Microhydrodynamic Model Research Articles

The use of a microhydrodynamic model, kinetic analysis and optimization tools for the development of corn starch nanosuspensions via wet-stirred media milling

The use of a microhydrodynamic model, kinetic analysis and optimization tools for the development of corn starch nanosuspensions via wet-stirred media milling

Do Mixtures of Beads with Different Sizes Improve Wet Stirred Media Milling of Drug Suspensions?

The impacts of bead sizes and bead mixtures on breakage kinetics, the number of milling cycles applied to prevent overheating, and power consumption during the nanomilling of drug (griseofulvin) suspensions were investigated from both an experimental and theoretical perspective. Narrowly sized zirconia beads with nominal sizes of 100, 200, and 400 µm and their half-and-half binary mixtures were used at 3000 and 4000 rpm with two bead loadings of 0.35 and 0.50. Particle size evolution was measured during the 3 h milling experiments using laser diffraction. An nth-order breakage model was fitted to the experimental median particle size evolution, and various microhydrodynamic parameters were calculated. In general, the beads and their mixtures with smaller median sizes achieved faster breakage. While the microhydrodynamic model explained the impacts of process parameters, it was limited in describing bead mixtures. For additional test runs performed, the kinetics model augmented with a decision tree model using process parameters outperformed that augmented with an elastic-net regression model using the microhydrodynamic parameters. The evaluation of the process merit scores suggests that the use of bead mixtures did not lead to notable process improvement; 100 µm beads generally outperformed bead mixtures and coarser beads in terms of fast breakage, low power consumption and heat generation, and low intermittent milling cycles.

Elaborating the crystal transformation referenced microhydrodynamic model and fracture mechanism combined molecular modelling of irbesartan nanosuspensions formation in wet media milling

In recent years, polymorphic transformation involved in media milling has become a key factor in inducing the instability of nanosuspensions (NSs). The variation trend of microhydrodynamic parameters, including milling intensity factor (F), can be observed under different milling conditions. Therefore, this study first referenced the microhydrodynamic model to explore how formulations and process parameters affect Irbesartan (IRB) form A crystallinity during wet media milling. As a result, the crystallinity of form A was affected by the intermolecular interactions between drug particles and stabilizers. The crystallinity of form A decreased with decreasing drug loading, increasing stirrer speed and bead loading, which depended on the role of F. Milling could promote the transformation from a 1H to 2H tetrazole ring with stabilizers containing –OH, and form B was changed to form A and finally to an amorphous state. Molecular modelling shows that forms A and B are ductile and fragile materials, respectively, and both present anisotropy. When milling beads hit both polymorphs paralleling to the (010) surface, the bead-bead collisions are more helpful in fracturing IRB particles. The results of this study may provide a foundation for controlling crystal transformation and obtaining ideal crystal forms.

Review of nanosuspension formulation and process analysis in wet media milling using microhydrodynamic model and emerging characterization methods

Wet media milling is a popular technology used to prepare nanosuspensions. However, the theories and methods to guide the research on the formulation and process affecting wet media milling remain limited. The research on wet media milling follows a “black box” approach to a certain extent. This review focuses on exploring the formulation and process parameters factors in wet media milling. The formulation factors include the concentration, hydrophilicity/hydrophobicity, and structure of the drug and stabilizer, whereas the milling process parameters include the milling speed, milling time, and material, size, and filling volume of milling beads. Contrary to other reviews, this review attempts to quantify and visualize these factors by combining a microhydrodynamic model with emerging characterization methods to provide a scientific basis for the selection of nanosuspension formulations and process parameters, as opposed to the conventional trial-and-error approach.

Effects of bead packing limit concentration on microhydrodynamics-based prediction of breakage kinetics in wet stirred media milling

We studied wet-milling kinetics of a drug in a stirred mill using a microhydrodynamic model with various radial distribution functions (RDFs). An nth-order kinetics model was fitted to the median size evolution data at several stirrer speeds and loadings of polystyrene/zirconia beads to identify the breakage rate constant k. Microhydrodynamic parameters were calculated using three RDFs: Carnahan–Starling, Lun, and Ma–Ahmadi. The first one, used in previous microhydrodynamic studies, does not account for the bead packing limit concentration. The Lun and the Ma–Ahmadi RDFs similarly predicted much higher frequency of less energetic–forceful bead–bead collisions than the Starling RDF. A subset selection algorithm determined the best multiple linear regression models (MLRMs) of k with the microhydrodynamic parameters (semi-theoretical) or the process–bead parameters (empirical) as predictors. The Lun RDF-based MLRM had the best fitting–predictions of the kinetics among the semi-theoretical MLRMs, which outperformed the empirical MLRMs.

