4. IPPP-II (Diffusion and Dissolution) pdf.pdf

12/11/2025 DIFFUSION AND DISSOLUTION 1
DIFFUSION AND DISSOLUTION

Learning Objectives
 After finishing this chapter the student will have thorough knowledge
of:
Definition of diffusion, osmosis, dialysis, ultrafiltration
Fick’s law of diffusion (steady state, diffusion through a membrane)
Applications of diffusion in pharmaceutical sciences
Dissolution of particles (Noyes-whetney equation, factors affecting
dissolution)
Intrinsic dissolution rate
Sink conditions, Lag time and burst effects

Introduction
 Diffusion
defined as a process by which molecules transfer spontaneously
from a region of higher concentration to a region of lower
concentration
As a result of random molecular motion
associated with a driving force such as a concentration gradient.
governs the transport of the great majority of drugs across various
biological barriers after administration.

Introduction…
 The theory of diffusion has been used :
in investigating the mechanism of drug transport
applied to the design and development of various controlled or
sustained release

Introduction…
 Drug release (Dissolution) of drugs from its dosage form
 Passage of gasses, moisture, and additives through the packaging
material of the container
 Permeation of drug molecules in living tissue (absorption,
distribution, Elimination of drugs)

Introduction…

Introduction…
 The molecules that migrate from one location to another are termed
as diffusants, permeants or penetrants
 The medium in which the diffusant migrates is called the diffusional
barrier.
 The concentration gradient is the concentration profile of the
diffusant in the diffusional barrier.
 The concentration gradient is the driving force for diffusion

Introduction…
Osmosis
 Movement of water across a selectively permeable membrane
 Down its concentration gradient
 Toward the solution containing the higher solute concentration

Introduction…
 Osmosis is important in the development of DF
 Isotonicity
Parenteral, ophthalmic, and nasal solutions should be isotonic
relative to the osmotic pressure of blood.

Introduction…
 Osmotically controlled drug delivery system
use osmotic pressure as a driving force for the controlled
delivery of drugs.

Introduction…
 Reverse Osmosis in Pharmaceuticals
• uses a semi-permeable membrane to separate water from impurities

Introduction…
Ultrafiltration
 is used to separate colloidal particles and macromolecules by the
use of a membrane.
 Hydraulic pressure is used to force the solvent through the
membrane
 the microporous membrane prevents the passage of large solute
molecules.
 similar to a process called reverse osmosis

Introduction…

Introduction…
Microfiltration
 a process that employs membranes of slightly larger pore size
(100nm to several micrometers)
 Used to removes bacteria from intravenous injections, foods, and
drinking water

Introduction…
Dialysis
 as a separation process based on unequal rates of passage of
solutes and solvent through microporous membranes
 Hemodialysis is used in treating kidney malfunction to rid the blood
of metabolic waste products (small molecules) while preserving the
high-molecular weight components of the blood.

Introduction…
Hemodialysis

Fick’s law of diffusion
 In 1855, Fick described diffusion of molecules in quantitative terms
 The quantitative description of diffusion through a given unit area,
expressed as follows, is called Fick’s first law
 Flux (J) is the amount of material M (units = grams or moles) crossing
a unit area S (units = cm2) in time t
 Flux (J) is a measure of the rate
J =
dM
Sdt
Adolf Fick

Fick’s law of diffusion….
 The flux, in turn, is proportional to the concentration gradient
 To change from the proportionality sign to an equal sign, a constant is
added:
Where, D is the diffusion coefficient, or diffusivity(cm2/sec)
dC/dx is the concentration gradient
C is its concentration in g/cm3
x is the distance in centimeter
J α
dC
dx
J = −D
dC
dx

Fick’s law of diffusion….
 The negative sign of equation indicate that diffusion occurs in a
direction (the positive x direction) opposite to that of increasing
concentration.
 Diffusion will stop when the concentration gradient no longer exists
(i.e., when dC/dx = 0).
 D is affected by concentration, temperature, pressure, solvent
properties, and the chemical nature of the diffusant

