Non-Newtonian Fluids & Rheology

• Non-Newtonian bodies do not follow Newton's equation of flow.
• Examples include dispersions, suspensions, and ointments
• Turbulent flow involves the mixing or exchange of a substance from one layer to another during flow.

Types of Non-Newtonian Fluids

• Plastic bodies (Bingham systems)
• Pseudoplastic bodies (fluidifiant systems)
• Dilatant systems

Rheograms

• Newtonian fluids show a linear relationship between shear stress and shear rate.
• Plastic (Bingham) fluids require a certain amount of shear stress before flow begins, then exhibit a linear relationship.
• Pseudoplastic fluids show a decreasing viscosity with increasing shear rate, resulting in a curved rheogram.
• Dilatant fluids exhibit an increasing resistance to flow with increasing shear rate, also shown as a curved rheogram.

Rheologic Equation of Plastic Systems

• Plastic systems' curves do not pass through the origin but intersect the shearing stress axis at the yield value.
• A Bingham body begins to flow only after a shearing stress exceeds the yield value.
• The rheologic equation is τ = τ₀ + α.ε
  • τ is the total shear stress.
  • τ₀ is the yield value
  • α is a constant.
  • ε is the shear rate.
• Plastic viscosity is calculated as v = (τ - τ₀) / ε.
• Mobility (w) is the inverse of viscosity (1/v).
• Contact between adjacent particles must break down for flow to occur.

Rheologic Equation of Pseudoplastic Systems

• n < 1
• Viscosity decreases as the rate of shear increases

Behavior of Pseudoplastic Systems

• Before shear, molecules are in a state of entanglement.
• Under shear, molecules align linearly.
• This alignment results in the system becoming more fluid.
• Many pharmaceutical products exhibit pseudoplastic flow.
• These include natural and synthetic gums such as liquid dispersions of tragacanth, sodium alginate, methylcellulose, and sodium carboxymethylcellulose.
• As a general rule, polymers in solution exhibit pseudoplastic flow.
• Plastic systems are composed of flocculated particles in suspension.

Rheologic Equation of Dilatant Systems

• Certain suspensions with a high percentage (>50%) of dispersed solids increase their resistance to flow.
• This occurs with increasing rates of shear.
• This type of flow is the reverse of pseudoplastic systems.

Behavior of Dilatant Systems

• As shear stress increases, the bulk system expands or dilates and is termed "dilatant."
• As particles move quickly past each other, they adopt an open form of packing.
• Such an arrangement leads to an increase in the interparticle void volume.

Thixotropy

• Thixotropic properties are the behavior of materials with a time-dependent decrease in viscosity.
• These materials are subjected to shear stress and recover their viscosity once stress is removed.
• Thixotropic materials become less viscous when stirred or shaken and return to their original, more viscous state when left undisturbed.
• Key characteristics:
  • Time-Dependent Shear Thinning: Under stress or agitation, materials become less viscous.
  • Reversible Process: After stress ends, the material slowly returns to its original state
  • Non-Newtonian Fluid: Thixotropic materials do not have constant viscosity like Newtonian fluids.

Thixotropy of Non-Newtonian Systems

• Thixotropy measures the duration of shear stress on the behavior of a non-Newtonian body.
• System behavior depends on previous treatments applied to the system.
• Shear stress induces a momentum reversible deformation to the system.
• Thixotropy is recovery from consistency lost through shearing.
• That recovery is isothermal and comparatively slow while standing
• As defined, thixotropy applies only to shear-thinning systems.

Thixotropy Behavior

• In shear-thinning systems (plastic and pseudoplastic bodies), the down-curve is frequently displaced to the left of the up-curve.
  • This indicates that the material has a lower consistency at any rate of shear on the down-curve compared to the up-curve.
• The material undergoes a gel-to-sol transformation and exhibits shear thinning
• Hysteresis loops in thixotropic materials indicate a breakdown of structure that doesn't reform immediately when stress is removed or reduced.

Thixotropy in Formulation

• Thixotropy is a desirable property in liquid pharmaceutical systems that need high consistency in the container and pour/spread easily.
• A well-formulated thixotropic suspension will not settle out readily, becomes fluid on shaking, and maintains suspended particles.
• Emulsions, lotions, creams, ointments, and parenteral suspensions should exhibit the same behavior.

Measurement of Viscosity

• Viscosity is measured using a rheometer, or an Ostwald viscometer.

