Abstract
In recent years response surface analysis has been increasingly used to optimise membrane separation. It has many advantages, such as reducing the number of experiments to be performed, which requires lower energy consumption and significantly less laboratory work. For more accurate data analysis and forecasting, mathematical models are used that analyse the relevance of the factors examined and the interaction effects between the factors. In this research, two experimental designs that use response surface methodology are presented, namely, the central composite design and the Box–Behnken design. After the general characterisation of the experimental designs, their application in membrane technology is presented.
1 Introduction
Response surface methodology (RSM) is a mathematical and statistical method widely used to model and analyse various processes where the desired response is influenced by various variables and the goal is to optimise the response. They are very effective because they take into account main effects and interaction effects with a minimum number of experiments, thus clarifying the causal relationship between factors and responses. Experiment design and optimisation methodology play an important role in modern research and development. The traditional approach to the optimisation problem is the one-factor method, where we examine the effect of one variable while keeping the other variables at a constant level (Bezerra et al., 2008). In order to achieve optimal conditions, this procedure is repeated with other variables. The main disadvantage of this method is that it does not represent the interactive effects between the investigated variables, so it cannot provide the full effect of the variables on the process. In addition, the one-factor approach increases the number of experiments required to conduct the research, so it would be costly and time-consuming (Ba and Boyaci, 2007; Bezerra et al., 2008). Consequently, factor optimisation procedures using multivariate techniques have been encouraged, as they are faster, more economical, and more efficient and allow the simultaneous optimisation of more than one variable (Ferreira et al., 2007; Leardi, 2009; Tarley et al., 2009; Kemény et al., 2017). Response surface methodologies are multivariate techniques that mathematically fit the experimental range under consideration in theoretical design via a response function (Myers and Montgomery, 1995). It was originally developed by Box and Wilson (1951) to improve yields in the chemical and other processing industries. RSM is now used to optimise systems in many fields due to its high efficiency, such as electronics, biotechnology, aerospace, automotive, life sciences, agricultural environment, and manufacturing (Anderson-Cook et al., 2009; Zolgharnein et al., 2013).
In RSM, mathematical models generated using experimental design data determine the relationships between independent variables (factors) and dependent variables (responses). These models are used to analyse the effects and interactions of independent variables on responses and to optimise the process. The application of RSM as an optimisation tool consists of several steps. These include (i) selecting independent variables and their ranges, (ii) selecting the experimental design and conducting the experiments, (iii) creating a linear regression model equation based on the experimental results, (iv) checking the appropriateness of the model, and (v) graphing the model representation and achieving optimal conditions (Nair et al., 2014).
The two most common designs used in response surface modeling are the central composite design and the Box–Behnken design. Membrane technology is a field where experimental design is widely used for optimisation, so this paper aims to introduce the theory and applications of Box–Behnken design and central composite design in the fields of membrane technology.
2 Box–Behnken design
The Box–Behnken design (BBD) is a widely used response surface methodology design that is particularly useful for establishing cause-and-effect relationships between factors and responses in experiments. It was developed by George E. P. Box and Donald Behnken in 1960 (Box and Behnken, 1960).
Box–Behnken designs are a class of rotatable or nearly rotatable second-order designs based on three-level incomplete factorial designs. For three factors, the graphical representation is a cube consisting of a center and the middle points of the edges, the points being located on the surface of a sphere, as shown in Fig. 1. The coded values for three factors are shown in Table 1. To form the response surface, BBD requires three levels (−1, 0, and +1) and can be used for factors between 3 and 21. The center points are marked with “0” and are used to generate quadratic model terms and to analyse the second-order interaction effect between the factors.
