**Diffusion**

__Contents of
This Chapter__

•Definition and concept of diffusion

•Concept of steady state diffusion and the laws involved
with it

•Methods and procedures of conducting diffusion studies

•Applications of diffusion

__Learning
Objectives__

• At the end of this lecture, student will be able to

– Explain the concept of diffusion

– Explain steady state and sink condition

– Explain the different laws involved in the process of
diffusion

– Explain the different methods and procedures to conduct
the in vitro diffusion experiment

__Diffusion-Definition
and Concept__

• Diffusion is defined as a process of mass transfer of
individual molecules of a substance from a region of higher concentration to a
region of lower concentration along a concentration gradient

• The process of diffusion occurs across a barrier

• Barrier is a
region or regions
that offers resistance
to the passage of materials

• The material that undergoes the transport is known as
diffusant or penetrant or permeant

__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

__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.

__DIFFUSION
BASED PROCESS__

• Drug absorption

• Drug elimination

• Drug release

• Osmosis

• Ultra filtration

• Dialysis Membrane

__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’.

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, and the solute diffuses through the central barrier from solution to
solvent side.

__Steady
State Diffusion__

• The diffusion of molecules is estimated using a transport
cell shown below.

• Steady state- a system is said to be steady state, if the conditions
do not vary with time

• In case of diffusion, the mass transfer remains constant
with time i.e., dc/dt or dM/dt is constant

• If the condition vary with time the system is under
unsteady state

• During the diffusion process, the concentrations of solute
in the donor and acceptor compartments must be maintained constant

• Both the compartments are connected to large reservoirs of
solutions and recirculated

• Sink condition – It is a state in which the concentration
in the receptor compartment is maintained at a lower level compared to the
concentration in the donor compartment

• During diffusion study, the donor compartment acts as a
source and the receptor compartment acts as a sink

• This condition is maintained by connecting the receptor
compartment to a large reservoir from which the solution is recirculated

• It is easy to maintain sink condition rather than steady
state, because recirculation in one compartment is sufficient.

• Sink condition is employed in practice and mass transfer
is approximated as steady state

__Fick’s
First Law__

• In diffusion, molecules (mass) get transported from one
compartment to another over a period of time i.e., rate of mass transfer (dM/dt).This
is expressed as flux

• Flux is equal to the rate of mass transfer across a unit
surface area of a barrier

• The flux J, can be mathematically expressed as:

**𝟏
𝒅𝑴**

** J= -- ----- ……………….(1)**

**𝑺
𝒅****t**

Where, dM=change in the mass of material, g

S=barrier surface area,cm2

dt=change in time, sec

• The units for flux are g.cm-2sec-1

• In SI units, it can be expressed as
kilogram.meter-2.time-1

• Time may be given in minutes, hours or days

• Fick’s first law states that the flux is directly proportional
to the concentration gradient

• Fick’s law can be expressed as:

**𝒅𝑪**

** J= -D----- ………………..(2)**

**𝒅****x**

Where, dC=change in
concentration of material, g/cm3

D=diffusion coefficient of a penetrant, cm2/sec dx=change in
distance, cm

• Flux is a positive quantity and increases continuously
during the process

• The dx is perpendicular to the surface of the barrier

• Combining equations (1) and (2) we get:

**𝒅𝑴 ****𝒅𝑪**

** ----- = -DS -------- …………. (3)**

**𝒅𝒕 ****𝒅****x**

• Equation (3) represents the rate of mass transfer as per
Fick’s first law

• The diffusion coefficient, D, may change in its value with
high concentration

• The diffusion coefficient, D, is affected by temperature,
pressure, solvent properties and chemical nature of diffusant.

• ‘D’ is not a constant but a coefficient

__Fick’s
Second Law__

• Fick’s second law states that the change in concentration
with time in a particular region is proportional to the change in the concentration
gradient at that point of time

• The second law explains the change in the concentration
with time at a definite location with respect to x, y and z axes

• In a particular volume element, the concentration, C,
changes as a result of net flow of molecules into and outside the region

• dC is due to difference in the input and output, at the
same time dC also changes with time i.e., (ΔC/ Δt)

• Change in dC is as a result of flux or amount of diffusing
molecules changes with distance, (ΔJ/ Δx) in the x direction.

• This relationship can be expressed as:

**δ C δ
J**

** ------ = − ----- ……….(4)**

**δt δx**

Considering Fick’s first law expression from equation (2)

** dC**

**J= -D----**

** d𝑥**

And differentiating the equation with respect to x gives:

**δJ δ ^{2}C**

** ---- = −D
------- …………………(5)**

**δx δx ^{2}**

δ C δ J

Substituting
the ---- in equation (5) for -----, we
get

δt δx

**δ C δ ^{2}C**

** ------- = D
------- …………….(6)**

**δt δx ^{2}**

• Equation (6) represents diffusion in x-direction only.

• Extending the equation (6) in all the coordinates, Fick’s
second law can be given by:

__Methods and Procedures__

• For the diffusion studies, two compartment cells are used.

**1. Horizontal
transport cell**

**2. 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.

3. Vertical transport cell

• Horizontal cells are designed to study the skin permeation
of drugs. This systems
are used as
in vitro models
for drug absorption

• Vertical cells are used for diffusion of gases and
liquids. The diffusion of drugs from ointments, transdermal drug delivery
systems can be studied using these cells

• The diffusion cells are made up of glass, plexiglass,
pyrex or plastic

• The cells are jacketed and thermostated in order to
maintain the temperature

__Applications
of Diffusion Studies__

• It is used for the interpretation of the release of drugs
from the different dosage forms.

• Molecular weight of polymer can be estimated from
diffusion studies

• The transport of drugs (absorption) from GIT, skin, etc.,
can be predicted

• The diffusion of drugs into tissues and their excreation
through kidneys can be anticipated

• The processes such as dialysis, microfiltration,
ultrafiltration, haemodialysis, osmosis etc., use the principles of diffusion

__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)

**PH-partition
Hypothesis**

• Biologic membranes are predominantly lipophlic, and drugs
penetrated these 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.

Transport of a drug by diffusion across a membrane such as
the gastrointestinal mucosa is governed by Ficks law

Gut compartment has high conc. and a large volume compared
to Cp, Cg becomes constant and Cp relatively small. Equation becomes

**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

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

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

__Modification
of 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

• 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.

__Summary__

• Diffusion is defined as a process of mass transfer of
individual molecules of a substance from a region of higher concentration to a
region of lower concentration along a concentration gradient

• Steady state- a
system is said to be steady state, if the conditions do not vary with time

• Sink condition – It is a state in which the concentration
in the receptor compartment is maintained at a lower level compared to the
concentration in the donor compartment

• In diffusion, molecules (mass) get transported from one
compartment to another over a period of time i.e., rate of mass transfer (dM/dt).This
is expressed as flux

• Flux is equal to the rate of mass transfer across a unit
surface area of a barrier

• Fick’s second law states that the change in concentration
with time in a particular region is proportional to the change in the
concentration gradient at that point of time

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