Diffusion final

Diffusion
• Diffusion is defined as a process of mass
transfer of individual molecules of a substance
• Diffusion is Migration of solute molecules
from higher concentration to lower
concentration to achieve equilibrium
• In case of osmosis escaping tendency of
solvent molecules is measured
• In case of diffusion escaping tendency of
solute molecule is measured
• In pharmacy diffusion through natural barrier
or polymeric barrier is important

• membrane is film separating the phases which
may be porous or non porous
• Diffusant or permeant orpenetrant is The
material that undergoes the transport by
passive diffusion
Application
• Controlled and sustained release follows
diffusion controlled
• Molecular weight of polymer can be
estimated
• Transport of drug from GIT can be predicted
through diffusion studies

• Diffusion of drugs into tissues and their
excretion through kidney can be studied
through diffusion
• Dialysis,micronisation,ultrafiltration,haemodia
lysis,osmosis use the principle of diffusion

STEADY STATE DIFFUSION
• At Steady state - conditions do not vary with
time
• In case of diffusion mass transfer remains
constant with time OR mass transfer takes
place at constant rate through the study and
diffusion process is not allowed to attain
equilibrium
• If condition vary with time then the system is
under unsteady state

Transport cell
• Transport cell is used to study the diffusion
• Which consists of donor and receptor
compartment separated by membrane
• Permeant dissolved in solvent and placed in
donor compartment
• Vehicle is placed in receptor compartment
• The permeant get transported in to receptor
comportment through membrane
• At steady state mass transfer remains constant

SINK CONDITION
• It is the state in which the concentration in the
receptor compartment is maintained at lower
level compared to its concentration in the donor
compartment
• This can be maintained by connecting receptor
compartment to a large reservoir from which
solution is reticulated
• It is easy to maintain sink condition than steady
state condition due to maintaining constant
gradient in donor compartment is difficult

Flux
• Rate of mass transfer (dM/dt) expressed as of
flux(J)
• Flux (J) is rate of mass transfer across unit
surface area of a barrier and mathematically
expressed as: J ≡ atoms / area / time

1 dM dM = change in mass of material, g
J= S = surface area.cm2
S dt d t = change in time.sec

Units for flux are g.cm -2sec -1 OR kg .meter -2sec -1

Flux is always positive quantity because it
increases continuously during process

Fick’s I law
• Fick’s first law states that the flux is directly proportional
to the concentration gradient
J ≡ atoms / area / time ∝ concentration gradient

dc OR dc Negative sign indicates
J∝ J = − D ...( 2) a decrease in concentration
dx dx But flux is positive quantity
flux in steady state flow
dc=change in conc. of material g/cm 3.
D=diffusion coefficient of a penetrant, cm/sec2.
Dx=change in the distance, cm.
1 dM dc
J= J = −D 1 dM dc
S dt dx J= = −D
Combining equation and i.e. S dt dx
dM dc
...(3)
Eqn 3 explains Rate of
We get = −DS mass transfer as per fick’s first law
dt dx
D is effected by temperature, pressure etc hence it is not constant it is coefficient

Fick’s I law
Diffusion coefficient/ diffusivity
No. of atoms dM dc
crossing area A = − DS Cross-sectional area
per unit time dt dx Concentration gradient

Mass transport is down the concentration gradient

Flow direction
A

Application of fick’s first law
• Used to explain drug diffusion across
biomembranes with desirable parameters

• Applied in the design of sustained and
controlled release systems

Fick’s Second Law ; Non-steady state Diffusion
It explains the change in conc. at definite location
with respect to x , y and z axes(or direction)
Fick’s second law states that the change in y J
y
concentration With time in a particular region
is proportional to the change In the concentration Jx
gradient at that point of time Jz x
z
∆c
The concentration ∂c i.e.  
∆t
changes with time due to
∆J
change in amount or flux ∂J i.e.   of diffusing
∆x
molecules with in the x direction

• The relationship can be expressed w.r.t -x ,y and z
as: = − ∂J
∂c ∂c ∂J ∂c ∂J
=− =−
∂t ∂x ∂t ∂y ∂t ∂z
Partial derivatives notation used due to
concentration is a function of both x or y or z and t
dc dc dc
J = −D J = −D J = −D
dx dy dz
Differentiating above equation w.r.t x ,y and z respectively
∂J ∂C 2 ∂J ∂ 2C ∂J ∂ 2C
= −D 2 = −D = −D 2
∂x ∂x ∂y ∂ y2 ∂z ∂z
substituting for ∂C , ∂C and ∂C in above equation for ∂J , ∂J and ∂J
∂t ∂t ∂t ∂x ∂y ∂z
∂C ∂C 2 ∂C ∂ 2C ∂C ∂ 2C
= −D 2 = −D = −D 2
∂t ∂x ∂t ∂ y2 ∂t ∂z