Box–Behnken design of three factors
| Experiment | x1 | x2 | x3 |
| 1 | −1 | −1 | 0 |
| 2 | +1 | −1 | 0 |
| 3 | −1 | +1 | 0 |
| 4 | +1 | +1 | 0 |
| 5 | −1 | 0 | −1 |
| 6 | +1 | 0 | −1 |
| 7 | −1 | 0 | +1 |
| 8 | +1 | 0 | +1 |
| 9 | 0 | −1 | −1 |
| 10 | 0 | +1 | −1 |
| 11 | 0 | −1 | +1 |
| 12 | 0 | +1 | +1 |
| 13 (C) | 0 | 0 | 0 |
| 14 (C) | 0 | 0 | 0 |
| 15 (C) | 0 | 0 | 0 |
| 16 (C) | 0 | 0 | 0 |
One of the advantages of BBD is that it does not contain combinations in which all factors are at the highest or lowest levels at the same time, so in this case it is not necessary to perform measurements in extreme situations (the vertices of the cube).
The Box–Behnken design is widely used in membrane technology. Some of the experiments are related to membrane fouling, which is the main drawback of membrane technology and which causes a decrease in system performance, mainly observed in lower permeate flux or changed membrane selectivity. The degree of fouling is highly dependent on the membrane properties, the feed solution, and the hydrodynamics of the process. Alventosa-DeLara et al. (2014), Kyllönen et al. (2005), and Peeva et al. (2012) investigated the problem of membrane fouling during ultrafiltration of dye-containing wastewater. They investigated the cleaning efficiency that can be achieved by changing the transmembrane pressure (TMP) (0.5, 1.5, and 2.5 bar), the crossflow velocity (1, 2, and 3 m s–1) and the ultrasound power level (40%, 70%, and 100%). The crossflow velocity appeared to be the most influencing factor, followed by the TMP and the ultrasound power level. The maximum estimated cleaning efficiency was 32.19%, which can be achieved with 1.1 bar TMP, 3 m s–1, and 100% ultrasound power.
During ultrafiltration (UF) of pomegranate juice, Baklouti et al. (2013) investigated the flux behavior with a resistance-in-series model, which included the resistance of the membrane, fouling, and solute concentration polarisation. A Box–Behnken experimental design with three parameters, namely transmembrane pressure, feed rate, and temperature, was used to determine the relationships between operating parameters and the efficiency of ultrafiltration and to determine the optimal conditions. The three response functions are the fouling resistance (Rf), the resistance due to concentration polarisation (Rcp), and the permeate flux. The optimal conditions were: 3 bar TMP, 0.95 L min–1 feed rate, and 30 °C temperature. Then the Rf was 18%, the Rcp is 72%, and the optimal value of the permeate flux was 19 L h–1 m–2.
Figueroa et al. (2011) analysed the performance of polysulfone ultrafiltration hollow fiber membranes in the clarification of orange press liquor. Transmembrane pressure (0.2–1.4 bar), temperature (15–35 °C), and feed flow-rate (85–245 L h−1) were varied between the given ranges. They investigated how these factors affect permeate flux, fouling index, and blocking index. The quadratic values of TMP, temperature, and feed flow rate showed significant effects on the UF membrane performance. The goal was to maximise permeate flux and minimise fouling index values. For an overall desirability of 0.76, permeate fluxes were estimated to be 23.7 kg m−2 h−1 and the fouling index as 48.0% under optimised operating variables (TMP = 1.4 bar, temperature = 15 °C, and feed flow-rate = 167.7 L h−1).
