An official website of the United States government
In this paper, we present a mathematical model and numerical simulation for the evaporation and drying of a liquid droplet containing suspended solids, relevant to processes such as spray drying and spray pyrolysis in the food and pharmaceutical industries. The model comprises three stages: first is the evaporation of the liquid droplet consisting of solid particles, followed by the second stage starting with the formation of a porous crust around a wet-core region and, finally, the third stage with sensible heating of the dry particle. Using a finite difference method with a moving grid, we account for the moving interface between the crust and wet core. Our model incorporates spatial temperature variations and is validated against experimental data on colloidal silica droplet drying, showing good agreement. We examine model assumptions and analyze the impact of drying conditions on drying rate and final particle morphology. Along with the temperature and velocity of the drying gas, we also find that the shape of suspended solid particles inside the droplet and assuming continuum flow of vapor through the crust influence drying quality. Finally, we develop a regime map to predict whether the final particle will be solid or hollow based on operating conditions.
more »
« less
This content will become publicly available on April 21, 2026
Exploring the role of hydrodynamic interactions in spherically confined drying colloidal suspensions
We study the distribution of colloidal particles confined in drying spherical freestanding droplets using both dynamic density functional theory (DDFT) and particle-based simulations. In particular, we focus on the advection-dominated regime typical of aqueous droplets drying at room temperature and systematically investigate the role of hydrodynamic interactions (HIs) during this nonequilibrium process. In general, drying produces transient particle concentration gradients within the droplet in this regime, with a considerable accumulation of particles at the droplet’s liquid–vapor interface. We find that these gradients become significantly larger with pairwise HIs between colloidal particles instead of a free-draining hydrodynamic approximation; however, the solvent’s boundary conditions at the droplet’s interface (unbounded, slip, or no-slip) do not have a significant effect on the particle distribution. DDFT calculations leveraging the radial symmetry of the drying droplet are in excellent agreement with particle-based simulations for free-draining hydrodynamics, but DDFT unexpectedly fails for pairwise HIs after the particle concentration increases during drying, manifesting as an ejection of particles from the droplet. We hypothesize that this unphysical behavior originates from an inaccurate approximation of the two-body density correlations based on the bulk pair correlation function, which we support by measuring the confined equilibrium two-body density correlations using particle-based simulations. We identify some potential strategies for addressing this issue in DDFT.
more »
« less
- Award ID(s):
- 2223084
- PAR ID:
- 10627953
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 162
- Issue:
- 15
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The problem of a suspension droplet falling under gravity was examined for polydisperse droplets composed of a mixture of particles with different densities and sizes. The study was conducted using both simulations based on oseenlet particle interactions and laboratory experiments. The hydrodynamic interactions of the particles within the suspension droplet allow a polydisperse collection of particles to fall as a coherent droplet, even for cases where the difference in particle terminal velocity would cause them to separate quickly from each other in the absence of hydrodynamic interactions. However, a gradual segregation phenomenon is observed in which particles with lower terminal velocity preferentially leave the suspension droplet by entering into the droplet tail, whereas particles with higher terminal velocity remain for longer periods of time within the droplet. When computations and experiments are performed for bidisperse mixtures, a point is eventually reached where all of the lighter/smaller particles are ejected into the droplet tail and the droplet continues to fall with only the heavier/larger particles.more » « less
-
Flow-based manipulation of particles is an essential tool for studying soft materials, but prior work has nearly exclusively relied on using two-dimensional (2D) flows generated in planar microfluidic geometries. In this work, we demonstrate 3D trapping and manipulation of freely suspended particles, droplets, and giant unilamellar vesicles in 3D flow fields using automated flow control. Three-dimensional flow fields including uniaxial extension and biaxial extension are generated in 3D-printed fluidic devices combined with active feedback control for particle manipulation in 3D. Flow fields are characterized using particle tracking velocimetry complemented by finite-element simulations for all flow geometries. Single colloidal particles (3.4 μm diameter) are confined in low viscosity solvent (1.0 mPa s) near the stagnation points of uniaxial and biaxial extensional flow for long times (≥10 min) using active feedback control. Trap stiffness is experimentally determined by analyzing the power spectral density of particle position fluctuations. We further demonstrate precise manipulation of colloidal particles along user-defined trajectories in three dimensions using automated flow control. Newtonian liquid droplets and GUVs are trapped and deformed in precisely controlled uniaxial and biaxial extensional flows, which is a new demonstration for 3D flow fields. Overall, this work extends flow-based manipulation of particles and droplets to three dimensions, thereby enabling quantitative analysis of colloids and soft materials in complex nonequilibrium flows.more » « less
-
Contact line dynamics is crucial in determining the deposition patterns of evaporating colloidal droplets. Using high-speed interferometry, we directly observe the stick-slip motion of the contact line in situ and are able to resolve the instantaneous shape of the inkjet-printed, evaporating pico-liter drops containing nanoparticles of varying wettability. Integrated with post-mortem optical profilometry of the deposition patterns, the instantaneous particle volume fraction and hence the particle deposition rate can be determined. The results show that the stick-slip motion of the contact line is a strong function of the particle wettability. While the stick-slip motion is observed for nanoparticles that are less hydrophilic ( i.e. , particle contact angle θ ≈ 74° at the water–air interface), which results in a multiring deposition, a continuous receding of the contact line is observed for more hydrophilic nanoparticles ( i.e. , θ ≈ 34°), which leaves a single-ring pattern. A model is developed to predict the number of particles required to pin the contact line based on the force balance of the hydrodynamic drag, interparticle interactions, and surface tension acting on the particles near the contact line with varying particle wettability. A three-fold increase in the number of particles required for pinning is predicted when the particle wettability increases from the wetting angle of θ ≈ 74° to θ ≈ 34°. This finding explains why particles with greater wettability form a single-ring pattern and those with lower wettability form a multi-ring pattern. In addition, the particle deposition rate is found to depend on the particle wettability and vary with time.more » « less
-
Inkjet-based three-dimensional (3D) printing is widely used for fast and efficient non-contact manufacturing, yet it suffers from several drawbacks, such as coarse resolution, lack of adhesion, manufacturing inconsistency, and uncertain final part mechanical properties. These undesirable effects are related to complex flow phenomena in colloidal droplets in inkjet 3D printing, particularly the internal flows and droplet deformations during the deposition and drying processes. These challenges are due to the colloidal suspension droplets being kept in the liquid state during printing. To overcome these disadvantages, this paper presents a novel freezing-sublimation-based inkjet 3D printing concept that freezes the colloidal droplets upon impact followed by sublimation, eliminating the undesirable particle transport and fluid motions during deposition. A series of experiments were conducted to characterize the colloidal droplet behaviors during the impinging/freezing and sublimation processes and evaluate the effects of the freezing process on droplet impinging dynamics as well as the final deposition patterns through sublimation. It was demonstrated that the deposition patterns obtained from this new method are much more uniform than the conventional evaporation-based deposition method. Both qualitative and quantitative methods were applied to analyze the colloidal droplet profiles during the printing process (impinging, freezing, and sublimation), as well as the final deposition patterns. The study shows promising results of using this new method, providing a foundation for the development of the novel freezing-sublimation-based inkjet 3D printing technique.more » « less