∂C ∂ C ∂ C ∂ C 
2 2 2
= −D 2 + + 2
∂t ∂ x ∂y 2
∂z 

Fick’s second law refers to change in concentration
of diffusant with time at any distance x i.e. non
steady state flow

DIFFUSION CONTROLLED RELEASE
HIGUCHI’S EQUATION
• Sustained and controlled release of a drug
form a table has been obtained by
incorporating the drug in insoluble matrix
such as plastic ,resin, wax and fatty alcohol
• In this matrix model ,outside layer of the drug
is exposed to the bathing solution
• Then the drug diffuses out of the matrix
• The rate of dissolution of drug particle within
the matrix must be faster than that of
diffusion rate of drug leaving the matrix

The rate of release of drugs dispersed in an inert
matrix system has been derived by higuchi
dM Cs
= C0 dx − ........(1)
dt 2

where
dM = change in the amount of drug released per unit time
dx = change in the thickness of the zone of matrix
that has been depleted of drug
C 0 = total amount of drug in unit volume in the matrix
Cs = saturated conc of the drug in the matrix

Dm Cs
From diffusion theory dM = dt........( 2 )
x

Where Dm is diffusion coefficient in the matrix
Equating eqn 1 and 2 ,integrating and solving for x gives

M = [ Cs Dm ( 2C0 − C s ) t ]
1
2

When the amount of drug in excess of saturation concentration
that is Co>Cs
M = [ C s Dm 2C0t ] 2 ......( 3)
1

Eqn 3 indicates that the amount drug released is a function of square root time

M = kt
1
OR 2

Methods and procedures
• Two types
• A) horizontal transport cell
wurester cell
Viles chein permeation cell
• B) vertical transport cell
Aquair and weiner diffusion cell
biber and rhodes cell
franz diffusion cell

Horizontal Transport Cell
wurester cell
Receptor and donor
compartment made of pyrex glass
material
Animal or human skin acts as semi
permeable cell and barrier may be
supported on a perforated plate
Drug sample solution taken in donor
compartment and solvent in the
receptor compartment
Whole set up placed in constant
temperature bath to maintain the
temp of 37±0.2
The liquid in receptor stirred by
using magnetic beads to obtain

vertical Transport Cell
Viles chein skin permeation cell
Receptor and donor compartment
made of pyrex glass or glass or
plexi glass material
permeable cell
This system used for as in vitro
models for drug absorption and used
to test drug diffusion from
ointments ,transdermal patches etc
Whole set up placed in constant The liquid in receptor stirred by using
temperature bath to maintain the magnetic beads to obtain uniform
distribution
temp of 37±0.2

Aquair and weiner diffusion cell
made of pyrex glass or plastic
material
Drug sample solution taken in upper
lower compartment
temp of 37±0.2

biber and rhodes cell
This is three compartment cell
Two Receptor and one donor
compartment
Synthetic or isolated biological
membrane can be used
Drug sample solution allowed to
diffuse from two donor
compartment to inner receptor
compartment
liquid in receptor stirred by
using magnetic beads to
obtain uniform distribution

scheuplein cell
made of pyrex glass material
temp of 37±0.2
uniform distribution

franz diffusion cell
modified version of
different cell for in-vitro studies
Excised human cell membrane acts
as semi permeable membrane
Drug sample solution filled in donor
temperature bath to maintain the The liquid in receptor stirred by using
temp of 37±0.2 magnetic beads to obtain uniform
distribution

Transport across GI tract
• Most of drugs ,when administered ,have to
pass through GI membrane to reach blood
• The structure and nature of GI tract decide
the transport of drugs
• These barrier are highly complex structure
composed of lipids ,proteins , lipoproteins and
polysaccharides and lipoidal in nature

Polar heads Fluid Mosaic
love water Model of the
& dissolve. cell membrane

Non-polar
tails hide
from water.
Carbohydrate cell
markers

Proteins

Types of diffusion
• Passive diffusion
• Active transport
• Facilitated diffusion
• pinocytosis

Answer any Four Questions
Each question carries 5 marks
1) List out the method to determine interfacial tension
explain any one method
2) Write a note on factors influencing rate of reaction
3) What are chelates give its application
4) What are adsorption isotherms explain different
types
5) Explain chemical degradation by oxidation
6) Write a note on size distribution curves
7) Explain-how particle sizes are expressed
8) Define and differentiate order and molecularity of a
reaction

Diffusion final

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