In another group of experiments, the Box–Behnken experimental design was used in membrane technology separation procedures, because their operation is simple, there is no phase change and no need to add any chemicals to achieve the expected separation. These properties have made them suitable as substitutes for other separation and treatment technologies while meeting their separation objectives (Madaeni and Samieirad, 2010; Miao et al., 2013). Ultrafiltration was used as a separation process to purify and concentrate solutions according to Xue et al. (2019). A Box–Behnken design was used to investigate the effect of ultrafiltration pH, temperature, and pressure on the extraction rate for Chinese yam polysaccharide (CYP). The optimal parameters were a temperature of 20 °C, a pH of 6.5, and a pressure of 0.03 MPa, at which time the experimental extraction ratio of CYP was 88.7%. Malaisamy et al. (2000) also used the BBD experimental design for evaluation of separation operations. Membranes containing different concentrations of polyethylene glycol were prepared to investigate vitamin B2 separation. The investigated parameters were additive concentration, feed concentration, and solvent evaporation time. The maximum vitamin B2 retention was 56.25%. The effect of process variables on the performance of Micellar Enhanced Ultrafiltration (MEUF) for the removal of nickel ions from aqueous solutions was studied by Lin et al. (2020). The process variables were pressure, nickel concentration, sodium dodecyl sulfate (SDS) concentration, and molecular weight cut-off (MWCO), and quadratic models for nickel rejection rate and flux were generated using RSM. Optimum conditions for maximum nickel removal and flux to remove 1 mM nickel ion were: pressure = 30 psi, SDS = 10.05 mM, and MWCO = 10 kDa, giving a retention rate of 98.16% and 119.20 L h–1 m–2 results in a flux.
Salehi et al. (2019) analysed the MEUF process for the removal of the drug sotalol hydrochloride from synthetic wastewater using RSM, and also investigated the effects of surfactant concentration, TMP, and pH on rejection and permeate flux. The results of the experiments showed that the retention of the sotalol hydrochloride active ingredient using an ultrafiltration membrane was a maximum of 32.41%, while this amount increased to 96.82% with the addition of the surfactant and the formation of micelles.
Aloulou et al. (2022) optimised the filtration of oily wastewater, while Sivakumar et al. (1999) used cellulose-acetate-polyurethane blend membranes for effective aqueous separation by ultrafiltration. An experimental design was used to develop an additive mathematical relationship between time and pressure. The new mixture membrane showed better results in the separation of protein (BSA) (96%).
In the food industry, the Box–Behnken experimental design was mainly used to optimise extraction and drying processes. The two most commonly used variables in extraction processes are temperature and time. Fan et al. (2008) investigated the extraction of anthocyanins from purple sweet potatoes (Ipomoea batatas (L.) Lam). In addition to temperature and time, the third parameter that was changed was the solid-liquid ratio. As a response function, the yield anthocyanin and colour coordinates were investigated. In another study, Prakash Maran and Manikandan (2012) investigated the aqueous extraction of pigments from the prickly pear (Opuntia ficus-indica) fruit. In this case, the third parameter was the weight of the fruit and the yield of betacyanin and betaxanthin was optimised. The extraction of acid-soluble collagen from grass carp (Ctenopharyngodon idella) was optimised by L. Wang et al. (2008), the third parameter was the concentration of acetic acid. Xie et al. (2012) conducted a study to examine the impact of ultrasound-assisted extraction on the antimicrobial and antioxidant properties of polysaccharides derived from Cyclocarya paliurus (Batal.) Iljinskaja.
Some applications of the Box–Behnken design in membrane technology and the food industry are summarised in Table 2.