Kinetic and Microhydrodynamic Modeling of Fenofibrate Nanosuspension Production in a Wet Stirred Media Mill.

This study examined the impact of stirrer speed and bead material loading on fenofibrate particle breakage during wet stirred media milling (WSMM) via three kinetic models and a microhydrodynamic model. Evolution of median particle size was tracked via laser diffraction during WSMM operating at 3000–4000 rpm with 35–50% (v/v) concentration of polystyrene or zirconia beads. Additional experiments were performed at the center points of the above conditions, as well as outside the range of these conditions, in order to test the predictive capability of the models. First-order, nth-order, and warped-time kinetic models were fitted to the data. Main effects plots helped to visualize the influence of the milling variables on the breakage kinetics and microhydrodynamic parameters. A subset selection algorithm was used along with a multiple linear regression model (MLRM) to delineate how the breakage rate constant k was affected by the microhydrodynamic parameters. As a comparison, a purely empirical correlation for k was also developed in terms of the process/bead parameters. The nth-order model was found to be the best model to describe the temporal evolution; nearly second-order kinetics (n ≅ 2) was observed. When the process was operated at a higher stirrer speed and/or higher loading with zirconia beads as opposed to polystyrene beads, the breakage occurred faster. A statistically significant (p-value ≤ 0.01) MLRM of three microhydrodynamic parameters explained the variation in the breakage rate constant best (R2 ≥ 0.99). Not only do the models and the nth-order kinetic–microhydrodynamic correlation enable deeper process understanding toward developing a WSMM process with reduced cycle time, but they also provide good predictive capability, while outperforming the purely empirical correlation.

Use of Bead Mixtures as a Novel Process Optimization Approach to Nanomilling of Drug Suspensions.

We aimed to evaluate the feasibility of cross-linked polystyrene (CPS)-yttrium-stabilized zirconia (YSZ) bead mixtures as a novel optimization approach for fast, effective production of drug nanosuspensions during wet stirred media milling (WSMM). Aqueous suspensions of 10% fenofibrate (FNB, drug), 7.5% HPC-L, and 0.05% SDS were wet-milled at 3000-4000rpm and 35%-50% volumetric loading of CPS:YSZ bead mixtures (CPS:YSZ 0:1-1:0 v:v). Laser diffraction, SEM, viscometry, DSC, and XRPD were used for characterization. An nth-order model described the breakage kinetics, while a microhydrodynamic model allowed us to gain insights into the impact of bead materials. CPS beads achieved the lowest specific power consumption, whereas YSZ beads led to the fastest breakage. Breakage followed second-order kinetics. Optimum conditions were identified as 3000rpm and 50% loading of 0.5:0.5v/v CPS:YSZ mixture from energy-cycle time-heat dissipation perspectives. The microhydrodynamic model suggests that YSZ beads experienced more energetic/forceful collisions with smaller contact area as compared with CPS beads owing to the higher density-elastic modulus of the former. We demonstrated the feasibility of CPS-YSZ bead mixtures and rationalized its optimal use in WSMM through their modulation of breakage kinetics, energy utilization, and heat dissipation.

Mechanistic Modeling of Wet Stirred Media Milling for Production of Drug Nanosuspensions.

Drug nanocrystals have been used for a wide range of drug delivery platforms in the pharmaceutical industry, especially for bioavailability enhancement of poorly water-soluble drugs. Wet stirred media milling (WSMM) is the most widely used process for producing dense, stable suspensions of drug nanoparticles, also referred to as nanosuspensions. Despite a plethora of review papers on the production and applications of drug nanosuspensions, modeling of WSMM has not been thoroughly covered in any review paper before. The aim of this review paper is to briefly expose the pharmaceutical scientists and engineers to various modeling approaches, mostly mechanistic, including computational fluid dynamics (CFD), discrete element method (DEM), population balance modeling (PBM), coupled methods, the stress intensity-number model (SI-SN model), and the microhydrodynamic (MHD) model with a main focus on the MHD model for studying the WSMM process. A total of 71 studies, 30 on drugs and 41 on other materials, were reviewed. Analysis of the pharmaceutics literature reveals that WSMM modeling is largely based on empirical, statistically based modeling approaches, and mechanistic modeling could help pharmaceutical engineers develop a fundamental process understanding. After a review of the salient features and various pros-cons of each modeling approach, recent advances in microhydrodynamic modeling and process insights gained therefrom were highlighted. The SI-SN and MHD models were analyzed and critiqued objectively. Finally, the review points out potential research directions such as more mechanistic and accurate CFD-DEM-PBM simulations and the coupling of the MHD-PBM models with the CFD.

