Transfer of Matter Diffusion- Osmosis- Dissolution rate

1. 
Transfer of Matter
Diffusion
Osmosis
Dissolution rate
Noha Gouda, M.Sc., PhD

2. MassTransfer
Mass transfer is the net movement of mass (atoms, molecules or
ions) from one location (stream, phase, fraction or component) to
another, driven by concentration gradients.
 Phase transition
 Separation
 Chemical processes

3. MassTransfer
Mass transport is involved in:
 Absorption
 Evaporation
 Sublimation
 Drying
 Precipitation
 Membrane filtration
 Distillation, etc.

4. MassTransfer
Mass transfer phenomena applying to the pharmaceutical sciences
include:
 Permeation and distribution of drug molecules in living tissues.
 Release and dissolution of drugs from tablets, powders, and granules
 Release from ointments and suppository bases
 Passage of water vapor, gases, drugs, and dosage form additives
through coatings, packaging, films, plastic container walls, seals, and
caps.
 Lyophilization
 Ultrafiltration

5. MassTransfer
Processes that will be studied:
 Diffusion
 Osmosis
 Dissolution (rate)

6. DIFFUSION
Diffusion of a dye in water
Spontaneous movement of solute molecules or ions (mass
transport) by random BROWNIAN MOVEMENT

7. High
Concentration
Low
Concentration
Movement According To The Concentration
Gradient

8. Movement is inversely proportional to the cross
sectional area of the solution (S)
Small surface
area
Large surface
area

9. Low amount
High amount
Movement is proportional to the amount flowing/unit time

10. Low viscosity
High viscosity
Movement is affected by the viscosity of the solvent

11. DIFFUSION
 Diffusion is the spontaneous
movement of solute molecules or
ions (mass transport) from a region
in which they are in high
concentration to regions of lower
concentration.
 The driving force is ONLY the
concentration gradient until the
diffused substance is evenly
distributed.
OnCourse Systems For Education

12. DIFFUSION
Diffusion takes place by random BROWNIAN MOVEMENT and NO
energy is consumed. In this case, the movement is known as
PASSIVE DIFFUSION.
Common examples for passive
diffusion are:
 Diffusion of dyes in water
 Diffusion of sugar in a cup of
tea,... etc

13. Fick’s first law of diffusion
Fick's first law relates the diffusive flux (J) to
the concentration field, assuming that:
The flux goes
 from regions of high solute
concentration to regions of low solute
concentration,
 with a magnitude that is proportional to
the amount, M, of material flowing per
unit time, t, (i.e. dM/dt) and inversely
proportional to the cross sectional area
of the solution (S):
𝑱 =
𝒅𝑴
𝑺.𝒅𝒕
……………….(1)
Adolf Eugen Fick (3 September
1829 – 21 August 1901) was a
German-born physician and
physiologist.
Wikipedia.com

14. Fick’s first law of diffusion
If:
 Concentration of the solute in a certain region is high (C1)
 In another region the concentration is low (C2),
 while the distance between these two regions is h,
Then
the flux (J) will be directly proportional to the CONCENTRATION
GRADIENT (difference in concentration C1-C2) and inversely
proportional to the distance traveled (h):
𝑱 = 𝑫
𝑪 𝟏−𝑪 𝟐
𝒉
……………….(2)
is the

15. Fick’s first law of diffusion
 From equations 1 & 2
𝑱 =
𝒅𝑴
𝑺. 𝒅𝒕
= 𝑫
𝑪 𝟏 − 𝑪 𝟐
𝒉
𝒅𝑴
𝒅𝒕
= 𝑫𝑺
𝑪 𝟏 − 𝑪 𝟐
𝒉
Fick’s First Law Of Diffusion

