Direct numerical simulation of water–ethanol flows in a T-mixer - Schikarski, Tobias; Peukert, Wolfgang; Avila, Marc (Chemical Engineering Journal, 2017)
The efficient mixing of fluids is key in many applications, such as chemical reactions and nanoparticle precipitation. Detailed experimental measurements of the mixing dynamics are however difficult to obtain, and so predictive numerical tools are helpful in designing and optimizing many processes. If two different fluids are considered, the viscosity and density of the mixture depend often nonlinearly on the composition, which makes the modeling of the mixing process particularly challenging. Hence water-water mixtures in simple geometries such as T-mixers have been intensively investigated, but little is known about the dynamics of more complex mixtures, especially in the turbulent regime. We here present a numerical method allowing the accurate simulation of two-fluid mixtures. Using a high-performance implementation of this method we perform direct numerical simulations resolving the spatial and temporal dynamics of water-ethanol flows for Reynolds numbers from 100 to 2000. The flows states encountered during turbulence transition and their mixing properties are discussed in detail and compared to water-water mixtures.
Keywords: Mixing; T-mixer; Direct numerical simulation; Miscible fluids; Water–ethanol; Transition to turbulence; Turbulent flows

Efficient quenching sheds light on early stages of gold nanoparticle formation - Biegel, Markus; Schikarski, Tobias; Cardenas Lopez, Paola Ivonne; Gromotka, Lukas; Lübbert, Christian; Völkl, Andreas; Damm, Cornelia; Walter, Johannes; Peukert, Wolfgang (RSC Advances, 2023)
The formation mechanism of plasmonic gold nanoparticles (Au NPs) by fast NaBH4 induced reduction of the precursors is still under debate. In this work we introduce a simple method to access intermediate species of Au NPs by quenching the solid formation process at desired time periods. In this way, we take advantage of the covalent binding of glutathione on Au NPs to stop their growth. By applying a plethora of precise particle characterization techniques, we shed new light on the early stages of particle formation. The results of in situ UV/vis measurements, ex situ sedimentation coefficient analysis by analytical ultracentrifugation, size exclusion high performance liquid chromatography, electrospray ionization mass spectrometry supported by mobility classification and scanning transmission electron microscopy suggest an initial rapid formation of small non-plasmonic Au clusters with Au10 as the main species followed by their growth to plasmonic Au NPs by agglomeration. The fast reduction of gold salts by NaBH4 depends on mixing which is hard to control during the scale-up of batch processes. Thus, we transferred the Au NP synthesis to a continuous flow process with improved mixing. We observed that the mean volume particle sizes and the width of the particle size distribution decrease with increasing flow rate and thus higher energy input. Mixing- and reaction-controlled regimes are identified.
CRIS-Team Scopus Importer:2023-07-21

eMoM: Exact method of moments—Nucleation and size dependent growth of nanoparticles - Pflug, Lukas; Schikarski, Tobias; Keimer, Alexander; Peukert, Wolfgang; Stingl, Michael (Computers & Chemical Engineering, 2020)
In this study we present a reformulation for a broad class of population balance equations that model nucleation and size dependent growth. This formulation enables the definition of new numerical methods, which have two advantages compared to existing schemes in the literature (e.g. finite volume type methods and methods based on the evolution of moments): i) higher precision due to non-smoothing and ii) less run-time in comparison to finite volume algorithms of equivalent accuracy. The described formulation represents the solution of the considered balance equation in terms of the solution of a scalar integral equation, which can then be exploited to establish efficient numerical solvers. The computation of a solution of an initial boundary value problem in space-time is thus reduced to a scalar integral equation, which considerably reduces the computational effort required for its approximation. The integral equation describes the exact evolution of the third moment of the solution, justifying the name for this method: the exact method of moments (eMoM).
CRIS-Team Scopus Importer:2020-03-20
Keywords: Crystallization; Fixed point equation; Growth; Integral equation; Method of moments; Nanoparticle; Nonlocal conservation laws; Nucleation; Population balance equation