Impact of media material and process parameters on breakage kinetics–energy consumption during wet media milling of drugs

While crosslinked polystyrene (CPS) beads and yttrium-stabilized zirconia (YSZ) beads have been commonly used as media for wet milling of poorly soluble drugs and their dissolution enhancement, no first-principle rationale exists for selecting the bead material. The aim of this study is to investigate the impact of stirrer speed (2000–4000 rpm) and CPS bead loading (~20–60%) on the breakage kinetics–energy consumption during milling of griseofulvin, a model poorly soluble drug, and compare the performance of CPS vs. YSZ at the highest bead loading. Laser diffraction, SEM, rheological analysis, and XRPD were used for characterization. The milling was most effective at the highest bead loading–stirrer speed. A microhydrodynamic model suggests that an increase in stirrer speed led to faster breakage due to more frequent and forceful CPS bead–bead collisions. Despite causing slight decrease in maximum contact pressure, an increase in CPS bead loading caused a dramatic increase in average frequency of drug particle compressions, which dominated the faster breakage observed. While YSZ generally required higher specific energy consumption than CPS, it achieved the same product fineness faster than CPS. The microhydrodynamic model rationalized the favorable use of YSZ over CPS beads within the experimental domain studied.

A microhydrodynamic rationale for selection of bead size in preparation of drug nanosuspensions via wet stirred media milling

Although wet stirred media milling has proven to be a robust process for producing nanoparticle suspensions of poorly water-soluble drugs and thereby enhancing their bioavailability, selection of bead size has been largely empirical, lacking fundamental rationale. This study aims to establish such rationale by investigating the impact of bead size at various stirrer speeds on the drug breakage kinetics via a microhydrodynamic model. To this end, stable suspensions of griseofulvin, a model BCS Class II drug, were prepared using hydroxypropyl cellulose and sodium dodecyl sulfate. The suspensions were milled at four different stirrer speeds (1000–4000rpm) using various sizes (50–1500μm) of zirconia beads. Laser diffraction, SEM, and XRPD were used for characterization. Our results suggest that there is an optimal bead size that achieves fastest breakage at each stirrer speed and that it shifts to a smaller size at higher speed. Calculated microhydrodynamic parameters reveal two counteracting effects of bead size: more bead–bead collisions with less energy/force upon a decrease in bead size. The optimal bead size exhibits a negative power-law correlation with either specific energy consumption or the microhydrodynamic parameters. Overall, this study rationalizes the use of smaller beads for more energetic wet media milling.

Nanomilling of Drugs for Bioavailability Enhancement: A Holistic Formulation-Process Perspective.

Preparation of drug nanoparticles via wet media milling (nanomilling) is a very versatile drug delivery platform and is suitable for oral, injectable, inhalable, and buccal applications. Wet media milling followed by various drying processes has become a well-established and proven formulation approach especially for bioavailability enhancement of poorly water-soluble drugs. It has several advantages such as organic solvent-free processing, tunable and relatively high drug loading, and applicability to a multitude of poorly water-soluble drugs. Although the physical stability of the wet-milled suspensions (nanosuspensions) has attracted a lot of attention, fundamental understanding of the process has been lacking until recently. The objective of this review paper is to present fundamental insights from available published literature while summarizing the recent advances and highlighting the gap areas that have not received adequate attention. First, stabilization by conventionally used polymers/surfactants and novel stabilizers is reviewed. Then, a fundamental understanding of the process parameters, with a focus on wet stirred media milling, is revealed based on microhydrodynamic models. This review is expected to bring a holistic formulation-process perspective to the nanomilling process and pave the way for robust process development scale-up. Finally, challenges are indicated with a view to shedding light on future opportunities.