Summary of some application of Box–Behnken design in the membrane technology and food industry
| Application | Independent variables | Response(s) studied | Reference |
| The ultrasound-enhanced cleaning of an ultrafiltration ceramic membrane. | Transmembrane pressure, cross-flow velocity, ultrasound power level | Cleaning efficiency | Alventosa et al. (2014) |
| Optimising operating conditions in ultrafiltration fouling of pomegranate juice. | Transmembrane pressure, feed flow rate, temperature | Fouling resistance, polarised layer resistance, membrane resistence, permeate limit flux | Baklouti et al. (2013) |
| Optimisation for permeate flux and fouling index. | Transmembrane pressure, temperature, feed flow rate | Permeate flux, fouling index, blocking index | Figueroa et al. (2011) |
| Optimisation of the ultrafiltration-assited extraction of Chinese yam polysaccharide. | Ultrafiltration pH, ultrafiltration temperature, ultrafiltration pressure | Extraction rate | Xue et al. (2019) |
| Performance optimisation of polysulfone ultrafiltration membranes for riboflavin separation. | Additive concentration, feed concentration, evaporation time | Vitamin B2 rate | Malaisamy et al. (2000) |
| Micellar-Enhanced Ultrafiltration to remove nickel ions. | Pressure, Ni concentration, Surfactant sodium dodecyl sulfate (SDS) concentration, molecular weight cut-off (MWCO) | Nickel rejection rates, permeate flux | Lin et al. (2020) |
| Assessment of micellar-enhanced ultrafiltration process performance for removal of pharmaceutical contaminant from wastewater. | Surfactant sodium dodecyl sulfate (SDS) concentration, pH, transmembrane pressure | Permeate flux, rejection | Salehi et al. (2019) |
| To determine the optimised ultrafiltration conditions for industrial wastewater treatment loaded with oil and heavy metals generated from an electroplating industry. | Initial oil concentration, temperature, tansmembrane pressure | Chemical oxygen demand, permeate flux | Aloulou et al. (2022) |
| Cellulose acetate-polyurethane ultrafiltration membranes for BSA separation. | Polyvinylpyrrolidone (PVP) concentration, time, rejection rate | Separation of BSA | Sivakumar et al. (1999) |
| Optimising conditions for anthocyanins extraction from purple sweet potato. | Extraction temperature, time, solid-liquid ratio, | Anthocyanins yield, colour attributes (L*, C*, H) | Fan et al. (2008) |
| Optimisation of process parameters for aqueous extraction of pigments from prickly pear (Opuntia ficus-indica) fruit. | Extraction temperature, extraction time, mass of the fruit | Total betacyanin and betaxanthin contents | Prakash Maran and Manikandan (2012) |
| Optimisation of conditions for extraction of acid-soluble collagen from grass carp (Ctenopharyngodon idella). | Acetic-acid concentration, time, temperature | Acid-soluble collagen yield | Wang et al. (2008) |
| A Cyclocarya paliurus (Batal.) Iljinskaja ultrasound-assisted extraction of polysaccharides, antimicrobial and antioxidant effects. | Ratio of liquid to solid, temperature, time | Polysaccharides yield | Xie et al. (2012) |
3 Central composite design
The central composite design (CCD) is one of the most commonly used response surface design, which was introduced by Box and Wilson in 1951 as an alternative to the full-level factorial design (Box and Wilson, 1951). It applies a second-order (quadratic) model to the response variable without using a three-level factorial experiment, therefore widely used for experimental response surface optimisation. CCD is an extended form of three-level factorial design with star points or axial points. This is used when factorial designs detect curvature in the data, so it is necessary to expand from the previous linear design to a quadratic response surface design (Singh and Beg, 2013). In this context, CCD extends the factorial design by adding center points and star points, which allows for the estimation of the curvature effect (Hanrahan et al., 2005).
The CCD consists of three parts: factorial points, axial/star points, and center points. The factorial points contain a possible combination of points at two different levels (−1, +1) and have an important role in the estimation of main effects, linear interaction effects, and quadratic effects. The center points are one of the important points of the design that are represented with level “0”, their total number is between 3 and 5. These are used to generate quadratic model terms and to analyse the quadratic interaction effect between the factors. The axial or star points are CCD features only and are represented by –α/+α. A CCD always contains twice as many star points as the number of factors in a design (Otto, 1999). The appropriate symmetry of the design is ensured by the value of “α”, which indicates the degree of rotatability. In general, the number of factors in CCD can range between 2 and 50 and requires 5 levels for each of the selected factors, which are –α, +α, −1, 0, and +1. In the case of three factors, Table 3 presents the coded values of the experimental design.
