Lesson 4B

Types of viscosity

Dynamic, kinematic, relative, specific, reduced and intrinsic

Dynamic viscosity (η)

Coefficient relating shear stress to shear rate for a Newtonian liquid: η = σ/γ. Units Pa.s (Nm⁻²s)

Units of shear stress (σ)

N/m² (also Nm⁻² or Pascal, Pa)

Units of rate of shear (γ)

s⁻¹ (m s⁻¹ / m cancels to s⁻¹)

Kinematic viscosity (ν)

Relates viscosity to inertial force (density): ν = η/ρ. Units m²s⁻¹ (1 m²s⁻¹ = 1,000,000 mm²s⁻¹)

Density (ρ)

Mass (kg) divided by volume (m³). Note 1 m³ = 1000 litres

Worked example - dynamic viscosity

Stress 10 and rate 5 gives η = 10/5 = 2 Nm⁻²s (2 Pa.s)

Worked example - kinematic viscosity

Density = 4 kg / 0.002 m³ = 2000 kg/m³. ν = 2/2000 = 0.001 m²s⁻¹ (1000 mm²s⁻¹)

Capillary viscometer

Measures viscosity by testing how fast the sample flows

Rotating viscometer

Measures viscosity by testing how hard it is to stir the sample

Falling viscometer

Measures viscosity by testing how long it takes something to fall through the sample

Three ways surfaces acquire charge in water

Ion dissolution, ionisation, ion adsorption

Ion dissolution

Ions have different solubilities. e.g. in silver iodide the more soluble Ag⁺ dissolves into the water leaving I⁻ behind so the surface is negatively charged

Ionisation (surface charge)

Ionisable molecules at the particle surface become ionised giving a surface charge. Influenced by the pKa of the groups and the pH of the dispersant

Ionisation above and below pKa

Above pKa of a group protons are lost or anionic charge gained (negative). Below pKa the opposite happens (positive)

Isoelectric point (pI)

The pH at which a molecule has no overall net charge (neutral zwitterion)

pI calculation (phenylalanine)

pI = (pKa1 + pKa2)/2 = (1.83 + 9.13)/2 = 5.48

Amino acid at acidic pH

Ammonium salt (cationic)

Amino acid at basic pH

Carboxylate salt (anionic)

Ion adsorption

Unequal adsorption of ions onto the surface gives a net charge. More anions adsorbed gives a negative surface. Can involve OH⁻ and H3O⁺

Why are particle surfaces in water usually negative?

Cations are generally more hydrated than anions so stay in the water phase leaving anions free to adsorb to the surface

Electrical double layer (EDL)

Layer around a charged particle with different ion composition from the bulk. Inner region (charged surface and adsorbed ions) plus diffuse region. Beyond it is the electrically neutral region

Counterions

Ions of opposite charge to the particle surface that are attracted to it. Excess near the surface, fewer further away

Co-ions

Ions of the same charge as the particle surface. More present further from the surface in the diffuse region

Electroneutral region

Bulk continuous phase beyond the EDL where ion distribution is uniform and electrically neutral

Stern plane

Runs through the layer of ions strongly adsorbed to the particle surface

Shear plane

Lies at the outer edge of the tightly associated layer. Beyond it is the diffuse layer

Electrical potential

Difference in charge between two areas. Greatest at the particle surface and decreases with distance (linearly to the Stern plane then exponentially to zero)

Debye-Huckel length (1/κ)

Distance from the Stern plane to the electroneutral region. The thickness of the electrical double layer (exponential region)

Effect of electrolytes on the double layer

Adding electrolytes increases κ and therefore decreases 1/κ so the EDL becomes thinner

Nernst potential (E)

Potential between the actual particle surface and the electroneutral region

Stern potential (ψ)

Potential between the Stern plane and the electroneutral region

Zeta potential (ζ)

Potential between the shear plane and the electroneutral region. Measures the repulsion between adjacent similarly charged particles

Zeta potential and stability

Higher ζ means more stable. For stability ζ should be greater than +30 mV or less than -30 mV. As ζ approaches zero attractive forces exceed repulsive forces and particles stick together

Why do dispersed particles associate?

