Abstract
This research is motivated by the desire to control the solids distribution during the drying of a film containing particles of two different sizes. A variety of particle arrangements in dried films has been seen experimentally, including a thin layer of small particles at the top surface. However, it is not fully understood why this would occur. This work formulates and solves a colloidal hydrodynamics model for (i) diffusion alone and (ii) diffusion plus excluded volume diffusiophoresis, to determine their relative importance in affecting the particle arrangement. The methodology followed is to derive partial differential equations (PDEs) describing the motion of two components in a drying film. The diffusive fluxes are predicted by generalising the Stokes–Einstein diffusion coefficient, with the dispersion compressibility used to produce equations valid up until close packing. A further set of novel equations incorporating diffusiophoresis is derived. The diffusiophoretic mechanism investigated in this work is the small particles being excluded from a volume around the large particles. The resulting PDEs are scaled and solved numerically using a finite volume method. The model includes the chemical potentials of the particles, allowing for incorporation of any interaction term. The relative magnitudes of the fluxes of the differently sized particles are compared using scaling arguments and via numerical results. The diffusion results, without any inter-particle interactions, predict stratification of large particles to the top surface. Addition of excluded volume diffusiophoresis introduces a downwards flux on the large particles, that can result in small-on-top stratification, thus providing a potential explanation of the experimental observations.
Highlights
This work concerns stratification in drying films, examining how a mixture of differently sized particles arranges itself upon drying
The initial volume fractions are φ1,ˆt=0 = φ2,ˆt=0 = 0.10, and the maximum packing fraction is taken as φm = 0.64, the value for randomly packed monodisperse spheres
The numerical results from the diffusion–diffusiophoresis model demonstrate that diffusiophoresis is a feasible explanation of the experimental observations of a thin layer of small particles at the top surface of a dried film, but it is dependent on the size of the excluded volume
Summary
This work concerns stratification in drying films, examining how a mixture of differently sized particles arranges itself upon drying. Typically preferentially accumulate at the top surface, but it is not fully understood why (Routh 2013) Understanding this could have applications across a wide range of industries, from the surface of catalyst pellets, to coating surfaces with biocides (Mardones et al 2019). In light of experimental observations of small particles at the top surface, it is thought that a simple diffusional model may not suffice. The aim is to use the numerical results to determine whether diffusiophoresis could explain these experimental observations. It will be shown that diffusiophoresis may result in small-on-top stratification, including a thin layer of small particles at the top surface.
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