En route towards a comprehensive dimensionless representation of precipitation processes - Schikarski, Tobias; Avila, Marc; Peukert, Wolfgang (Chemical Engineering Journal, 2022)
Precipitation of (nano-) particles is a unit operation for the preparation of suspensions. Despite its widespread use, no general understanding is established of how different operating conditions, such as mixing rates or reactant concentrations, affect the precipitation outcome (e.g. the particle size distribution). We obtain overarching relations between the operating conditions and the precipitation outcome by deriving dimensionless numbers governing the precipitation process. In particular, we consider the interdiffusion of two chemical compounds reacting to a sparingly soluble salt by coupling the reaction–diffusion equations for the solute concentrations, to a population balance equation for the evolution of the dispersed phase including nucleation and growth. We vary the relevant process parameters for different chemical systems and uncover three dimensionless numbers, which fully determine the precipitation outcome under the assumption of fast chemical reactions. Two of these dimensionless numbers are Damköhler numbers, which put the relevant mixing kinetics in relation to the relevant time scales for the nucleation and the growth kinetics, respectively. The third dimensionless number corresponds to a dimensionless solid concentration. Simple functional expressions for the Damköhler numbers valid for any chemical system allow estimating whether the precipitation product is controlled by mixing, or solely by the kinetics of solid formation. In the mixing-controlled regime, scaling laws relate the mean particle sizes and the number of particles to the Damköhler number.
Keywords: Reactive precipitation; Nanoparticles; Nucleation; Growth; Damköhler number; Population balance equation

Highly accurate and numerical tractable coupling of nanoparticle nucleation, growth and fluid flow - Bänsch, Eberhard; Pflug, Lukas; Schikarski, Tobias (Chemical Engineering Research & Design, 2023)
Supersaturation as the thermodynamic driving force of particulate precipitation couples the mixing of solute compounds with the solid formation consisting of nucleation and molecular growth. Because the process spans many orders of magnitude in space and time, gathering spatio-temporal information by experiments is hardly achievable. Numerical simulation of the nonlinear, non-local balance equations for mass, momentum and dispersed phase provide detailed solution information in space and time. We here introduce a novel, highly accurate and very efficient numerical formulation of the population balance equations for the dispersed phase coupled to the concentration and velocity field. We reformulate the problem in terms of a fixed-point equation solving the population balance equation along Lagrangian paths with the recently developed exact Method of Moments (eMoM, Pflug et al., 2020) coupled to the concentration field (Eulerian frame). The analytical reformulation provides the information about the full particle size distribution while the computational effort remains in the order of classical moment methods and is much less than numerical schemes approximating the full particle size distribution such as finite volume methods. Furthermore, we explore the difference between an Euler-Euler and Euler-Lagrange coupling considering moderate to large P é clet numbers for the solutes and particles. It turns out that the mean particle size as a solution of the population balance is much more sensitive to the numerical discretization of the advection term than the approximation of the number density function. Based on this finding, we eventually explore the impact of particle diffusion on the solid formation process and give guidelines, when particle diffusion should be taken into account.
CRIS-Team Scopus Importer:2023-03-24
Keywords: Computational fluid dynamics; Euler-Euler and Euler-Lagrange coupling; Fixed-Point-Reformulation; Moment methods; Nanoparticle diffusion; Nucleation and size-dependent growth; Population balance equations

Impact of solvent properties on the precipitation of active pharmaceutical ingredients - Schikarski, Tobias; Trzenschiok, Holger; Avila, Marc; Peukert, Wolfgang (Powder Technology, 2023)
In antisolvent precipitation, water and an organic drug-containing solvent induces particle formation. For each water-solvent mixture, the fluid properties such as viscosity, density and diffusion coefficient but also the drug solubility depend nonlinearily on the fluid mixture compositions. Each property in itself has a strong impact on the solid formation, and thus on the outcome of the precipitation. The simulation framework recently developed by Schikarski et al. [1] allows investigating separately the impact of each fluid property on the precipitation. For a T-mixer and a novel 3-inlet-mixer, we first show that the viscosity and density variations largely determine the macroscopic mixing behavior and, thus, the build-up of supersaturation. The composition-dependent diffusion properties of the drug molecules largely govern the transport-controlled nucleation and particle growth at small scales. In a second step, we numerically predict the experimentally obtained full particle size distribution of the precipitated Ibuprofen nanoparticles using different water-solvent mixtures and different operating conditions. Our numerical results are in excellent agreement with our experimental measurements using ethanol, methanol and 2-propanol as solvents.
CRIS-Team Scopus Importer:2023-01-13
Keywords: Active pharmaceutical ingredients; Antisolvent precipitation; Binary mixtures; Computational fluid dynamics; Nucleation and growth of particles; Population balance equation; Water; ethanol; methanol; 2-propanol