16. Diffusion coefficient
Described by Stokes-Einstein equation
𝐷 =
𝑘 𝐵 𝑇
6𝜋𝜂𝑟
D the diffusion coefficient of solute in a solvent
kB Boltzmann constant
T absolute temperature
𝜼 Viscosity of the solvent
𝒓 radius of the solute molecule
This equation is first derived by Einstein in his Ph.D thesis for the diffusion coefficient of a "Stokes" particle undergoing Brownian Motion in
a quiescent fluid at uniform temperature. The result was formerly published in Einstein's (1905) classic paper on the theory of Brownian
motion.
Thermopedia.com

17. Diffusion cell
The diffusion cell is composed of two compartments:
1. The donor compartment containing the drug (solute) solution
‘Diffusant’
2. The acceptor compartment containing the solvent alone
 The solute molecules diffuse through a semipermeable
membrane from solution in the donor compartment (high
solute concentration) to the acceptor compartment (low solute
concentration)
 The solution in the receptor compartment is constantly
removed and replaced with fresh solvent to keep

18. Diffusion cell
Sink conditions
In diffusion studies, the concentration C2 is kept small either by
 Increasing the volume of solvent in receptor compartment (very
dilute) or
 Continuous removal of the solution in receptor compartment.
In this case, C2 ≃zero then the equation will be:
𝒅𝑴
𝒅𝒕
= 𝑫𝑺
𝑪 𝟏
𝒉
This simulates the drug permeation across the biological membrane.

19. lubrizolcdmo.com

20. Salamanca, C.H.; et al. Pharmaceutics 2018, 10, 148.

21. 1. Diffusion of drug from the dosage form (drug release) into the
biological fluids.
Biopharmaceutical applications of Diffusion
Disintegration Dissolution Diffusion Absorption
Gothainayaki et al Journal of
Drug Delivery &
Therapeutics. 2019; 9:563

22. Biopharmaceutical applications of Diffusion
2. 90% of drugs cross the biological membranes such as the GIT
(drug absorption), the skin (drug penetration), the kidneys (drug
elimination),... Via DIFFUSION
Drug absorption through intestinal wall

25. Types of diffusion
 Simple diffusion
 Facilitated diffusion
 Dialysis
 Osmosis

26. Facilitated Diffusion
Passive movement of molecules across the cell membrane from
the region of higher concentration to the region of lower
concentration by means of a carrier molecule.
https://comis.med.uvm.edu

27. Dialysis
Diffusion of solutes across a selectively permeable membrane.
 Selectively permeable membrane or a semipermeable membrane
is the one that allows only specific ions and molecules to pass
through, while obstructs the movement of others.
Kidney dialysis
https://comis.med.uvm.edu

28. OSMOSIS
Osmosis is a special type of diffusion,
It is:
The diffusion of SOLVENT through a semipermeable membrane
from a more dilute solution to a more concentrated solution
 This process is passive (no external energy is needed)
https://comis.med.uvm.edu

29. Biological importance of osmosis
Osmosis and Cells
The movement of LIQUIDS in and out living cells depends on the
concentration of salt solution surrounding it.
OnCourse Systems For Education

30. Hydrophobic (non-polar)
compounds can dissolve in
the non-polar intestinal
membrane
Large polar compounds
and charged molecules
are insoluble in the lipid
membrane
 are not able to pass
freely to the blood.
pharmacology2000.com

31. Osmosis and Cells
There are three possibilities:
1. ISOTONIC: where the external salt solution
concentration and the internal concentration
within the cell are the same.
2. HYPOTONIC: where the external salt
solution concentration is less than that within
the cell In this case, water will rush into the
cell and the cell swells and probably burst.
3. HYPERTONIC: where the external salt
solution concentration is greater than that
within the cell. In this case, the water will
rush out of the cell and the cell shrinks.
 That’s why, usually isotonic saline solution
(0.91 %w/v) is used for IV infusions, rinsing
contact lenses, nasal irrigations,... etc.
OnCourse Systems For Education

32. biowithvanessa.wordpress.com

33. Dissolution
Dissolution may be defined as the process by which a solute enters
into solution when added to an appropriate solvent
In this process, a solution of the gas, liquid or solid in the original
solvent is formed.
Dissolution is process of a solute dispersing/dissociating in
a solvent to form at a molecular level a physically and
chemically homogenous dispersion called solution.

