Rheology Flashcards
[sigma]
Shear stress
[gamma]
Shear rate
V
Velocity
D
Distance
n[eta]
Dynamic viscosity
F
Force
A
Area
v[nu]
Kinematic viscosity
p[rho]
Density
[Phi]
Volume fraction
M
Molecular weight
R
Radius
P
Pressure drop
Define rheology
The study of the deformation and flow of matter
Define viscosity
The viscosity of a liquid is its resistance to flow or move due to IMF.
Viscosity measure resistance to gradual deformation
E.g. Water has weak attractions between the molecules and low dynamic viscosity
Syrup has strong attractions between the molecules and higher dynamic viscosity
Areas in pharmaceutics where rheology is important - fluids
Mixing Particle size reduction Passage through orifices (opening on body e.g. Mouth,rectum) Pumping Physical stability
Areas in pharmaceutics where rheology is important - semisolid
Spreading and adherence to kin
Removal from jars or extrusion from tubes
Mixing of solids with miscible liquids
Release of drug base
Areas in pharmaceutics where rheology is important - solids
Powder flow
Areas in pharmaceutics where rheology is important - processing
Processing efficiency
Define shearing rate and equation
Difference in velocity between layers
Shearing rate = dv/dr
(Velocity/difference) unit s-1
Define newtons law
The rate of flow is directly related to the applied stress
Shearing stress equation
F/A
Dynamic viscosity equation
n = [sigma] / [gamma]
Nm-2 s or Pa s
Define dynamic viscosity
The measure of the internal resistance or friction involved in the relative motion of one layer of molecules with respect to the next resulting from an applied force
Kinematic viscosity
Takes into account the density p of the liquid: v = n/p
Unit: m2s-1 or stoke (S) cm2s-1
Define colloidal dispersion
One phase dispersed in another immiscible phase in the form of particles. E.g. Oil in water
Colloidal dispersion relative viscosity equation
nr = n/no
For colloidal dispersion the specific viscosity equation
nsp = n/no -1 = n-no/no = nr -1
n= viscosity of dispersion (dispersed phase plus solvent) no = viscosity of the solvent nsp = usually measure relative to a standard/reference liquid
Einstein equation
n = no (1+2.5 volume fraction)
n= viscosity of dispersion no = viscosity of solvent
Specific viscosity is only dependent on volume fraction
Characteristics of Newtonian flow
Liquids are classified according to their flow type as either Newtonian or non Newtonian.
Newtonian fluids are simple fluids - linear relationship between shear stress and rate of shear (directly proportional otherwise it’s non Newtonian), viscosity is not affected by shear rate
Boundary layer
Place of less stationary fluid. E.g. Water touching inside of tube will move slower than water water towards inside of the tube
Laminar flow
Flow between layer. When all materials move together
Transitional flow
Laminar to turbulent
Turbulent flow
Random
Reynolds number Re
Re= pvd/n For tubular flow If Re <2000 laminar flow If Re >4000 turbulent flow If 2000< Re <4000 depending on surface - if smooth laminar, if rough distributed
What does capillary viscometer measure
The flow time of a set volume of liquid between 2 marks at a given temperature
Hagen-Poiseuille equation for capillary viscometer
n= pi r4 tp / 8LV
r = radius of capillary P = pressure difference between ends of tube L = length of capillary V = volume of the liquid t = flow time
What is specific to a given viscometer
r L and V are specific to a given viscometer and can be combined together with pi into a constant k. P can be determined by measuring a reference liquid
Equation becomes n = kpt
Meaning if the time taken for a liquid to flow through the viscometer is greater the viscosity is higher
How does a falling sphere viscometer (Hoppler) obtain viscosity and what law applies
Obtains viscosity by messing the time it takes for a cylindrical or spherical object to fall through a sample over a specific distance
Stoke law applied (the diffusivity is inversely proportional to the viscosity)
Equation for stokes law
Sedimentation - stokes law
v = 2r2 (p2-p1) g / 9n
v is the velocity of sedimentation r is radius of the spherical particle p2 is density of the particle p1 is density of the medium n is viscosity g is the acceleration of gravity
What particles does stokes law apply to and when can viscosity be calculated
Spherical
Viscosity can be calculated after v is determined from the time needed to travel a certain distance
How does a rotational viscometer obtain viscosity
By turned a disc, bar or cylinder immersed in a liquid. The more viscous the liquid the stronger the resistance and hence higher the torque. Viscosity can be calculated from measured rotation speed vs applied torque
Define non Newtonian fluids
Complex pharmaceutical systems
Applied shear stress causes a change or interaction inside the system
Viscosity becomes non linear, it varies with shear rate
What are the 3 types of non Newtonian fluids
Plastic
Pseudo-plastic
Dilatant
Define plastic flow