Inflow boundary conditions determine T-mixer efficiency - Schikarski, Tobias; Trzenschiok, Holger; Peukert, Wolfgang; Avila, Marc (Reaction Chemistry & Engineering, 2019)
We report on a comprehensive experimental-computational study of a simple T-shaped mixer for Reynolds numbers up to 4000. In the experiments, we determine the mixing time by applying the Villermaux-Dushman characterization to a water-water mixture. In the numerical simulations, we resolve down to the smallest (Kolmogorov) flow scales in space and time. Excellent agreement is obtained between the experimentally measured mixing time and numerically computed intensity of segregation, especially in the turbulent regime, which validates both approaches. We confirm that the mixing time is mainly determined by the specific power input, as assumed in most mixing-models. However, we show that by suitably manipulating the inflow conditions, the power input necessary to achieve a given mixing time can be reduced by a factor of six. Our study enables detailed investigations of the influence of hydrodynamics on chemical reactions and precipitation processes, as well as the detailed testing of turbulence and micromixing models.
CRIS-Team WoS Importer:2019-03-15

Influence of Mixing on the Precipitation of Organic Nanoparticles: A Lagrangian Perspective on Scale-up Based on Self-Similar Distributions - Schikarski, Tobias; Trzenschiok, Holger; Avila, Marc; Peukert, Wolfgang (Chemical Engineering & Technology, 2019)
Precipitation of nanoparticles is applied in various fields with a rising interest in the formulation of poorly soluble drugs. The impact of fluid mixing on the precipitation of organic nanoparticles is analyzed. Direct numerical simulations are applied to determine the spatiotemporal evolution of the liquid phase composition and to estimate the particle evolution along Langragian trajectories. The simulation results are compared with laboratory experiments of mixing and particle size evolution, which use a recently developed approach to rapidly stabilize the precipitated nanoparticles. The impact of mixing on precipitation is revealed, thereby enabling a parameter-free estimation of the mean particle sizes and the particle size distributions. The distributions of residence time, supersaturation time, and particle size are self-similar for Reynolds numbers in the turbulent regime and allow the derivation of scale-up rules.
CRIS-Team Scopus Importer:2019-06-25
Keywords: Direct numerical simulations; Ibuprofen; Lagrangian mixing; Nanoparticle precipitation; T-micromixer

Mechanistic insights into silver-gold nanoalloy formation by two-dimensional population balance modeling - Traore, Nabi; Schikarski, Tobias; Cardenas Lopez, Paola Ivonne; Körner, A.; Cardenas Lopez, Paola Ivonne; Hartmann, Lukas; Fritsch, B.; Walter, Johannes; Hutzler, A.; Pflug, Lukas; Peukert, Wolfgang (Chemical Engineering Journal, 2024)
The large-scale synthesis of nanoparticles (NPs) with defined properties requires detailed understanding of the underlying formation mechanisms and kinetics. The formation mechanisms of bimetallic NPs are still not sufficiently understood due to the complex reaction chemistry, which makes the control of the supersaturation as the thermodynamic driving force challenging. Particle size, chemical composition, and the distribution of the elements within the particles change dynamically during particle formation. In this work, we propose a mechanism for the formation of bimetallic silver-gold alloy NPs via a green liquid-phase co-reduction synthesis and develop a two-dimensional population balance model to quantitatively describe the evolution of particle size distribution, composition, and optical properties. We shed light on the complex multi-stage formation mechanism of a highly relevant bimetallic NP system, lay the foundation for tailoring the process conditions to achieve targeted optical particle properties and unravel predictive property-process relationships.
CRIS-Team Scopus Importer:2024-02-23
Keywords: Alloy Nanoparticle; Formation Mechanism; Gold Nanoparticle; Nanoparticle Synthesis; Population Balance Equation; Silver Nanoparticle