34. Dissolution of solid in liquid
Bulk Solution
Dissolution is the process by which a solid solute enters into solution when
added to an appropriate solvent
kinetic process in which solute particles interact with solvent particles to become
homogenous phase with solvent

35. Drug dissolution is the process by which
drug molecules are liberated from a solid
phase and enter into a solution phase.
Only drugs in solution can be
 Absorbed
 Distributed
 Metabolized
 Excreted, or
 Exert therapeutic effect.
Dissolution is an important process in the
pharmaceutical sciences.
Dissolution of solid in liquid
Disintegration Dissolution Diffusion Absorption
Gothainayaki et al Journal of Drug Delivery & Therapeutics. 2019; 9:563

36. DISSOLUTION RATE
 Dissolution rate refers to the rate at which this solid dissolves in solvent under
standard conditions of temperature, pH, solvent composition
 Dissolution rate process differs from solubility
Bulk Solution
Solubility is a saturation
process independent of time
The amount of solute that goes into solution per Unit Time

37. MajorTypes Of Dissolution
In solid in liquid solution , there are 2 major types of dissolution:
1. Solution phase contains the same solute chemical entity as found in
the original solid phase, upon removing the solvent we can recover
the original solute unaltered by the dissolution process:
 Example: dissolution of sucrose in water
2. Original solute is not recoverable or not completely recovered.
 The resulting solution contains a solute different from the original solid
phase.
 Some chemical reaction has occurred between the solvent and solute.
 When the solvent is removed, some or all of the solute is different from
the original added.
 In order to dissolution to occur , the solute was ionized and the solvent
was required to exert certain influence on the ions to overcome the
cohesive forces.

38. Example, Aspirin(Acetylsalicylic acid) in plain water. While in solution, aspirin
hydrolyzes forming acetic acid and salicylic acid .

39. Types of Dissolution
In both cases, in order to dissolution to occur, the solute particle
size is first reduced to initiate the dissolution process.
The dissolution process is measured as a rate.
 Noyes-Whitney equation describes the dissolution in a single
equation
Dissolution rate can :
 Be one step consideration with one associated rate, or
 Involve multiple steps each with its own rate, the collection of
individual rates results in an overall dissolution rate

40. Theories of Mechanism of Dissolution
Mechanism of Dissolution
 1. Diffusion layer model (film theory)
 Drug dissolution is a function of diffusion.
 2. Danckwert’s model (Penetration or Surface Renewal Theory)
 3. Interfacial barrier model (Double barrier or Limited solvation theory)
 Drug dissolution is a function of solubility rather than diffusion.

41. Mechanistic representation of the drug release process from solid dosage forms by disintegration
and dissolution. Unknown source
Dissolution Steps of a Solid Dosage Form

42. Mechanistic representation of the drug release process from a tablet by disintegration and
dissolution. (Courtesy of Wells and Rubinstein, 1976.)
Dissolution Steps of a Solid Dosage Form
For tablets and capsules
there are 3 steps involved in
dissolution:
1. Disintegration
2. Deaggregation
3. Dissolution

43. Mechanistic representation of the drug release process from a tablet by disintegration and
dissolution. (Courtesy of Wells and Rubinstein, 1976.)
Dissolution Steps of a Solid Dosage Form
 From any point direct,
dissolution can occur.
 From all steps dissolution
occur simultaneously
 Each step of dissolution has
its own dissolution rate
 Even dissolution from a
powder form can be
multistep process depending
on the solute particle size
(degree of particle size
reduction )

44. Process Of Fine Particles Dissolution
The process of fine particles dissolution involves 3 steps:
1. Wetting of solute by solvent
2. Immersion of the solute in the solvent : involving interfacial
and thermodynamics energetics.
3. Diffusion of molecules of solute into bulk solution.

