Titanium dioxide (titania) is used in chemical sensors, pigments, and paints and holds promise as an antimicrobial agent. This is due to its photoinduced activity and, in nanostructured form, its high specific surface area. Particle size and surface area result from the interplay of fluid, chemical, and thermal dynamics as well as nucleation, condensation and coagulation. After nucleation, condensation, and coagulation are the dominant phenomena affecting the particle size distribution. Manufacture of nanostructured titania via gas-phase synthesis often occurs under turbulent flow conditions. This study examines the competition between coagulation and condensation in the growth of nanostructured titania. Direct numerical simulation is utilized in simulating the hydrolysis of titanium tetrachloride to produce titania in a turbulent, planar jet. The fluid, chemical, and particle fields are resolved as a function of space and time. As a result, knowledge of titania is available as a function of space, time, and phase (vapor or particle), facilitating the analysis of the particle dynamics by mechanism. Results show that in the proximal region of the jet nucleation and condensation are the dominant mechanisms. However once the jet potential core collapses and turbulent mixing begins, coagulation is the dominant mechanism. The data also shows that the coagulation growth-rate is as much as twice the condensation growth-rate.

High rate synthesis of nanoparticles from vapor requires operation in the turbulent flow regime [

Nakaso et al. [

In this work, the hydrolysis of titanium tetrachloride (

The mass, momentum, and energy equations are solved to obtain the fluid velocity

The fluid contains five chemical species, the transport of which is given by the conservation of species equations:

The aerosol general dynamic equation (GDE) describes particle dynamics under the influence of various physicochemical phenomena, convection, diffusion, coagulation, surface growth, nucleation, and other internal/external forces. The GDE is utilized in discrete form as a population balance on each cluster or particle size. The methodology uses the nodal/sectional method of to approximate the GDE [

The flow under consideration is a three-dimensional, isothermal, turbulent reacting jet issuing from an orifice of diameter _{4} and 99.99% N_{2} by mass. The simulation utilizes stoichiometric mixtures and the molar ratio of 1 : 2 for

In this work, several assumptions and approximations are utilized. These are stated below for clarity.

Ceramic powders such as

The nanoparticles are small enough to follow the fluid path lines. Additionally, the particle volume fraction is of order

Condensation is dominated by the collision rate of monomers with other monomers, clusters, and particles. This means the condensable species in the simulations is the

The clusters and particles are stable because of the high supersaturation of the monomers. As a result, at these temperatures, there is no evaporation or sublimation of particles back to the gas-phase.

The fractal dimension,

A fractal dimension of

Ten bins are used to discretize the particle field (

The vorticity is the curl of the velocity vector and is an indicator of fluid mixing. The vorticity magnitude is the local rate of rotation. In nonpremixed chemically reacting flows, vorticity has the effect of increasing the interfacial area between the reactants. An isosurface of the instantaneous vorticity magnitude, the

An instantaneous isosurface of the vorticity magnitude,

The chemical conversion of the

Instantaneous contour of the

As the chemical reaction proceeds, more titania is produced. The monomers collide with each other to produce dimers; those dimers collide with monomers (condensation) to produce trimers and collide with each other to produce larger particles (coagulation). An advantage of the nodal approach is the fact that the particle field is obtained as a function of size (in addition to space and time). A detailed view of the

Instantaneous contours of the

To convey the spatial inhomogeneity of the particle field, a three-dimensional view is presented in Figure

Instantaneous isosurfaces of 1 nm, 2 nm, and 3 nm particles at

Particle size distributions (PSDs) are often characterized by the mean diameter and the geometric standard deviation (GSD). Though the nodal approach employed contains the full PSD, conveying that all of the information is not trivial [

An instantaneous isosurface of vorticity colored by the geometric standard deviation,

More insight into the particle field may be obtained by considering the relationship between the mean diameter and the GSD. A scatter plot of

Scatter plot of the geometric standard deviation,

The particle growth-rate is an important parameter to consider as, in combination with residence time or reactor size, it is a predictor of particle size. A diameter-based growth-rate

Instantaneous contours of the

The particles grow via two mechanisms: condensation (collisions between monomers and particles) and coagulation (collisions between particles). Because the particle data is available as a function of size, the contribution of each mechanism is readily available. Particle growth, by mechanism, is shown in Figure

Instantaneous contours of the nanoparticle growth-rate decomposed by mechanism;

Particle growth by coagulation is shown in Figure

The spatial relationship between condensation growth and coagulation growth is elucidated by showing the contribution of each at every grid point in the computational domain. A scatter plot of the two growth-rates is shown in Figure

Scatter plot of the particle growth-rate by condensation versus the particle growth-rate by coagulation.

The growth mechanisms of titania during hydrolysis of titanium tetrachloride in a three-dimensional planar jet are studied via direct numerical simulation. The mass, momentum, enthalpy, and species transport equations are solved in a model-free manner. Titania was produced via the hydrolysis of titanium tetrachloride, modeled via a 1-step infinitely fast chemical mechanism. The particle field was represented using a nodal method and solves for the evolution of the concentration of particles of various sizes in an Eulerian manner. When coupled to the Navier-Stokes solver, the fluid, thermal, chemical, and particle fields are obtained as a function of space and time.

The results show that fluid turbulence/gas mixing plays a very important role in particle growth. The results indicate that the particle formation and growth are greatly affected if not dominated by mixing and chemical reaction. Reactant conversion or titania production is limited by the ability of the flow to bring the

These results help to shed light on, and improve our understanding of, the underlying growth dynamics occurring in nanoparticle synthesis processes. The change from condensation-dominated to coagulation-dominated growth is useful in modeling the complete synthesis process, including sintering, and the formation of hard and soft agglomerates. Spanning the size range from single molecules (particle inception) to hundreds of nanometers, as the particles found in many industrial processes and applications, is compute intensive [

One strategy to reduce polydispersity may be to delay the transition to turbulence vis a vis delaying collapse of the jet core. While the particle field is known as a function of size, it should be noted that in this work we are unable to distinguish the various phases of titania, rutile, anatase, or brookite [

The author declares that there is no conflict of interests regarding the publication of this paper.

Funding for this research was provided by the University of Minnesota. Computational resources were provided by Minnesota Supercomputing Institute.

_{2}nanoparticles with narrow size distribution by sol-gel method

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