Modeling and Simulation of Process Technology for Nanoparticulate Drug Formulations-A Particle Technology Perspective. - Uhlemann, Jens; Diedam, Holger; Hoheisel, Werner; Schikarski, Tobias; Peukert, Wolfgang (Pharmaceutics, 2020)
Crystalline organic nanoparticles and their amorphous equivalents (ONP) have the potential to become a next-generation formulation technology for dissolution-rate limited biopharmaceutical classification system (BCS) class IIa molecules if the following requisites are met: (i) a quantitative understanding of the bioavailability enhancement benefit versus established formulation technologies and a reliable track record of successful case studies are available; (ii) efficient experimentation workflows with a minimum amount of active ingredient and a high degree of digitalization via, e.g., automation and computer-based experimentation planning are implemented; (iii) the scalability of the nanoparticle-based oral delivery formulation technology from the lab to manufacturing is ensured. Modeling and simulation approaches informed by the pharmaceutical material science paradigm can help to meet these requisites, especially if the entire value chain from formulation to oral delivery is covered. Any comprehensive digitalization of drug formulation requires combining pharmaceutical materials science with the adequate formulation and process technologies on the one hand and quantitative pharmacokinetics and drug administration dynamics in the human body on the other hand. Models for the technical realization of the drug production and the distribution of the pharmaceutical compound in the human body are coupled via the central objective, namely bioavailability. The underlying challenges can only be addressed by hierarchical approaches for property and process design. The tools for multiscale modeling of the here-considered particle processes (e.g., by coupled computational fluid dynamics, population balance models, Noyes-Whitney dissolution kinetics) and physiologically based absorption modeling are available. Significant advances are being made in enhancing the bioavailability of hydrophobic compounds by applying innovative solutions. As examples, the predictive modeling of anti-solvent precipitation is presented, and options for the model development of comminution processes are discussed.
Keywords: comminution; modeling and simulation; nanocrystal; oral bioavailability; pharmaceutical material science; poorly soluble drug; precipitation; product design

Population balance modeling of InP quantum dots: Experimentally enabled global optimization to identify unknown material parameters - Wang, Zhuang; Traore, Nabi; Schikarski, Tobias; Stiegler, Lisa; Drobek, Dominik; Apeleo Zubiri, Benjamin; Spiecker, Erdmann; Walter, Johannes; Peukert, Wolfgang; Pflug, Lukas; Segets, Doris (Chemical Engineering Science, 2023)
Despite great progress in the synthetic chemistry of InP QDs, a predictive model to describe their temporal formation is still missing. In this work, we introduce a population balance model incorporating liquid phase reactions, homogeneous nucleation and reaction-limited growth of InP supported with the highly reproducible and reliable experimental data acquired from an automated robotic synthesis platform. A comparison between experimental kinetic data (different initial concentrations and temperatures) and simulations was made. The proposed model describes the temporal evolution of solid concentration, particle diameter and particle size distribution very well. The quantitative agreement between experiments and simulations was only achieved by global optimization to identify unknown and hardly measurable material parameters and kinetic constants such as surface energy, growth rate constants or activation energies. We see this model rendering the first step towards the development of more refined models that enable rigorous optimization and control of the production process for III-V semiconductors.
CRIS-Team Scopus Importer:2023-08-11
Keywords: Automated synthesis; InP; Population balance equation; Simulation

Quantitative modeling of precipitation processes - Schikarski, Tobias; Avila, Marc; Trzenschiok, Holger; Güldenpfennig, Andreas; Peukert, Wolfgang (Chemical Engineering Journal, 2022)
Precipitation from the liquid phase is a powerful and common unit operation for the continuous, highly reproducible production of nanoparticles. However, a general, predictive and quantitative modeling framework is still missing due to the inherent multiscale nature of the precipitation process and the complex interplay between the relevant sub-processes. We apply direct numerical simulation of the fluid flow coupled with a population balance framework to investigate the precipitation of stabilized ibuprofen nanoparticles in a T-mixer. Our findings suggest that the Damkohler number (the ratio between the mixing time and solid formation time) determines the precipitation outcome. We demonstrate how the primarily unknown solid formation kinetics can be estimated in the simulations with the guidance of experimental input at a single process condition. We subsequently vary the Damkohler number by changing the inflow rates (global mixing time) and the initial ibuprofen concentration. In doing so, excellent agreement between numerical simulations and experiments in the full particle size distribution at different process conditions (from laminar to turbulent flow and different initial ibuprofen concentrations) is obtained using the beforehand estimated solid formation kinetics. Our model opens avenues for the predictive simulation of particle-formation dynamics and is a stepping stone for the tailored, scalable production of nanoparticles.
CRIS-Team WoS Importer:2022-06-17