Rotatable central composite design of three factors
| Experiment | x1 | x2 | x3 |
| 1 | −1 | −1 | −1 |
| 2 | +1 | −1 | −1 |
| 3 | −1 | +1 | −1 |
| 4 | +1 | +1 | −1 |
| 5 | −1 | −1 | +1 |
| 6 | +1 | −1 | +1 |
| 7 | −1 | +1 | +1 |
| 8 | +1 | +1 | +1 |
| 9 | −α | 0 | 0 |
| 10 | +α | 0 | 0 |
| 11 | 0 | −α | 0 |
| 12 | 0 | +α | 0 |
| 13 | 0 | 0 | −α |
| 14 | 0 | 0 | +α |
| 15 (C) | 0 | 0 | 0 |
| 16 (C) | 0 | 0 | 0 |
| 17 (C) | 0 | 0 | 0 |
| 18 (C) | 0 | 0 | 0 |
3.1 Rotatability in CCD
Table 4 provides some specific values of α as a function of the number of factors that maintain the rotatability of CCDs. The α is the distance of each axial point (star point) from the center of the CCD. If α is less than one, the axial points are in the cube, if the value of α is equal to one they are on the faces of the cube, and if the value of α is greater than one they are located outside the cube (Draper and Lin, 1990).
Relationship between the number of factors and value of “α” (Beg, 2021)
| Number of factors | Factorial portion | Scaled value for α relative to ±1 |
| 2 | 22 | 22/4 = 1.414 |
| 3 | 23 | 23/4 = 1.682 |
| 2 | 24 | 24/4 = 2.000 |
| 5 | 25−1 | 24/4 = 2.000 |
| 5 | 25 | 25/4 = 2.378 |
| 6 | 26−1 | 25/4 = 2.378 |
| 6 | 26 | 26/4 = 2.828 |
3.2 Types of CCD
CCDs can be classified into two main types based on the levels and positions of the axial/star points:
Rotatable central composite design (RCCD): In this type of CCD, the axial/star points are not aligned with the plane of the factorial points. Instead, they are located at a distance (α) from the center of the design and can extend beyond the faces of the factorial cube. The main advantage of this design is its rotatability, which means that the design exhibits constant variance prediction at all points that are equidistant from the center. This property is desirable for robust and reliable analysis of the experimental data (Fig. 2a).
Face-centered central composite design (FCCD): In this type of CCD, the axial/star points are aligned with the plane of the factorial points. The axial points are located at a specific distance (α) from the center of the design and lie on the faces of the factorial cube. In this design, the axial points are at the center of each face of the factorial space; therefore the levels −1/+1 for factorial points are the same as the axial/star points and both points are on the same plane (Nekkanti et al., 2009). One advantage of FCCD is that it allows for efficient estimation of main effects and interactions, providing useful information about the linear and interaction effects of the factors. The design points are strategically placed on the faces of the factorial cube and in the center, allowing for a balanced and efficient exploration of the factor space. However, a potential weakness of FCCD is the poor accuracy in estimating pure quadratic coefficients. Since the axial/star points are aligned with the plane of the factorial points, the design may not adequately capture the curvature effects. This limitation makes FCCD less suitable for accurately estimating pure quadratic terms in the response surface model (Fig. 2b).
(a): Rotatable central composite design (RCCD), (b): Face-centered central composite design (FCCD)
Citation: Acta Alimentaria 52, 4; 10.1556/066.2023.00235
CCD is widely used in the membrane separation optimisation process to determine the ideal state of the experimental parameters. CCD is a preferable method compared to other methods like Box–Behnken design etc., because the CCD methodology gives better information within or beyond the limits of the spinning process, while the BBD method does not give information about the spinning process limitations and cannot be built in two steps from the 2k design (Shakir et al., 2015).
Landaburu-Aguirre et al. (2010) used face centered central composite design to understand the concentration polarisation phenomenon and the effect of factors on heavy metal retention and permeate flux. Additionally, the recovery of the anionic surfactant sodium dodecyl sulfate was studied. The investigated factors where the following: pressure (P), nominal molecular weight limit (NMWL), heavy metal feed concentration (CZn, CCd), and SDS feed concentration (CSDS).
The rotatable central composite design was used in the works described below.