46. Wetting and Immersion of Solute
 Ability of solvent to wet a solute depends interfacial
interactions between the solute and the solvent and on surface
tension of the solvent ( it will be discussed later) which in turns
depends on the intermolecular interactions between solute and
solvent molecules.
 Physically, air pockets if entrapped on surface of particles it can
slowdown the initial ability of the solute powder to contact the
solvent well.
 If work of adhesion exceeds work of cohesion, wetting of solute
will occur.
 Spreading of a liquid on solute surface will occur. Spreading is
favored when forces between different molecules exceeds those
between similar molecules

47. Wetting and Immersion of Solute
 To improve wetting, surfactants can be used that reduce
surface tension and allow particle wetting more easily
 Wetting of a solid can be an issue with any liquid form: solution,
suspension and emulsion.
 Once wetting of solute accomplished, the rest of dissolution
process continues: diffusion

48. Diffusion layer model/FilmTheory
It involves two steps :-
1. Solution of the solid to form stagnant film or
diffusive layer which is saturated with the drug
2. Diffusion of the soluble solute from the stagnant
layer to the bulk of the solution; this is rate
determining step in drug dissolution.

49. Diffusion Process
To illustrate diffusion process, diffuse double layer (DDL) method
was developed which help describe the parameters responsible for
the rate of diffusion.
The Noyes Whitney equation provides mathematical description of
the DLL model.

50. When solid dissolves, the solutes molecules pass down a diffusion gradient (diffusion
layer) until the particles completely dissolves and enters bulk solution.
Bulk Solution
Bulk
Solution
Diffusion
LayerSolid
Matrix
h
Cs
Ct
In the dissolution theory, it is assumed that:
An aqueous diffusion layer (stagnant liquid film) of a thickness (h)
exists at the surface of the solid (particle, tablet, drug crystal,...)
undergoing dissolution
h

51. Dissolution Rate
This liquid film will be saturated
with the dissolved solute
In this case, the concentration
of the solute (drug) Cs will
represent the solubility of the
drug
The solute molecules will then
migrate gradually (by diffusion)
through the aqueous diffusion
layer to the bulk of solution,
where the bulk concentration
will be Ct
Ct varies with time until the
dissolution process has been
completed.
Bulk
Solution
Diffusion
Layer
Solid
Matrix
h
Cs
Ct

52.  Migration of the solute is driven by the concentration gradient (change in
concentration with distance (Cs-Ct)/h)
 The DISSOLUTION RATE is determined by the RATE OF DIFFUSION OF SOLUTE
across the static liquid film.
 This is mathematically described by NOYES-WHITNEY EQUATION (derived from
Fick’s law of diffusion):
𝒅𝑴
𝒅𝒕
= 𝑫𝑺
𝑪 𝒔 − 𝑪 𝒕
𝒉
𝒅𝑪
𝒅𝒕
= 𝑲𝑨 𝑪 𝒔 − 𝑪 𝒕
𝒅𝑪
𝒅𝒕
= 𝒅𝒊𝒔𝒔𝒐𝒍𝒖𝒕𝒊𝒐𝒏 𝒓𝒂𝒕𝒆 =
𝒎𝒈
𝒎𝑳
𝑪𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒕𝒊𝒎𝒆
 Where, dC/dt is the dissolution rate, K is the dissolution rate constant (= D/h)
Dissolution Rate
NOYES-WHITNEY EQUATION
Fick’s First Law Of Diffusion