Fick’s law of diffusion…
 Therefore, combining the previous two equations:, Fick’s first law is
written as
 The concentration gradient across the membrane (dC/dx) from the
donor side to the receptor side can be simplified as:
 Therefore, the rate of transport (dM/dt) will be given as:
dM
dt
= −DS
dC
dx
dC
dx
=
C1 − C2
h
dM
dt
= DS
C1 − C2
h

Fick’s law of diffusion…
The concentration
gradient of solute
across the membrane.

Steady state diffusion
 When the amounts of diffusant enter and leave the given space at the
same rate, the concentration of the diffusant in the given volume is a
constant.
 The diffusion process that meets this condition is considered a steady
state diffusion
 The concentration in the given space is independent of time.

Non-steady state diffusion
 A diffusion process in which the concentration of diffusant in a given
space is a function of time
 the concentration of diffusant in the diffusional barrier varies with time
 In this case, the Fick’s second law to study the diffusion process.

Distribution or partition coefficient
 Distribution or partition coefficient is a measure of the ability of a
compound to distribute in two immiscible phases.
 The partition phenomenon is of paramount importance for the
diffusion across skin and other epithelia.
 Many pharmaceutical processes based on the partition principles
absorption from the gastrointestinal tract after oral administration
 drug distribution following entry into systemic circulation

Distribution or partition coefficient…
extraction and isolation of pure drugs after synthetic
manufacturing or from crude plant sources
formulation of a stable dosage form (emulsion, etc.),
assay of plasma concentrations,
 These all are based on the partition principles

 The ability of drugs to penetrate a biological membrane has been
evaluated using its partition in an octanol and water system.
 Occasionally, other organic solvents such as chloroform, ether, and
hexane have been used as a lipid vehicle.
 When a drug is placed in an immiscible system composed of
octanol and water,
the drug distributes in each solvent and eventually reaches
equilibrium.

 The ratio of drug concentration in each phase is termed its
distribution coefficient or partition coefficient (K)

 Practically, concentration in an aqueous phase is determined by
chemical assays, such as
high performance chromatography
ultra violet spectroscopy
gas chromatography,
gas chromatography–mass spectroscopy
 Conce. In octanol is obtained by??

Example:
 Succinic acid (0.15 g) dissolved in 100 ml of ether was shaken with 10
ml of water at 37ºC. After equilibrium was achieved, the water layer
contained 0.067 g of succinic acid. What is the partition coefficient (K)
of succinic acid?
Answer = 0.124

Diffusion coefficient & permeability coefficient
 A diffusion coefficient (D) represents the mobility of a molecule in a
specific medium, the diffusional barrier.
 The mobility of a substance in a diffusional barrier is determined by:
the physicochemical properties of the diffusant
the diffusional barrier
the temperature.
J = −D
dC
dx

Diffusion coefficient & permeability coefficient…
 The relationship of the diffusion coefficient and these factors is
expressed quantitatively in the Strokes–Einstein equation,
 which states the diffusion coefficient as a function of temperature (T),
viscosity (η), and size of the diffusant (r)
where k is the Bolzmann constant.
D =
kT
6πղr

 The set-up has two compartments divided by the diffusional barrier,
for example, a membrane with a thickness of h.
 The concentrations of diffusant in each compartment are denoted
Cd and Cr.
 The concentrations of diffusant in the diffusional barrier are denoted
C1 and C2 for each side of the barrier

 Cd and Cr can be determined experimentally, but C1 and C2 are
usually not known.
 The concentrations of a diffusant in the diffusional barrier and the
adjacent medium can be related by using partition coefficients (K) as
follows:
 Therefore, the concentrations of diffusant in the diffusional barrier can
be expressed as:
K =
C1
Cd
=
C2
Cr
C1 = KCd C2 = KCr