Capillary Rheometer for Newtonian Flow: Ostwald -Cannon-Fenske viscometer

• Uses Poiseuille's law.
• Uses the equations:
  • η = (r^4 * π * ΔP * t) / (8lV)
  • η = (r^4 * π * h * g * ρ * t) / (8lV) = K * ρ * t
  • K = (r^4 * π * h * g) / (8lV)
• Where:
  • η is viscosity
  • r is the radius of the capillary tube
  • ΔP is the pressure difference
  • t is time
  • l is the length of the tube
  • V is the volume
  • h is the height of the liquid
  • g is the acceleration due to gravity
  • ρ is the density
  • K is a constant
• It is based on the time a volume V of liquid takes to pass between two marks via gravity through a vertical capillary tube (r-l).

Measurement of Viscosity of Newtonian Liquid

• ηs = K * ρs * ts
• ηu = K * ρu * tu
• ηs/ηu = (ρs * ts) / (ρu * tu)
• vs/vu = ts/tu
• ns/nu = relative viscosity
• vs/vu = relative viscosity
• nu = unknown viscosity
• ns = viscosity of the standard

Falling Sphere Viscometer: Hoeppler viscometer

• A glass or steel ball rolls down an almost vertical glass tube with the test liquid at a known constant temperature.
• The rate at which a ball with a defined density/diameter falls is inversely related to the sample's viscosity.
• Viscosity (η) is calculated as t * (ρb - ρl) * B
  • t is the falling time.
  • ρb is the density of the ball.
  • ρl is the density of the liquid.
  • B is the viscometer constant.

Rheometers for Non-Newtonian Flow

• Cup and Bob Viscosimeters:
  • Couette type: the cup is revolved (MacMichael viscosimeter)
  • Searle type: stationary cup and rotating bob (Rotovisco viscosimeter, Stormer viscosimeter)
• Cone and Plate Viscosimeters:
  • Ferranti-Shirley viscosimeter
• Creep Rheometers

Cup and Bob Viscometers

• Test system goes between the cup and bob to reach temperature equilibrium.
• Weight on the hanger rotates the bob 100 times, recorded by an operator.
• Repeat with increased weight to convert data to rpm.
• rpm versus weight added form a rheogram.
• Use constants to convert rpm to shear rates (sec-1) and weights to shear stress (dynes.cm-2).
• The sample is sheared in the space between the bob's outer wall and the cup's inner wall.
• Viscosity is based on the torque on the bob/it being rotated.

Cone and Plate Viscometer

• M = (2πR³τ) / 3

• ε = ω₀ / ψ

  • M is Torque
  • R is the radius of the cone
  • τis shear stress
  • ε is the Shear Rate
  • ω₀ is Angular velocity
  • ψ is the cone angle

• Instrumental constants/variable:

  • C= instrumental constant
  • T = torque reading
  • V= speed of the cone in revolutions per minute
  • Tf= torque at the shearing stress axis
  • Cf= instrumental constant

• n = C.T/v for newtonian flow

• U =(C(T-Tf)/v for plastic viscosity.

• The sample in the center of the plate is raised to become positioned under the cone.

• A variable-speed motor drives the cone.

• The sample shears in the narrow gap between stationary plate and the rotating cone.

• Increase or decrease the shear rate to read viscous traction, or torque (shearing stress), on the indicator scale.

• Plot rpm versus scale reading to gather results.

Viscoelasticity

• Viscoelastic measurements indicate materials exhibiting viscous (liquid) and elastic (solid) properties.
• Many systems in pharmacy belong in this class such as creams, lotions, ointments, suppositories, suspensions, and colloidal dispersions.
  • Biologic materials, as well as blood and cervical fluid, also exhibit such properties.
• Continuous shear alters the tested material’s ground state through substantial deformation
• Measurements provide information on the intermolecular and interparticle forces in the material.

Viscoelastic Rheogram

• Viscoelastic rheograms are creep curves that use a creep viscometer.

Psychorheology

• Topical preparations must meet feel, spreadability, color, odor, and psychological/sensory criteria, in addition to pharmaceutic/pharmacologic.
• Butter, chocolate and mayonnaise need consistency during manufacture, packing, and end use
• Sensations in the mouth, between fingers and on skin need to be taken into consideration for food, cosmetics and dermatologic products
• Products can be divided up into 3 classes:
  • Class I: soft products for ophthalmic use.
  • Class II: Intermediate consistency like common ointments
  • Class III: stiff protective products

Importance of Rheology in Pharmacy

• Rheology is involved in the mixing/flow of materials, packaging, extraction from tube, or syringe.
• Consistency affects the patient acceptability, physical stability, biologic availability, and absorption rate of drugs from the gastrointestinal tract.
• The rheologic properties of the pharmaceutical system can influence the choice processing equipment for manufacturing.

