Search Results (14)

This comprehensive review of the synergistic use of Quality by Design (QbD) and the Pi–Buckingham theorem explores an innovative approach to enhancing product development and process optimization within the pharmaceutical industry. QbD is a systematic, proactive methodology that integrates quality considerations throughout the product lifecycle to ensure that pharmaceutical products meet regulatory standards for safety and efficacy from the outset of development. The Pi–Buckingham theorem serves as a foundational principle in dimensional analysis, facilitating the simplification of complex models by transforming physical variables into dimensionless parameters. This synergy enables researchers to better understand and control the factors affecting critical quality attributes (CQAs), thereby improving manufacturing outcomes and minimizing variability. Full article

The hydrodynamics characteristics of artificial water diversion canals with long-distance and inter-basin multi-stage sluice gate regulations are prone to sudden increases and decreases, and sluice gate discharge differs from that of natural rivers. Research on the change characteristics of hydrological elements in artificial canals under the control of sluice gates is lacking, as are scientifically accurate calculations of sluice gate discharge. Therefore, addressing these gaps in long-distance artificial water transfer is of great importance. In this study, real-time operation data of 61 sluice gates, pertaining to the period from May 2019 to July 2021, including data on water levels, flow discharge, velocity, and sluice gate openings in the main canal of the Middle Route of the South-to-North Water Diversion Project of China, were analyzed. The discharge coefficient of each sluice gate was calculated by the dimensional analysis method, and the unit-width discharge was modeled as a function of gate opening ($e$), gravity acceleration ($g$), and energy difference ($H$). Through logarithmic transformation of the Buckingham Pi theorem-derived equation, a linear regression model was used. Data within the relative opening orifice flow regime were selected for fitting, yielding the discharge coefficients and stage–discharge relationships. The results demonstrate that during the study period, the water level, discharge, and velocity of the main canal showed an increasing trend year by year. The dimensional analysis results indicate that the stage–discharge response relationship followed a power function ($Q\propto {(\frac{H}{e})}^{constant}$) and that there was a good linear relationship between $l{g}^{(\frac{H}{e})}$ and $l{g}^{(\frac{K}{e})}$ (R² > 0.95, $K={(q^2/g)}^{1/3}$). By integrating geometric, operational, and hydraulic parameters, the proposed method provides a practical tool and a scientific reference for analyzing sluice gates’ regulation and hydrological response characteristics, optimizing water allocation, enhancing ecological management, and improving operational safety in long-distance inter-basin water diversion projects. Full article

Dimensional analysis is an effective tool for designing laboratory tests, and it is also a successful method to reasonably predict the results of large-scale or field tests, which are difficult and costly to perform, by considering the outcomes obtained from small-scale tests. This paper therefore focuses on predicting the compression load–settlement relationship of soft clay soil under a rigid foundation by dimensional analysis. For that purpose, a series of dimensionless pi (π) terms were first produced for the relevant problem by employing Buckingham’s pi (π) theorem via the MATLAB program. Secondly, the results of a small-scale physical test reported in the literature that investigated the load–settlement relationship of soft clay soil under a rigid foundation subjected to compression load were verified with the finite element method. Thereafter, the small-scale problem was scaled up several times using dimensionless terms, and the compression load–settlement relationship for the large-scale cases was investigated with both dimensional analysis and the validated finite element method. The findings indicate that dimensional analysis produces reasonably successful outcomes considering the computational ease. In addition, the MATLAB program presented in this paper is quite useful for those desiring to determine the dimensionless terms belonging to any sort of problem. Full article

Controlling droplet sizes is one of the most important aspects of droplet generators used in biomedical research, drug discovery, high-throughput screening, and emulsion manufacturing applications. This is usually achieved by using multiple devices that are restricted in their range of generated droplet sizes. In this paper, a co-flow microfluidic droplet-generation device with flexible walls was developed such that the width of the continuous (C)-phase channel around the dispersed (D)-phase droplet-generating needle can be adjusted on demand. This actuation mechanism allowed for the adjustment of the C-phase flow velocity, hence providing modulated viscous forces to manipulate droplet sizes in a single device. Two distinct droplet-generation regimes were observed at low D-phase Weber numbers, i.e., a dripping regime at high- and medium-channel widths and a plug regime at low-channel widths. The effect of channel width on droplet size was investigated in the dripping regime under three modes of constant C-phase flow rate, velocity, and Capillary number. Reducing the channel width at a constant C-phase flow rate had the most pronounced effect on producing smaller droplets. This effect can be attributed to the combined influences of the wall effect and increased C-phase velocity, leading to a greater impact on droplet size due to the intensified viscous force. Droplet sizes in the range of 175–913 µm were generated; this range was ~2.5 times wider than the state of the art, notably using a single microfluidic device. Lastly, an empirical model based on Buckingham’s Pi theorem was developed to predict the size of droplets based on channel width and height as well as the C-phase Capillary and Reynolds numbers. Full article