 Substituting into the previous equation, the rate of transport in a
diffusion system is:
 For any given system, the other parameters (i.e., DK/h) are constant
termed as permeability or permeability coefficient (P)
dM
dt
= DSK
Cd − Cr
h
dM
dt
= DS
C1 − C2
h
P =
DK
h

Sink Condition Approximation
 In most pharmaceutical systems, the concentration of drug in the
receptor side (Cr) is significantly lower than that at the donor side.
 When the concentration Cr is approximately zero, this state is defined
as the sink condition.
 Sink conditions occur when the rate of exit of drug from a
compartment is much greater than the rate of entry.

Sink Condition Approximation…
 Under sink conditions, it can be assumed that Cr = 0 and:
 This equation can be written as:
dM
dt
=
DSK
h
Cd
dM
dt
= PSCd
dM = PSCddt

Sink Condition Approximation…
 Integrating the equation from zero to infinity, it is possible to find the
equation
 Used for the amount of drug transported through a membrane as a
function of time:
M = PSCdt

Example 1
A drug passing through a 1-mm-thick membrane has a diffusion
coefficient of 4.23 × 10− 7 cm2/s and an oil–water partition coefficient of
2.03. The radius of the area exposed to the solution is 2 cm, and the
concentration of the drug in the donor compartment is 0.5 mg/mL.
Calculate the permeability (P) and the diffusion rate of the drug.
Solution
h =1mm=0.1cm
D= 4.23 × 10− 7 cm2/s
K= 2.03
r = 2cm, S = πr2 =12.57cm2
Cd =0.5mg/mL
P=DK/h = [(4.23 × 10− 7 cm2/s)(2.03)]/0.1cm = 8.59 x 10-5 cm/s
dM/dt = PSCd = 0.19 mg/h

Example 2
To study the oral absorption of paclitaxel from an oil-in-water emulsion
formulation, an inverted closed-loop intestinal model was used. The drug was
instilled in the intestine, and the system was maintained at 37°C (98.6°F) in an
oxygen-rich buffer medium. The surface area available for diffusion was 28.4
cm2, and the concentration of paclitaxel in the intestine was 1.50 mg/mL.
Calculate the amount of paclitaxel that will permeate the intestine in 6 h of study
if the permeability coefficient was 4.25 × 10−6 cm/s. Assume zero-order
transport under sink conditions.
Solution
Using the equation M = PSCdt, the amount of paclitaxel permeated in 6 h
(21,600 s) will be: M= (4.25 x10-6)(28.4)(1.50)(21,600) =3.91mg

Experimental methods
 The diffusion process can be studied by using various methods
 The most commonly used method in pharmaceutical research is the
permeation method using simple diffusion cell.
 The experimental set-up for this method consists of two chambers
separated by a diffusional barrier.
 The donor chamber is filled with drug solution

Experimental methods…
Simple diffusion cell

Experimental methods….
 Samples are collected from the receiver compartment
 The amount of diffusant permeating the diffusional barrier is
determined quantitatively by chemical analysis.
 Mathematically, the amount of cumulative permeation of diffusant (M)
can be derived from integration
 The permeation coefficient (P) can be obtained from the slope of a
plot of cumulative permeation of diffusant vs time.
dM
dt
= PSCd
M = PSCdt

Experimental methods….

Lag-Time and Burst Effects
 The time required to reach steady state is called the lag time (tL).
 It is the time required to saturate the membrane
 The lag time can be determined by extrapolating the linear portion of
permeation vs. the time curve to the time axis
 The lag-time effect (tL) is dependent on the thickness of the
membrane and the diffusion coefficient of the drug
𝑡𝐿 =
ℎ2
6𝐷

Lag-Time and Burst Effects…
Diffusion of lidocaine through
poly(vinyl alcohol acetate)
membrane

 Therefore, correcting for the lag time into the equation of the
amount released as a function of time:
 The burst effect is observed in:
 systems that have been stored for a long time
the rate-controlling membrane is pre-saturated with the drug
M = PSCd(t−tL)

 The burst effect (tB) is also dependent on the thickness of the
membrane and the diffusion coefficient and is expressed as:
 Correcting for the burst effect, the equation for amount released is
written as:
tB =
h2
3D
M = PSCd(t−tB)

Zero-order release in the presence of lag-time and burst effects.