Pharmaceutical area in which rheology is significant

• Fluid form: mixing, particle size reduction, passage thru orifices/needles, physical stability
• Semisolids: spreading, adherence to the skin, removal from jars/tubes, mixing solids with miscible liquids, release of medicine.
• Solids: Powder flow from hopper/into die or capsules during tabletting
• Processing in general need to be factored in.

Definitions

• Interface: The boundary when two phases of matter meet
• Surface: The boundary when any solid or liquid meets gas, which typically meets the atmosphere.

Classification Of Interfaces

• The following interfaces exist:
• Gas/Gas
• Liquid/Liquid
• Solid/Solid
• Gas/Liquid
• Liquid/Solid
• Gas/Solid

Liquid Interfaces

• Liquid surfaces appear spheric in small containers
• Liquid surfaces appear planar in large containers

Surface Tension

• The total effect has molecules at the liquid surface experiencing an inward force towards the bulk.
• This force pulls the interface's molecules together, causing surface contraction.
• Liquid droplets assume a spherical shape because of the above.
• "Tension" in the surface is the force/unit of length, applied parallel to counterbalance this pull.

Interfacial Tension

• Interfacial tension is the force/unit length at two immiscible liquid phases, in dyne/cm.
• Measurements are less than surface tensions because adhesive forces between liquid phases are higher, when both phases are next to each other

Examples of Surface Tension

Examples of Interfactial Tension (Against Water)

Surface Tensions

• Soap film has two liquid/gas interfaces (above and below the plane).
• The total length of the contraction is twice the length of the bar.
• Equation: γ=F/2L (dynes.cm-¹)

Liquid interfacial phenomena

• Work of cohesion, and adhesion
• Miscibility
• Spreading co-efficient
• Laplace Pressure

Work of Cohesion

• Work involved in separating a liquid column into two equal parts.
• When column A splits into A1 and A2, two tensions are creates with each
  • Wcoh Water =144 mj/m
  • Wcoh Octane = 44 mj/m

Work of Adhesion

• Work needed to separate one unit of interface area isothermally and reversibly (Dupré 1896).
• Separating the operation consists of creating two free surface tension A+ B and destroying the AB interface
• Equation: WdaAB = γA + γB + γAB

Miscibility

• Requirements for requirements: - WAdAB ≥ WCobAA - WAdAB ≥ WCobBB - WAdAB ≥ 1/2 (WCobAA + WCobBB). - Meaning γAB ≤ 0, or There are no interfaces between two miscible liquids

Electric Properties of Interfaces

• Surfaces get involved charge relation to their surrounding liquid environment
• Particles disperse get charge selective adsorption of particular ionic species or from ionization of groups
• Electric double layer has aqueous solutions, of an electrolyte. Some ions should adsorb, giving it a positive charge. .
  • Remaining ions are repelled by their charges, or attracted to the opposite surface.
  • At a the certain point of surface is neutral.

Potential Zeta

• Changes in potential with distance from surfaces
  • Potential at the solid surface AA' : electrothermodynamic E
  • Potential at the shear plane Bb' : elecrokinetic or zeta
• Electrical potential is considered at the elecrokinetic
• Surface potential is difference in potential compared to the tight bound and that electroneutral region.

Importance of Potential Zeta in Pharmacy

• Practical application in system stability of dispersed particles
• Rather than Nernst potential, governs degree of repulsion of dispersed particles
• When reduced below a value, then attraction forces is high, so particles come together (Flucollation)

Surface or Interfacial Active Agents

• Substance accumulates more at the liquid surface, of itself
• The tendency to deposit offers interests
• Is has a polar and non polar
• Wdes= work wetting the hydrocarbon agent

Hydrophile Lipophile Balance (HLB)

• Griffith scale is a common technique to measuring HLB
• 10-value ranges with the Lipophile agent
• Ester can both Saponify and difficult to saponify HLB depends on this

Guidelines for Assigning Surfactants

Types and Properties of Surface Active Agents

Properties:

• Wetting
• Spreading
• Emulsifying
• Suspension
• Solubilizing
• Foaming
• Antifoaming
• Detergent
• Complexation
• Chelating
• Sequestration
• Antimicrobial

Types:

• Anionic
• Cationic
• Amphiphilic
• Non-ionic

Special Agents

Examples of Special Agents

• Polysorbate 85
• Glycol Distearate
• PEG-80 Sorbitan Laurate

HLB Table for Various Emulsifiers