Krishnan et al. (2020) minimised the production cost of xylitol by optimising the xylose reductase (XR) enzyme purification process. Ultrafiltration was used for their experiments, as membrane-based processes play a critical role in the separation/purification of biotechnological products (Sharma and Bracewell, 2019). Operating conditions such as transmembrane pressure (TMP) and cross-flow velocity (CFV) affect the cleaning performance and the fouling phenomenon (Dereli et al., 2019). In addition to transmembrane pressure and cross-flow velocity, the third process variable was filtration time. Membrane permeability and xylitol content were investigated as response variables.
Sadeghian et al. (2015) investigated the ultrafiltration ability of the hollow fiber polyvinylidene fluoride membrane in an oil-in-water emulsion pretreated with polyaluminum chloride. A central composite design and a response surface method were used to optimise the operating variables: transmembrane pressure and velocity. The three response functions were permeate flux (PF), turbidity removal, and chemical oxygen demand (COD).
Candéa et al. (2015) studied the effect of process variables on the production of flaxseed oil emulsions by cross-flow membrane emulsification. The effects of transmembrane pressure, crossflow velocity, and surfactant concentration on dispersed phase flux, emulsion stability, and droplet size distribution and uniformity were evaluated.
C. Wang et al. (2016) used central composite design and the response surface method to predict and optimise a polyvinylidene fluoride (PVDF) membrane cleaning process. Four independent variables were taken into account (sodium hydroxide (NaOH) concentration, sodium hypochlorite (NaClO) concentration, citric acid concentration, and the duration of cleaning), and the cleaning efficiency was investigated as a response. Park et al. (2018) used CCD to predict the cleaning efficiency of a reverse osmosis (RO) membrane with organic-fouling, where the variables were the concentration of cleaning solution, the cleaning time, the flow rate, and the temperature.
MEUF was used by Vani et al. (2023) to remove fluoride using polyethersulfone (PES) based ultrafiltration membranes and a cationic surfactant (cetylpyridinium chloride-CPC) and by Xiarchos et al. (2008) to optimise the extraction of copper from aqueous solutions. Cojocaru and Zakrzewska-Trznadel (2007) also deals with the removal of copper ions from aqueous solutions. The work presents the application of RSM for the optimisation of dead-end and cross-flow polymer-assisted ultrafiltration (PAUF) using a polyacrylic acid (PAA) chelating agent. MEUF was used by Abhari et al. (2022) to remove Pb2+ ions from aqueous solution. The process was used to simultaneously maximise the retention of Pb2+ and the flux of permeates. SDS and sodium lauroyl sarcosine (Sarkosyl) were used as anionic surfactants.
In the food industry, the rotating center experimental design was used for optimise stabiliser and swelling time of oat in the production of oat milk (Akal et al., 2023). It was used for colour extraction by Yolmeh et al. (2014), who extracted pigments from annatto seeds using ultrasound, and Sinha et al. (2012), who extracted dye from the petals of the Flame of forest (Butea monosperma) flower. It was used for the extraction of phenolic substances by Gan and Latiff (2011) and Gong et al. (2012).
Kumar et al. (2014) used a rotatable central experimental design for drying processes, and optimised the hot air drying conditions of the okra with the help of a microwave oven. Han et al. (2010) optimised the process parameters of microwave vacuum drying for apple slices.
Some applications of the Central composite design in membrane technology and the food industry are summarised in Table 5.