Dimensional analysis through the Buckingham Pi theorem was confirmed as an efficient mathematical tool to model the otherwise non-linear high order ultrasonic micro-injection molding process (UMIM). Several combinations of processing conditions were evaluated to obtain experimental measurements and validate the derived equations. UMIM processing parameters, output variable energy consumption, and final specimen’s Young modulus were arranged in dimensionless groups and formulated as functional relationships, which lead to dimensionless equations that predict output variables as a function of the user-specified processing parameters and known material properties. Full article

Permeable Interlocking Concrete Paver (PICP) systems provide onsite stormwater management by detaining runoff and removing contaminants. However, a major problem with PICPs is the significant maintenance cost associated with their clean-out to restore the original functionality, which discourages landowners and municipalities from adopting the systems. A combination of laboratory experiments and machine-learning techniques are applied to address this challenge. A total of 376 laboratory experiments were conducted to investigate four independent variables (cleaning equipment speed over the pavement, air speed in the cleaning jets, top opening width of the cupule, and filter media gradation) that affect the cleaning of PICPs. The Buckingham Pi-Theorem was used to express the four main input variables in three dimension-less parameters. This current investigation provides a novel understanding of variables affecting the sustainable and economically feasible maintenance of PICPs. A new model is derived to more accurately predict the percentage of mass removal from PICPs during clean-out using a machine-learning technique. The Group Method of Data Handling (GMDH) model exhibits high performance, with a correlation coefficient (R2) of 0.87 for both the training and testing stages. The established simple explicit equation can be applied to optimize the maintenance costs for industrial applications of Regenerative Air Street Sweepers for sustainable and cost-effective PICP maintenance. Pavements with larger surface areas are found to have lower maintenance costs ($/m²/year) compared to the ones with smaller surface areas. This study estimates $0.32/m²/year and $0.50/m²/year to maintain pavements with larger (5000 m²) and smaller (1000 m²) surface areas, respectively. Full article

The formation of fouling deposits on heat exchanger surfaces is one of the major concerns in thermal processes. The fouling behavior of food materials is complex, and its mechanism remains, in general, unclear. This study was aimed at developing a predictive model for soymilk fouling deposit formed on heated surfaces using dimensional analysis. Relevant variables affecting fouling deposit mass could be grouped into six dimensionless terms using Buckingham’s pi-theorem. Experimental data were obtained from a lab-scale plate heat exchanger. A simple model developed using the experimental data under the process conditions with the product inlet temperature, the product outlet temperature, and plate surface temperature in the ranges of 50–55 °C, 65–70 °C, and 70–85 °C, respectively, exhibited a good performance in the prediction of soymilk fouled mass. The correlation coefficient between the predicted and experimental values of fouled mass was 0.97 with an average relative error of 9.03%. Within the ranges of product inlet temperature and plate surfaces temperature studied, this model offers an opportunity to estimate soymilk fouling mass with acceptable accuracy. Full article

Structures in various industries are exposed to dynamic loads. The dissipative properties of adhesively bonded joints can contribute to the damping of dynamically stressed structures. Dynamic hysteresis tests are carried out to determine the damping properties of adhesively bonded overlap joints by varying the geometry and test boundary conditions. The dimensions of the overlap joints are full-scale and thus relevant for steel construction. Based on the results of experimental investigations, a methodology is developed for the analytic determination of the damping properties of adhesively bonded overlap joints for various specimen geometries and stress boundary conditions. For this purpose, dimensional analysis is carried out using the Buckingham Pi Theorem. In summary, it can be stated that the loss factor of adhesively bonded overlap joints investigated within this study is in the range between 0.16 and 0.41. The damping properties can particularly be increased by increasing the adhesive layer thickness and reducing the overlap length. The functional relationships of all the test results shown can be determined by dimensional analysis. An analytical determination of the loss factor considering all identified influencing factors is enabled by derived regression functions with a high coefficient of determination. Full article

An open-cell metal foam gains a lot of interest from researchers due to its unique porous structure, which provides high surface area and good tortuosity, as well as being lightweight. However, the same structure also induces a massive pressure drop which requires an optimum design to suit applications, for example, a partially filled setup or staggered design. Thus, better attention to the slip velocity at the interface between the porous structure and non-porous region is required to maximize its potential, especially in thermal fluid applications. This study proposed a slip velocity model of an open-cell metal foam by using a reverse engineering method and 3D printing technology. A series of experiments and a dimensionless analysis using the Buckingham-Pi theorem were used to compute the slip velocity model. Results show that the pressure drop increases with decreasing pore size. However, the blockage ratio effects would be more significant on the pressure drop with foams of smaller pore sizes. The proposed slip velocity model for an open-cell metal foam agrees with the experimental data, where the predicted values fall within measurement uncertainty. Full article

