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DIFFUSION
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WHAT IS DIFFUSION ?
Diffusion is a process of migration of solute molecules
from a region of higher concentration to a region of lower
concentration and is brought by random molecular motion.
Movement from one side of membrane to another side.
Diffusion is a time dependent process.
Movement is based on kinetic energy(speed), charge, and
mass of molecule
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DIFFUSION
 It is defined as a process of mass transfer of individual
molecules of a substance brought about by random
molecular motion and associated with a driving force
such as a concentration gradient.
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DIFFUSION BASED PROCESS
Drug absorption
Drug elimination
Drug release
Osmosis
Ultra filtration
Dialysis
Mambrane
Barrire
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STEADY STATE DIFFUSION
A system is said to be steady state , if the condition do
not vary with time
dc/dt or dm/dt
should be constant for diffusion
 To described steady state diffusion fick’s I and II laws
should be described
 Fick’s first law gives flux in a steady state of flow. Thus it
gives the rate of diffusion across unit cross section in the
steady state of flow.
 Second law refers to the change in concentration of diffusant
with time ‘t’ at any distance ‘x’.
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Consider the diffusant originally dissolved in the left
hand compartment of the cell , solvent alone is placed on the
right hand side of the barrier, the solute diffuses through the
central barrier from solution to solvent side.
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FICK´S I LAW
The amount “M” of material flowing through a unit
cross section “S” of a barrier in unit time “t” is known as the
flux “J”
dM
J
S .dt
The flux, in turn, is proportional to the concentration
gradient, dc/dx:
dc
J  D
dx
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Diffusion coefficient/ diffusivity
No. of atoms
crossing area A
per unit time
dn
dc
  DA
dt
dx
Cross-sectional area
Concentration gradient
Matter transport is down the concentration gradient
Flow direction
A
As a first approximation assumed D ≠ f(t)
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J  atoms / area / time  concentration gradient
dc
J
dx
dc
J  D
dx
1 dn
dc
J
 D
A dt
dx
dn
dc
  DA
dt
dx
Fick’s first law
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FICKS SECOND LAW
An equation for mass transport that emphasizes the
change in concentration with time at a definite location
rather than the mass diffusing across a unit area of barrier in
unit time is known as Fick’s second law
c
J

t
x
Differentiating the first law expression with respect to
x one obtains
J
c

D 2
x
x
2
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substituting Dc/dt From
the above equation
c
 2c
D 2
t
x
Its represents diffusion only in x direction
  2c  2c  2c 
c
 D 2  2  2 
t
 x y z 
Its represents diffusion in three dimensions
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STEADY STATE
The solution in the receptor compartment is constantly
removed and replaced with fresh solvent to keep the
concentration at low level . This is know as “ SINK
CONDITION ” . The left compartment is source and right
compartment is sink.
The diffusant concentration In the left compartment
falls and rises in the right compartment until equilibrium is
attained , based on the rate of removal of diffusant from the
sink and nature of barrier .
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When the system has been in existence a sufficient time,
the concentration of diffusant in the solution at the left and
right compartments becomes constant , but obviously not
same .
Then within each compartment the rate of change of
concentration dc/dt will be zero and by second law.
dc
d 2c
D 2 0
dt
dx
Concentration will not be constant but rather is likely to
vary slightly with time, and then dc/dt is not exactly zero.
The conditions are referred to as a “QUASI STATIONARY
STATE” and little error is introduced by assuming steady
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state under these conditions.
Diffusion through membranes
Steady Diffusion Across a Thin Film and Diffusional
Resistance
• steady Diffusion across a thin film of thickness “h”,
•the concentration of both sides cd&cr kept constant,
•Diffusion occurs in the direction the higher concentration(Cd) to lower
concentration(Cr) the concentration of both sides cd&cr kept constant,
• after sufficient time steady state is achieved and the concentrations are constant at all
points,
•At steady state (dc/dt=0), ficks second law becomes
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Permeability
after sufficient time steady state is achieved and the concentrations are
constant at all points
at steady state (dc/dt=0), ficks second law becomes
 2e
D 2 0
z
Integrating above equation twice using the conditions that at z=0,c=Cd and at
z=h, C=Cr yields the fallowing equation
D
J  (c1  c2 )
h
The term h/D is called deffusional resistance “R” the flux equation can be
written as
c1  c2
J
R
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If a diaphragm separates the two compartments of a diffusion
cell, the first law of fick’s may be written as
dM
 c1  c2 
J
 D