53. DISSOLUTION RATE
Factors Affecting the Dissolution Rate of a Drug
Cs  Solubility of the drug in the dissolution medium which depends on?
A  Surface area of the undissolved solid. It can be changed by?
Ct  Concentration of solute in solution at time t. If the volume of dissolution medium is
small  C will approach Cs: is not favored
k  Dissolution rate constant : is a function of?
NOYES-WHITNEY EQUATION
The molecular structure of the solute, shape and size of solid, the nature of the dissolution
medium, Temperature, pH, the presence of other additives in the medium.
Varying the size, dispersability, porosity of the solid particles.
C must be kept negligible either by increasing the volume of dissolution
medium or by continuous replacement the solution by fresh dissolution
medium “sink conditions”.
• Diffusion coefficient, D
• Thickness of the boundary layer, h, (affected by the degree of agitation
𝒅𝑪
𝒅𝒕
= 𝑲𝑨 𝑪 𝒔 − 𝑪 𝒕

54. Diffusion coefficient
D is affected by the viscosity of dissolution medium
𝐷 =
𝑘 𝐵 𝑇
6𝜋𝜂𝑟
kB Boltzmann constant
T absolute temperature
𝜼 Viscosity of the solvent
𝒓 radius of the solute molecule

55. Modified Noyes-Whitney’s equation
 D = diffusion coefficient (diffusivity) of the drug
 A = surface area of the dissolving solid
 Kw/o = water/oil partition coefficient of the drug.
 V = volume of dissolution medium
 h = thickness of the stagnant layer
 (Cs – Ct)= concentration gradient for diffusion of drug.
𝒅𝑪
𝒅𝒕
=
𝑫𝑨𝑲 𝒘
𝒐
𝑽𝒉
𝑪 𝒔 − 𝑪 𝒕

56. Dissolution rate
Conclusions and Special considerations
As:
 Solution temperature ↑ ↠ diffusion coefficient ↑ , dissolution rate↑
 viscosity of solvents ↑ ↠ the diffusion coefficient ↓, dissolution rate ↓
 Radius of solute ↓ ↠ total surface area of solutes ↑, dissolution rate ↑
Then
Warming solvents could be used to increase dissolution rate (if the drug is
thermostable)
But Note
By increasing temperature, some solutes dissolution rate is not increased.

57. Dissolution rate
Conclusions and Special considerations
 Solutes dissolves more slowly in viscous solvents (syrups, rather than
water)
↞Dissolve solutes in solvents prior to adding excipients that will increase
the overall viscosity of the preparation↠
 We cannot always alter the radius of the solute molecules (other than
by trituration of large particles), but we can anticipate:
↞ Larger solute molecules are slower to dissolve than smaller
ones, expect more time for dissolution to go to completion ↠
 ↑ solid surface area (S) ↠ ↑ dissolution rate
↞ Subdivision/trituration of the solute prior to its addition to
the solvent should improve dissolution rate ↠
 The thickness of the unstirred layer (h) can be decreased in vitro,
such as by stirring in a beaker, thus increasing dissolution rate.

58. Dissolution rate
Conclusions and Special considerations
 Saturation concentration of a solute (Cs)
 Do not to indiscriminately elevate temperatures in vitro to avoid:
 Degrading thermolabile solute
 Formation of a supersaturated solution which when the solute(s)
may precipitate out of solution.
 Solute concentration at time t (Ct)
 When Ct approach saturation concentration Cs, dissolution will
slow down.
 Hence prepare saturated solutions ahead of time since last stage of
dissolution will take a longer time.

59. Dissolution rate
Sink conditions
In sink conditions the Noyes-Whitney equation simplifies into:
When DDL is removed by stirring or in a large volume of bulk
solvent ↠ h is nearly zero.
The in-vivo dissolution is rapid as sink conditions are maintained
by absorption of drug in systemic circulation i.e. Ct=0 and rate of
dissolution is maximum.
𝒅𝑪
𝒅𝒕
=
𝑫𝑨𝑲 𝒘
𝒐
𝑽𝒉
𝑪 𝒔

60. Dissolution testing
Dissolution is a key step for drug release and absorption especially in
solid dosage forms.
Dissolution testing:
 Measures the rate at which the drug substance is released from the
dosage form and dissolves in a particular dissolution medium.
 is essential for the evaluation of solid dosage forms efficacy both in
vivo and in vitro
The in vitro dissolution test are carried out:
 For formulation and optimization of dosage forms
 As quality control tests during manufacture
 Demonstrating bioequivalence among equivalent generic drug products

61. Dissolution testing
 The in vitro dissolution test are carried out in bio-relevant
dissolution media mimicking the biological fluids at 37 °C .
 The selection of medium and volume is guided by
 Aim of the dissolution test,
 Solubility of the drug
 Type of apparatus used.
 The volume is 5 times the saturation volume of the drug.
 Samples of dissolution medium are removed after known times,
filtered and assayed.