Substance will not start to flow until a stress corresponding to the lower yield value is applied
Define pseudoplastic flow
Substance will start to flow immediately when stress is applied hence the curve passes through the origin. Viscosity decreases as shear rate increases
Define dilatant flow
Rarest of flow types. Materials increase in volume during shearing and exhibit shear thickening. Dilatant systems usually are suspensions containing high percentage of particles (>50%)
Apparent viscosity
napp used because shear rate calculated from tangent to curves in graphs
napp = shear stress (Pa) / shear rate (s-1)
For Newtonian fluids napp always remains the same
For non Newtonian fluids napp invariably changes
Shear thinning
Response of the system is non linear
Corresponding rate increases with stress and viscosity decreases
Pseudoplastic behaviour
Power law
[sigma]n = n’ [gamma]
n’ is the viscosity coefficient
n is the index of pseudo-plasticity or power law index
Take log on both sides of above equation
n log [sigma] = log n’ + log [gamma]
log [gamma] = n log [sigma] - log n’
Linear relationship between log gamma and log sigma
Different flow systems have different n value
n = 1
n >1
n <1
n = 1 Newtonian flow
n >1 pseudoplastic flow
n <1 dilatant flow
Yield value
Ideal plastic is characterised by a yield value followed by ideal flow
At stresses below yield value the substance act as elastic materials
A typical folcculated suspension demonstrates plastic flow properties: it doesn’t flow when shear is very low and starts to flow when shear is increased over certain value
Yield value
Plastic flow can be described by
U = stress - f / shearing rate
f = yield value
Once yield value is exceeded the plastic viscosity changes proportionally with shearing stress resembling Newtonian flow
Causes for shear thinning
Changes inside a system which can lead to viscosity decreases:
- breaking of non covalent bonds (H bonds, charge interactions, hydrophobic interactions)
- alignment of molecules/polymers along the direction of shear
- non linearity of response is caused by continuous random breaking and formation of bonds
Shear thickening
Response of system is non linear
Corresponding rate decreases with stress resulting in an increase of viscosity
Dilatant behaviour
Causes for shear thickening
Changes inside a system which can lead to a viscosity increase:
- the spaces between particles tend to increase under shear resulting in voids
- particles become less lubricated after the voids are increased to a certain degree hence increased friction inside the system
- more interaction between particles due to disturbance of system
Time dependent behaviour
Viscoelastic materials may not adapt immediately to new shear conditions
Thixothrooy
Structure does not re form at the same speed and in the same way it is broken down
Can be seen for both shear thinning and thickening
Examples of plastic flow in pharmacy
Flocculated particles in conc disperse systems e.g. Ointments pastes creams
Pseudo-plastic flow in pharmacy examples
Natural synthetic and semi systemic polymers in solution e.g. Acacia, sodium alginate, methyl cellulose, hydroxylropylmethyl cellulose
Examples of dilatant flow in pharmacy
40-50% w/v suspensions of starch/water
Define flocculated particles
Internet
Can viscosity be measured at any point for non Newtonian fluids
No it cannot, it matter where it is measured and also how
What are capillary viscometers not capable of giving
Not capable of giving multiple points
Ideally which viscometers are used
Rheometers as falling sphere and simple rotational viscometer can be tedious
Rotational rheometers
Allow to employ a wide range of shear stress and rate
Small sample volume and good temp control
Allow continuous monitoring of structural changes in a sample over a range of stress, rate, time , temp
What are the different geometries
Parallel plate
Cone and plate
Mixer
Concenteric cylinder
Concentric cyclometer
For low viscosities or evaporating samples
Cone and plate
For viscous samples preferred for flow curves
Parallel plate
For samples containing particulates for oscillation and creep experiments
Mixer
In line viscosity control during manufacturing
Advantages of concentric cylinder
Little possibility of sample evaporation or expulsion Can measure low shear stress which is useful for emulsions and suspensions Easy to load with liquid dosage forms n = T/kw n = dynamic viscosity T = torque (stress) K = constant w = speed of rotation
Disadvantages of concentric cylinder
Possible air incorporation or breaking of structure when loading semi solids
Large volume of material needed
Shear rate across gap in not constant varies with distance from wall. Can lead to slip or plug flow
Advantages of cone and plate
Cone has a very shallow angle of contact
Constant shear rate across radius
High shear rates possible
Small sample volume required
Easy to fill and clean even with highly viscous samples
Little disturbance of sample structure
Rapid temperature equilibration due to thin film