Large surface area so they associate to decrease surface area in contact with liquid. Permanent attachment leads to clumps, sedimentation and impossible redispersion

What determines rebound vs attachment on collision?

The balance of attractive and repulsive forces between particles. Particle charge is important for stability

Attractive interactions (VA)

From van der Waals forces between molecules in surface layers of particles. Decreases as distance increases and is stronger for larger particles (Hamaker constant A, radius a, distance H)

Repulsive interactions (VR)

From electrical charges on particle surfaces. Act over about the thickness of the double layer and decrease with distance more sharply than VA

Causes of repulsive interactions

Adsorption of charged polymers/surfactants, polarity differences between solid and liquid, ionisation of surface groups, adsorption of small inorganic ions

DLVO theory

Derjaguin, Landau, Verwey and Overbeek. Describes particle interaction as the net (VT) of van der Waals attraction (VA) and electrical repulsion (VR) from overlapping diffuse layers

VT

Total (net) of the attractive and repulsive forces between particles

Primary minimum

VA predominates at very low interparticulate distance (particles close together)

Primary maximum

Occurs at intermediate distances (within the EDL thickness) due to high VR. Height depends on VR and so surface and zeta potential

Secondary minimum

Occurs at large distance H because VR decreases more sharply than VA. Depth depends on particle size

Aggregation

Grouping of particles

Coagulation

Occurs at the primary minimum. Particles settle very quickly in a single large, closely packed aggregate. Very difficult or impossible to redisperse even with shaking

Deflocculation

Occurs at the primary maximum. Particles stay separate and settle slowly (Stokes' Law). VR lets them slide past each other so liquid is not trapped and sediment is compact with low sedimentation volume. Does not easily redisperse (caking)

Flocculation

Occurs at the secondary minimum. Loose aggregates that constantly break up and reform. Aggregates are large so sedimentation is rapid. Liquid is trapped so sediment has high sedimentation volume and is easily redispersed by shaking

Flocculation vs deflocculation - compromise

Deflocculated gives slow sedimentation but risks caking and irreversible sedimentation. Usually a flocculated suspension with increased viscosity is used (easy to redisperse and remains pourable)

Ways to stabilise suspensions and colloids

Alter zeta potential (pH, electrolytes), bridging agents (SAAs, hydrophilic polymers), steric stabilisation, polyvalent electrolytes

Altering zeta potential with electrolytes

Electrolyte of opposite charge associates with particles, reducing VR and zeta potential so particles repel less and flocculation can occur

Amount of electrolyte and effect

Small amount gives flocculation, large amount gives coagulation, very large amount gives charge reversal and deflocculation

Schultz-Hardy rule

Ability of an electrolyte to flocculate depends on its valency: trivalent > divalent > monovalent

Bridging agents (SAAs)

Non-ionic SAAs adsorb onto more than one particle at once forming a bridge and loose flocculated structures. Charged SAAs can work in combination with electrolytes

Bridging agents (hydrophilic polymers)

Long chain branched molecules. Part of the chain adsorbs onto a particle and the rest bridges to others forming a gel-like network that flocculates the system

Steric stabilisation

Non-ionic polymers adsorb onto the particle surface and their chains keep particles apart by repulsive steric interaction

Assessing suspension stability

Rate of sedimentation, final volume or height of sediment, ease of redispersion, particle size distribution

Accelerated stability testing

Shortens experiment time but behaviour under normal conditions cannot always be accurately predicted

Centrifugation (accelerated testing)

Increases sedimentation rate by increasing the acceleration due to gravity (g in Stokes' Law). May destroy the structure of a flocculated system by forming a tightly packed sediment

Temperature cycling

Moving between extremes of temperature (e.g. 40 and 0 °C) increases the rate of degradation, especially crystal growth

Sedimentation volume (F)

Ratio of final sediment volume to original suspension volume (F = Vu/Vo). Plotting F against time compares formulations and a plateau means sedimentation is complete

F = 1

Sediment volume equals original volume, no clear supernatant, "flocculation equilibrium". A desirable state for a pharmaceutical

Typical value of F

Normally

Degree of flocculation (β)

Relates the volume of the flocculated sediment to that of a deflocculated system (β = F/F∞). A more useful measure than