62. Dissolution testing
There are different methods officially used to test the dissolution
rate

63. Dissolution testing
Apparatus Classification in USP:
1. Apparatus 1 (rotating basket)
2. Apparatus 2 (paddle assembly)
3. Apparatus 3 (reciprocating cylinder)
4. Apparatus 4 (flow-through cell)
5. Apparatus 5 (paddle over disk)
6. Apparatus 6 (cylinder)
7. Apparatus 7 (reciprocating holder)

64. USP Apparatus I
Rotating Basket method
 Small wire mesh basket
fastened to end of shaft
connected to a motor.
 Immersed in a flask maintained
at 370C ± 0.50C.
 Samples are withdrawn at
regular intervals.

65. USP Apparatus II
Paddle Assembly method
 Basket in above method is replaced by
paddle.
 Paddle is continuous with the shaft.
 Tablet is placed at the bottom of the
medium.
Disadvantages:
 Since dissolution volume is limited, use of
poorly soluble drugs is limited.

66. Intrinsic dissolution rate (IDR)
 IDR is the rate of mass transfer per area of dissolving surface (units:
mg.mm−2.s−1).
 IDR is independent of boundary layer thickness and volume of solvent.
IDR = ki Cs
 IDR measures the intrinsic properties of the drug only as a function of the
dissolution media
 its pH,
 ionic strength,
 presence of counter ions, etc.,

67. Importance of Solubility and Dissolution
study
There are many reasons why it is vital to
understand
 The way in which drugs dissolve in solution
and,
 the factors that maintain solubility or
cause drugs to come out of solution, that
is, to precipitate.
 Many drugs are formulated as solutions or
are added in powder or solution form to
the liquids, such as infusion fluids, in which
they must remain in solution for a given
period.
health.ucdavis.edu

68. Importance of Solubility and Dissolution
study
 In whatever way drugs are presented to the body, they must
usually be in a molecularly dispersed form (that is in solution)
before they can be diffused and absorbed across biological
membranes
Current Pharmaceutical Design, Volume 20, Number 10, 2014, pp. 1422

69. Importance of Solubility and Dissolution
study
 The dissolution process will precede absorption unless the drug
is administered as a solution, but even solutions may precipitate
in the stomach contents or in blood, and the precipitated drug
will then have to re-dissolve before being absorbed.
 Drugs of low aqueous solubility (e.g. Taxol) frequently present
problems in relation to their formulation and bioavailability.
https://www.semanticscholar.org/paper/Quantitative-analysis-of-
multi-pharmaceutica

70. References
1. Florence, A.T. (2011). Physiochemical Principles Of Pharmacy. London:
Pharmaceutical Press.
2. Remington: The Science And Practice Of Pharmacy (22nd ed.) (Vols.1-2).
(2013). London; Philadelphia: Pharmaceutical Press.
3. Sinko, P. & Singh, Y. (Eds.). (2011). Martin's Physical Pharmacy And
Pharmaceutical Sciences: Physical Chemical And Biopharmaceutical
Principles In The Pharmaceutical Sciences. Baltimore, MD : Lippincott
Williams & Wilkins.
4. Aulton, M. E. (ed.) (2002). Pharmaceutics: The Science Of Dosage Form
Design (2nd ed.).Edinburgh: Churchill Livingstone.
5. Attwood, D. (2012). Physical Pharmacy. London: Pharmaceutical Press.