Sdt
 h 
Where,
S=cross sectional area
H=thickness
c1 ,c2= concentration on the left and right sides of the
membrane
(c1-c2)/h within the diaphragm must be assumed to be
constant for quasi-stationary state to exist.
The concentrations c1,c2 can be replaced by partition
coefficient multiplied by the concentration Cd on the donor
side or Cr on receiver side.
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c1 c2
K

cd cr
dM DSK (cd  cr )

dt
h
P
DK
(cm / sec)
h
If sink condition in the receptor compartment
Cr  0
dM DSKcd

 PSCd
dt
h
P=permeability coefficient
P is obtained from slope of a linear plot permeant (M) vs. t.
M  PSCd t
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Procedures and apparatus
assesing drug diffusion
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SIMPLE DIFFUSION CELL
The diffusion chambrer constructed in a simple way
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DIFFUSION CELL FOR PERMEATION THROUGH
STRIPPED SKIN LAYERS:
It is developed by wurster et al. to study the diffusion
through stratum corneum of various permeants , including
gases, liquids and gels.
A-glass stopper
B-glass chamber
C-aluminum collar
D-mambrane & sample holder
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BIOLOGIC DIFFUSION
Gastrointestinal absorption of drugs
Drug pass through living membranes according to two
main classes of transport
1) passive transfer
It involves a simple diffusion driven by differences in
drug concentration on the two sides of the membrane.
2)carrier mediated
This is 2types
a)active transport (requires energy)
b)facilitated diffusion(does not depend on energy )
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pH-partition Hypothesis
Biologic membranes are predominantly lipophlic, and
drugs penetrated theses barriers mainly in their molecular,
undissociated form.
drugs are absorbed from the gastrointestinal tract by
passive diffusion depending on the fraction of undissociated
drug at pH of the intestines.
pH-partition principle has been tested in a large number
of in vitro and in vivo studies, and it is only partly applicable
in real biologic systems.
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Transport of a drug by diffusion across a membrane such as the gastrointestinal mucosa
is governed by Ficks law

dM Dm SK

(c g  c p )
dt
h
Gut compartment has high conc. and a large volume compared to Cp, Cg becomes
constant and Cp relatively small. Equation becomes
dM Dm SKCg


dt
h
Where,
M= amount. Of drug in gut compartment at time ‘t’
Dm=diffusivity in intestinal membrane
S= area of the membrane
K= partition coefficient
h= membrane thickness
Cg=conc. of drug in intestinal compartment
Cp=conc. of drug in plasma compartment
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the left hand side converted in to concentration units, C(mass/unit volume) x
V(volume). On the right hand side of the diffusion constant, membrane area , partition
coefficient, and membrane thickness are combined to yield a permeability coefficient. These
changes leads to the pair of equations
V
dcg
V
dc p
dt
dt
 Pg C g
 Pp C g
1
2
Cg , Pg are the concentration And permeability coefficient for drug
passage from intestine to plasma for reverse passage of drug from plasma to
intestine
Cg and V are constants
dC g / dt
dC p / dt

Pg
Pp
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Modification PH -partition Hypothesis
PH partition principle is only approximate ,
assuming drugs that absorbed through intestinal
mucosa , in nondissociated form alone.
For Small , ionic and nonionic following
complicating factors must be considered
1. Metabolism of drugs in the gastrointestinal membrane
2. Absorption in micellar form
3. Enterohepatic circulatory effects
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Applications
• Release of drugs from dosage forms diffusion controlled
like sustained and controlled release products.
• Molecular weight of polymers can be estimated from
diffusion process.
• The transport of drugs from gastrointestinal tract, skin
can be predicted from principal of diffusion.
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• Processes such as dialysis, micro filtration, ultra
filtration, hemodialysis, osmosis use the principal of
diffusion.
• Diffusion of drugs into tissues and excretion through
kidney can be estimated through diffusion studies.
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References
‘SINKO .J PATRICK’ , “Martin’s physical pharmacy and
pharmaceutical sciences” , 5th edition , pp no.301 to 337.
‘SUBRAMANYAM.C.V.S’ , “A text book of physical
pharmaceutics” , pp no.-110 to 127.
The theory and practice of industrial pharmacy ,leo
lachmann ,heberta. Liberman ,joseph L. Kanio:3rd edition
,pg no- 158 to 159.
Encyclopedia of pharmaceutical technology , 2nd edition
,volume -2: pg no -1246 to 1247 ; edited by james swarbrick
,james C.Boylan.
www.phrmainfo.net
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