Aim of the assignment:

The assignment is designed to test and challenge the knowledge that you have gained during the particle engineering and colloids components of the module. It will draw on the lecture material, probe your understanding of it and then ask you to use it to analyse statements in recent journal publications in the field.

Description of the assignment

Let's investigate a system where a nanoparticle suspension is spray-dried to form larger structures/particles from evaporated droplets of suspended nanoparticles.

1. Explain why a high Peclet number can lead to hollow particles. Explain why a high Péclet number is necessary but not sufficient for hollow particles to be formed.

2. By deriving a mathematical expression for the Péclet number during the first period of drying, investigate the relationship between the Péclet number and the initial droplet diameter, d_o. Assume: i) a small droplet with low relative velocity and consequently the droplet Nusselt and Sherwood numbers both equal to 2. ii) the initial droplet drying rate is equivalent to a droplet of solvent only.

3. For droplets containing nanoparticles the diffusivity of the nanoparticles can be assumed to follow the Stokes-Einstein equation. Consequently, do you agree (clearly justifying your response) with the statements from Lintingre et al., 2016 shown below that:

a. the Péclet number is approximately 5000?
b. the effect of nanoparticle diffusion can be neglected for droplets above 1μm in diameter?

(Note: published papers do not always get everything correct!)

4. Let's assume a model system to be spray-dried which consists mainly of silicone dioxide nanoparticles dispersed in water. The final product being formulated requires some salt added to the formulation being spray-dried and therefore NaCl is added to the particle suspension.

For silicone dioxide nanoparticles of radius of 50nm and zeta potential (which can be assumed to be equal to the surface potential in this case) of -50mV, use excel to draw a single graph representing all 3 of the van der Waals repulsive interactions, the electrostatic repulsive interactions and the total (net) interactions as a function of inter-particle distance. By varying the NaCl concentration in your excel calculations to draw this graph, estimate the NaCl concentration for which the energy barrier reaches close to 10kT.

On this basis and in using Lintingre et al. article, explain why one of the two electrolyte concentrations in the 50nm silicone dioxide nanoparticle suspension below is more likely to result in hollow, buckled particles when spray dried.

i) 1mM NaCl, or ii) 50mM NaCl.