Example-1
A newly synthesized steroid is allowed to pass through a siloxane
membrane having a cross-sectional area, S, of 10.36 cm2 and a
thickness, h, of 0.085 cm in a diffusion cell at 25◦C. From the horizontal
intercept of a plot of Q = M/S versus t, the lag time, tL, is found to be 47.5
min. The original concentration C0 is 0.003 mmole/cm3. The amount of
steroid passing through the membrane in 4.0 hr is 3.65 × 10−3 mmole.
Calculate the parameter
 permeability, P
 diffusion coefficient, D
 partition coefficient, K

Example-1…

Example-2
The lag time of methadone, a drug used in the treatment of heroin
addiction, at 25°C (77°F) through a silicone membrane transdermal
patch was calculated to be 4.65 min. The surface area and thickness
of the membrane were 12.53 cm2 and 100 μm, respectively.
 Calculate the permeability coefficient of the drug at 25°C (77°F) (K = 10.5).
 Calculate the total amount in milligrams of methadone released from the
patch in 12 h if the concentration inside the patch was 6.25 mg/m

Solution

Dissolution
 Dissolution is a process in which a solid substance solubilizes in a
given solvent
i.e. mass transfer from the solid surface to the liquid phase.
 Rate of dissolution
 is the amount of drug substance that goes in solution per unit time
under standardized conditions of temperature and solvent
composition.

Dissolution process of solid dosage Forms :
DISINTEGRATION DISSOLUTION
DISSOLUTION ABSORPTION
IN-VIVO
IN-VIVO
DISAGGREGATION
DISSOLUTION
TABLETS OR
CAPSULES
GRANULES OR
AGGREGATES
FINE PARTICLES
DRUG IN
SOLUTION
(IN-VITRO OR IN-VIVO)
DRUG IN
BLOOD,OTHER
FLUIDS,AND
TISSUES

Dissolution mechanism
 The mechanism of dissolution could be explained by two models:
 diffusion-limited model
 Reaction limited model

Dissolution mechanism….
The reaction-limited dissolution can be explained by
 the interfacial barrier model
 the Danckwert model.

Dissolution…
Diffusion layer model/Film Theory of dissolution
 It involves two steps :-
 Solution of the solid to form stagnant film or diffusive layer which is
saturated with the drug
 Diffusion of the soluble solute from the stagnant layer to the bulk of
the solution.
Noyes–Whitney

Dissolution…

Dissolution…
 Noyes and Whitney described the quantitative analysis of the amount
of drug dissolved from solid particles as a function of time
𝐝𝐌
𝐝𝐭
=
𝐃𝐒(𝐂𝐬 − 𝐂𝐛)
𝐡
where
dM/dt = rate of drug dissolution at time t,
D = diffusion coefficient
S = surface area of the particle
h = thickness of the stagnant layer
Cs =the concentrations of the drug at the surface of the particle
Cb =the concentrations of the drug bulk medium

Dissolution…
 Under sink conditions, Cb << Cs,
 The Noyes–Whitney equation can
be simplified as:
 If the dissolution rate constant (k
= D/h, in cm/s)
𝑑𝑀
𝑑𝑡
=
𝐷𝑆𝐶𝑠
ℎ
𝑑𝑀
𝑑𝑡
=KSCs
Relationship of the amount dissolved as a
function of time under sink and non-sink
condition

Dissolution…

Solution

Solution…

Hixson-Crowell Cube-Root Relationship
 Major assumption in the Noyes-Whitney relationship is that the
surface area (S) term in the equation remains constant throughout the
dissolution process
 However, the size of drug particles from tablets, capsules, and
suspensions will decrease as the drug dissolves
 To take into account the changing surface area, Hixson and Crowell
modified the Noyes-Whitney equation