Wine research has as its core components the disciplines of sensory analysis, viticulture, and oenology. Wine quality is an important concept for each of these disciplines, as well as for both wine producers and consumers. Any technique that could help producers to understand the nature of wine quality and how consumers perceive it, will help them to design even more effective marketing strategies. However, predicting a wine’s quality presents wine science modelling with a real challenge. We used sample data from Pinot noir wines from different regions of New Zealand to develop a mathematical model that can predict wine quality, and applied dimensional analysis with the Buckingham Pi theorem to determine the mathematical relationship among different chemical and physiochemical compounds. This mathematical model used perceived wine quality indices investigated by wine experts and industry professionals. Afterwards, machine learning algorithms are applied to validate the relevant sensory and chemical concepts. Judgments of wine intrinsic attributes, including overall quality, were made by wine professionals to two sets of 18 Pinot noir wines from New Zealand. This study develops a conceptual and mathematical framework to predict wine quality, and then validated these using a large dataset with machine learning approaches. It is worth noting that the predicted wine quality indices are in good agreement with the wine experts’ perceived quality ratings. Full article

Excessive wear of gears will not only cause noise and vibration in the transmission system, but also reduce transmission efficiency and accuracy in severe cases, causing irreversible losses to the transmission system. It is desirable to develop a micro-gear unit model for evaluating the wear process and predicting the failure time of large gear units (such as wind turbine gear units), reducing losses due to sudden failures. Based on the Buckingham pi-theorem of dimensional analysis and Hertz formula, the similarity ratio of each parameter of the gear wear process was proposed. The maximum equivalent stress is calculated by establishing the FEM model and comparing it with the theoretical contact stress calculated by the Hertz formula, and the results were relatively consistent. Two pairs of gear friction and wear experiments with similar parameters were carried out to compare the wear evolution performance of two similar gears. The friction performance process of the test gears was observed by particle counter and analytical ferrograph. The results show that the friction and wear processes of the two groups of gears with similar parameters have a certain correlation, which was consistent with the proposed similarity model. The similarity model combined with the observation results of abrasive particles has a certain application value for the evaluation of the wear state of the transmission system. Full article

Scaling up bioprocesses from the experimental to the pilot or industrial scale involves heuristics and scale relationships that are far from the specific phenomena and are usually not connected to the experimental data. In complex systems, the scaling-up methodology must connect the experimental data with the tools of engineering design. In this work, a two-stage gold bioleaching process was used as a case study to develop a mathematical model of bioprocess scaling that combines the design of experiments with dimensional analysis using the Buckingham Pi theorem to formulate a predictive model that allows scaling up bioprocesses. It was found that the C/N, C/K, and T/C ratios are dimensionless factors that can explain the behavior of a system. Using the Pearson Product–Moment bivariate analysis, it was found that the dimensionless factors C/N and C/K were correlated with the leaching potential of the fermented broth at 1060 cm⁻¹. With these results, a non-linear logarithmic model based on dimensionless parameters was proposed to explain the behavior of the system with a correlation coefficient of R² = 0.9889, showing that the optimal conditions to produce fermented broth comprised a C/N ratio close to 50 and a C/K ratio close to 800, which allows predicting the scaling of the bioprocess. Full article

The rheological behavior of mineral slurries shows the level of interaction or aggregation among particles, being a process control variable in processes such as slurry transportation, dehydration, and wet grinding systems. With the aim to analyze the effect of medium viscosity in wet grinding, a series of monosize grinding ball mill tests were performed to determine breakage parameters, according to the generally accepted kinetic approach of grinding processes. A rheological modifier (polyacrylamide, PAM) was used to modify solutions viscosity. A model was proposed by means of dimensional analysis (Buckingham’s Pi theorem) in order to determine the behavior of the specific breakage rate (S_j) for a ball grinding process in terms of the rheology of the system. In addition to this, a linear adjustment was established for the relationship between specific breakage rates with and without PAM addition, based on the reduced viscosity, μ_r. Furthermore, within a certain interval of viscosity, it was proved that an increment of viscosity can increase the specific breakage rate, and consequently the grinding degree. Full article

The determination of a reliable tortuosity index is lacking in the aerospace industry. Therefore, a methodology is formulated via direct and indirect characterization methods of a fluid-filled porous media. Chemical, thermal, and mechanical characterization was performed to the PolyuMAC^TM polyimide foam. Tortuosity was measured considering a pressure difference as the resistivity variable, rather than electrical resistivity or molecular diffusivity, as proposed on previous models. This is an empirical establishment of the tortuosity index considering the correlation among hydraulic and structural dimensionless parameters obtained through the Buckingham’s Pi theorem. The behavior of the polyimide was studied for samples of different lengths compressed at 30%, 60%, and 90% of its original length on the foaming direction. Results show that, porosity, sample length, and fluid viscosity are relevant for the insulation performance of the material. Regression analysis produced a significant statistical model fit to the data correlated from the dimensionless parameters for each dynamic compression series. Full article