## Ostwald Ripening

### Quick Start

Those who make very fine emulsions (which naturally resist creaming) can be dismayed to find that the emulsion quickly coarsens. This is because of Ostwald Ripening, the unfair process where large drops get bigger at the expense of smaller ones.

The increase in average size is rapid at first, especially with very small particles. There are just three ways to slow things down

1. Decrease the interfacial energy (better surfactant via HLD) which is the driving force for the process
2. Ensure that your oil has a low solubility, c, in water.

### Ostwald Ripening

r0 nm
c mole %
γ dyne/cm
Tmax hr

Ostwald ripening shows the unfairness of physics. The bigger particles grow at the expense of the smaller ones. The driving force is the interfacial tension γ; the higher it is the more energy it requires to create a small radius (high curvature) droplet. The calculation is of rt (actually the average of rt), the radius at time t, which depends on:

• t - the time, assumed to be from 0 to 24hr
• r0 - the average droplet radius at t=0
• γ - the interfacial energy. A high energy (poor surfactant) increases the driving force
• D - the diffusion coefficient through the medium (assumed here to be 1E-6 cm²/s)
• V - the molar volume of the oil (assumed here to be 200 cc/mole)
• RT - the gas constant R and temperature T in °K, assumed to be 300.
• c - the Mole Fraction of the oil soluble in the water. Oils with high water solubility speed up Ostwald ripening. The impact of a bad choice of surfactant on c is discussed below

r_t^3-r_0^3 = (8γDcVt)/(9RT)

There are two lessons about choice of surfactant.

1. A low interfacial energy stops Ostwald ripening (the driving force decreases) so choosing a surfactant that brings the formulations close (but not too close as this destabilises via a different mechanism) to HLD=0 gives a lower interfacial energy and a greater stability.
2. If you have an inefficient surfactant which is spending a lot of time as micelles in the water phase then it is relatively easy for the oil to be "soluble" in the water phase within the micelles and to hitch a ride from drop to drop. This accelerates Ostwald ripening and is factor in addition to the actual solubilty of the oil in the water.

The above effects are explored in the Emulsion Stability section under NAC

One intriguing way to stop Ostwald ripening if you have an oil with a relatively high water-solubility is to add a small % (say 10%) of an insoluble oil such as hexadecane. There a various equivalent ways to describe the effect (e.g. via osmotic pressure) but the simplest is to say that as the soluble oil leaves the smaller drops, they start to contain lots of the insoluble oil which cannot take part in the ripening process so the ripening quickly stops. This is one of those important tricks that all practical formulators should know about, just in case.