Summary of some application of Central composite design in the membrane technology and food industry
| Application | Independent variables | Response (s) studied | Reference |
| Optimisation of cadmium and zinc removal from water samples by micellar-enhanced ultrafiltration. | Pressure, nominal molecular weight limit (NMWL), heavy metal feed concentration, sodium dodecyl sulfate (SDS) concentration | Permeate flux, heavy metal retention | Landaburu-Aguirre et al. (2010) |
| Optimisation of operating parameters for xylose reductase separation through ultrafiltration membrane. | Filtration time, transmembrane pressure, cross flow velocity | Membrane permeability, amount of xylitol | Krishnan et al. (2020) |
| The capability of ultrafiltration hollow fibre polyvinylidene fluoride membrane by polyaluminum chloride in pretreated oil-in-water emulsion. | Transmembrane pressure, velocity | Permeate flux, turbidity removal, chemical oxygen demand removal | Sadeghian et al. (2015) |
| The effect of process variables on the production of flaxseed oil emulsions by cross-flow membrane emulsification. | Transmembrane pressure, cross flow velocity, emulsifier concentration | Dispersed phase flux, droplet size, droplets' size uniformity (Span) | Candéa et al. (2015) |
| Prediction and optimisation of the chemical cleaning process of polyvinylidene fluoride (PVDF) ultrafiltration membranes. | Sodium hydroxide concentration, sodium hypochlorite concentration, citric acid concentration, cleaning duration | Cleaning efficiency | Wang et al. (2016) |
| Optimisation of chemical cleaning for reverse osmosis membranes. | Concentration of EDTA, cleaning time, temperature, flow rate | Flux recovery | Park et al. (2018) |
| Removal of fluoride by micellar enhanced ultrafiltration. | Surfactant concentration, pressure drop, time | Fluoride concentration | Vani et al. (2023) |
| Copper removal from aqueous solutions using micellar-enhanced ultrafiltration. | pH, surfactant concentration, surfactant/metal molar ratio | Copper rejection | Xiarchos et al. (2008) |
| Copper removal from aqua solutions using polymer assisted ultrafiltration. | Feed concentration of polyacrylic acid, ratio of polymer to copper, pH | Copper rejection | Cojocaru and Zakrzewska-Trznadel (2007) |
| Effect of various types of anions and anionic surfactants on the performance of micellar-enhanced ultrafiltration process in the removal of Pb(II) ions. | Lead concentration, NaCl concentration, lead salt, anionic surfactant | Lead removal | Abhari et al. (2022) |
| Optimisation of stabiliser usage conditions in oat milk production. | Stabiliser concentration, swelling time | Colour parameters (L*, a*, b*, ΔE), Rheological properties (yield stess, consistency index, fluid type) | Akal et al. (2023) |
| Optimisation of ultrasound-assisted extraction of natural pigment from annatto seeds. | Temperature, extraction time, duty cyde, seed to solvent ratio | Extraction yield, absorbance value | Yolmeh et al. (2014) |
| Extraction of natural dye from petals of Flame of forest (Butea monosperma) flower. | Time, temperature, mass of petals | Total amount of dye | Sinha et al. (2012) |
| Optimisation of the solvent extraction of bioactive compounds from Parkia speciosa pod. | Buffer to solid ratio, temperature, time | Total polyphenolic content, total flavonoid content, DPPH content, ABTS content, Ferric reducing/antioxidant power content | Gan and Latiff (2011) |
| Optimisation of extraction parameters of bioactive components from defatted marigold (Tagetes erecta L.) residue. | Ethanol concentration, temperature, time | Total polyphenolic content, total flavonoid content, DPPH content, ABTS content | Gong et al. (2012) |
| Optimisation of microwave-assisted hot air drying conditions of okra. | Air velocity, air temperature, microwave power | Colour change, hardness, rehydration ratio, specific energy | Kumar et al. (2014) |
| Optimisation of process parameters for microwave vacuum drying of apple slices. | Microwave power, vacuum level, initial moisture content | Drying time, sensor quality, porosity | Han et al. (2010) |
4 Conclusions
In general, ultrafiltration examinations are performed with one variable method at a time, where the effect of each factor is examined separately. However, this approach results in a large number of experiments and can often ignore interaction effects. Furthermore, process optimisation is inefficient, as it is difficult to find the true optimum in a reasonable amount of experiments. The use of statistical methods such as the response surface methodology overcomes the limitations of the univariate simultaneous approach. RSM is an effective statistical tool that is also used in the field of membrane technology to model and optimise many process variables.
Acknowledgement
This study was financed by the Hungarian National Research, Development and Innovation Office, project NKFI-FK-142414. S. Kertész is grateful for the financial support of the János Bolyai Research Scholarship of the Hungarian Academy of Sciences (BO/00576/20/4).
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