Sub-100 nm drug particle suspensions prepared via wet milling with low bead contamination through novel process intensification

There is sustained interest in sub-100nm particles of poorly water-soluble drugs as such small particles offer improved permeation through various biological barriers and result in rapid onset of therapeutic action. An intensified wet stirred media milling process was developed here for fast production of sub-100nm drug particles with low bead contamination and reduced energy consumption. Griseofulvin and indomethacin, two model poorly water-soluble drugs, were wet-milled. Yttrium-stabilized zirconia beads with a nominal size ranging from 50µm to 800µm were used in the baseline process, which was subsequently intensified with the optimal bead size by increasing rotor tip speed, bead loading, and suspension flow rate stepwise, as guided by a microhydrodynamic model. Laser diffraction, dynamic light scattering, scanning electron microscopy, and XRD were used to characterize the milled suspensions. Results from the baseline process indicated that sub-100nm griseofulvin particles were only produced when 50 or 100µm beads were used in the 360min milling experiments. Interestingly, using 50µm beads led to the formation of sub-100nm griseofulvin particles within 240min with the lowest bead (zirconium) contamination and specific energy consumption. This could be explained though the microhydrodynamic model, revealing that 50µm beads led to the highest frequency of drug particle compressions yet generated the lowest bead contact pressure. The processing time was further reduced to as low as 64min producing griseofulvin particle size of 100nm through step-wise intensification of the milling process with the 50µm beads, as quantified by a milling intensity factor. Due to the enhancement of the breakage kinetics, the process intensification enabled shorter milling to attain 100nm particles, thus resulting in significant energy savings and low bead contamination despite an increase in power consumption. The general applicability of the process intensification method was confirmed through milling of indomethacin, which also led to sub-100nm particles faster with reduced energy consumption and low contamination.

Impact of process parameters on the breakage kinetics of poorly water-soluble drugs during wet stirred media milling: A microhydrodynamic view

Wet stirred media milling has proven to be a robust process for producing nanoparticle suspensions of poorly water-soluble drugs. As the process is expensive and energy-intensive, it is important to study the breakage kinetics, which determines the cycle time and production rate for a desired fineness. Although the impact of process parameters on the properties of final product suspensions has been investigated, scant information is available regarding their impact on the breakage kinetics. Here, we elucidate the impact of stirrer speed, bead concentration, and drug loading on the breakage kinetics via a microhydrodynamic model for the bead–bead collisions. Suspensions of griseofulvin, a model poorly water-soluble drug, were prepared in the presence of two stabilizers: hydroxypropyl cellulose and sodium dodecyl sulfate. Laser diffraction, scanning electron microscopy, and rheometry were used to characterize them. Various microhydrodynamic parameters including a newly defined milling intensity factor was calculated. An increase in either the stirrer speed or the bead concentration led to an increase in the specific energy and the milling intensity factor, consequently faster breakage. On the other hand, an increase in the drug loading led to a decrease in these parameters and consequently slower breakage. While all microhydrodynamic parameters provided significant physical insight, only the milling intensity factor was capable of explaining the influence of all parameters directly through its strong correlation with the process time constant. Besides guiding process optimization, the analysis rationalizes the preparation of a single high drug-loaded batch (20% or higher) instead of multiple dilute batches.

Formation of Lubricant Film in Rotary Sealing Contacts: Part I—Lubricant Film Modeling

The lubricant film developed in rotary lip seals is a vital element in achieving long-lasting seals with low friction. In this paper the basic principles controlling the development of a lubricant film in lip seals are studied using a micro-hydrodynamic model. This model takes into account the visco-elastic effects of the rubber on the development of the sealing pressure. Central to the model’s hypothesis is the assumption of the predominant action of the surface micro-geometry in the formation of the lubricant film. Optical observations of the contact area of a lip seal, using blue light induced fluorescence, supported this concept. Using this basic lubrication model, the minimum and average film thickness and shear stress are calculated for different loading conditions, material stiffnesses and statistical parameters characterizing the micro-geometry of the sealing surfaces. In the model the effect of the viscoelastic properties of the rubber on the dynamic response of the seal and resulting pressure is also considered. To support the predictions of the theory, a new experimental method for the determination of the film thickness in elastomeric contacts is applied. Comparison between experimental and theoretical results indicates the ability of the model to deal with effects previously excluded from the analysis. The correlation between measured film thicknesses and thicknesses predicted using the present model was found to be good for the full range of speeds tested.

A Microhydrodynamic Model of the Sedimentation Process

Abstract A microhydrodynamic model is proposed to evaluate the turbulent transport effects on the sedimentation behavior of fine solid particles. The model is deduced from a material balance in a turbulent field which includes concentration effects on the turbulent diffusion coefficients and the settling velocities of solid particles. The microhydrodynamic model can simulate the practical sedimentation behavior of solid particles not only in the steady state but also in the dynamic as well as the decay state.