(489i) Buckling of a Drying Drop of Colloidal Dispersion: Theory

Drying of droplets of colloidal droplets is encountered in industrial processes, such as spray drying, where the final goal is to obtain dried granules of a desired morphology and density [1,2]. The final shape of the dried granule varies between a sphere to a toroid including buckled morphologies with either dense or hollow structures. The shape and bulk density of the final granule is dependent on several factors such as stability of the colloidal dispersion, properties of the particles such as their shape, size and hardness, and evaporation rates. When drops of colloidal dispersion are dried at a high rate such that the evaporation rate is much higher than the inverse of the particle diffusion time, the particles collect at the liquid-air interface to form a shell of packed particles [3]. Evaporation also causes the drop to shrink, which in turn induces compression in the particle shell. Beyond a critical compressive stress, the spherical shell buckles. In this talk, we present a mathematical model that relates the critical stress for buckling to the properties of the colloidal dispersion [4]. The stress field in the particle shell is determined using a constitutive relation that accounts for the microstructure of the packing and the non-linear deformation of the colloidal particles. We show that the critical compressive stress is related to a critical capillary pressure, which in turn is related to the properties of the packing, shell thickness and radius. Further, we derive an expression for the ratio of the critical shell thickness to the shell radius above which the shell will not buckle. The theoretical predictions are compared with experimental results reported in literature and we find good agreement between the two.

The attached figure shows a schematic of shell formation in a drying drop of a colloidal drop. (A) For evaporation rates that are large compared to the rate of particle diffusion, particles collect at the liquid–air interface. (B) The high concentration of particles at the interface eventually leads to the formation of a thin shell of packed particles. (C) The top panel shows a thin section of the shell with a liquid meniscus of radius, r_p. The shrinking drop compresses the shell in the tangent plane, which is represented by block arrows. The small arrows on the particles represent the contact forces in the packing. The lower panel is a schematic of the expected pressure variation in the shrinking drop. Here, the pressure difference, P(R-h)-P(R)>0, causes radially outward flow of liquid through the particle packing while the pressure jump across the liquid–air interface, given by P_atm - P(R) = 2 γ /r_p, is a result of the curvature of the menisci at the outer layer of particles.

References:

1. M. R. Lauro, C. Carbone, F. Sansone, B. Ruozi, R. Chillemi, S. Sciuto, R. P. Aquino and G. Puglisi, Drug Dev. Ind. Pharm., 2016, 42, 1127–1136.

2. L. Chen, T. Okuda, X.-Y. Lu and H.-K. Chan, Adv. Drug Delivery Rev., 2016, 100, 102–115.