Hixson-Crowell Cube-Root Relationship…
Where, Qt is the amount of drug released in time t,
Q0 is the initial amount of drug in the dosage form/product,
K is the rate constant for Hixson-Crowell cube root equation,
which describes the surface area-volume relationship..
𝑸𝟎
𝟏/𝟑 − Qt
1/3=Kt

Factors affecting Drug Dissolution
1. Factors relating to the physicochemical properties of drug
Solubility
Particle size and effective surface area of the drug
Polymorphism and amorphism
Salt form of the drug
Hydrates/solvates

Factors affecting Drug Dissolution
2. Factors relating to the dosage forms.
A) Pharmaceutical excipients
Vehicle
Diluents
Lubricants
Binders
Surfactants
Colorants

Factors affecting Drug Dissolution…
B ) Manufacturing processes
Method of granulation
Compression force
Intensity of packing of capsule content
Influence of compression force on dissolution rate of tablets

𝑑𝑀
𝑑𝑡
=
𝐷𝑆(𝐶𝑠 − 𝐶𝑏)
ℎ
S: Rate of dissolution  with S
Cs Rate of dissolution  with
differences in Cs-Cb
Cb: Rate of dissolution  with  Cb
D: Diffusion coefficient
h: Rate  with  h
Affected by
Size of solid particle
Dispersibility
T, Nature of dissolution
medium, crystalline form…
Volume of dissolution
medium…
Viscosity of medium
Degree of agitation

Intrinsic dissolution rate (IDR)
 IDR is the rate of dissolution of a pure pharmaceutical active
ingredient when the surface area, stirring speed, pH and ionic
strength of the dissolution medium is kept constant
 is a prime indicator of the bioavailability of a drug candidate

In-vitro dissolution testing
 Alternative to in vivo bioavailability determination
 may give an indication of drug bioavailability and bioequivalence
 Dissolution testing – Official in pharmacopeias (USP, BP, EP…..)
 Quantify the extent of release of drug
 Routinely used by Q.C. and R&D

Dissolution Apparatus
 Rotating Basket Apparatus (Apparatus 1)
 Rotating Paddle Apparatus (Apparatus 2)

Dissolution Apparatus….

Add the dissolution medium(±1 %) in the vessel
Equilibrate dissolution medium to 37±0.5°C
Place 1 tablet or capsule in the apparatus
Immediately operate the apparatus at the rate specified rate
Withdraw a specimen from a zone at specified time
Sample analysis
Diffusion and Dissolution 80

USP Acceptance Criteria for Dissolution Results
Stage Number
tested
Criteria
S1 6 Each unit is not less than D* + 5%
S2 6 Average of 12 units (S1 + S2) is equal to or greater
than D, and no unit is less than D – 15%
S3 12 Average of 24 units (S1 + S2 + S3) is equal to or
greater than D, not more than 2 units are less
than D – 15% and no unit is less than D – 25%.
*D is the amount of dissolved drug, expressed as a percentage

Summary
 Diffusion, Osmosis, Dialysis, Ultrafiltration
 Fick’s law of diffusion
 Types of diffusion
 Distribution or partition coefficient
 Factors affecting rate of diffusion
 Sink condition
 Dissolution theories
 Factors affecting dissolution rate

Quiz-2
 A pharmaceutical company is developing a new oral tablet
formulation for a poorly soluble drug. During preliminary testing,
they observe that the dissolution rate of the drug is significantly
lower than expected.
 Questions:
 Discuss potential physicochemical factors that could be influencing
the dissolution rate of the drug.
 Based on the Noyes-Whitney equation, how might the company
modify the formulation to enhance the dissolution rate?

4. IPPP-II (Diffusion and Dissolution) pdf.pdf

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