where, P1 = partial pressure of vapour at interface;
P2 = partial pressure of vapour in the atmosphere

Fluid/Fluid Mass transfer
• The transfer of mass between two immiscible fluids, which
maybe two liquids or a liquid and a gas (or vapour).
• In this case there will be boundary layers of both fluids on
each side of the interface, where the slope of the
concentration gradients depends on the diffusion
coefficients in the two materials.

Mass transfer Influence on Unit Operations
• Mass transfer theory can be applied to any operation in
which material changes phase, whether it is solid/liquid,
solid/vapour (or gas), liquid/liquid, or liquid/vapour (or
gas).
• The effect can be seen in simple operations, such as the
making of a solution of a solid in liquid, where the rate of
solution can be increased by:
– Agitation, which reduces the thickness of the boundary
layers and disperses any local concentrations of solution, so
increasing the concentration gradient
– Elevated temperatures (which increases the solubility of most
materials) which increase the diffusion coefficient and
decrease the viscosity of the liquid, so reducing boundary
layer thickness.
– Size reduction of the solid, which increases the area over
which diffusion can occur.

Fluid flow and mass transfer

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