Modelling of Batch Lactic Acid Fermentation in the Presence of Anionic Clay

The key process in biotechnology used to obtain fermented (cultured) dairy products is lactic acid fermentation, a microaerophilic process consisting mainly in converting lactose to lactic acid (LA) in the presence of lactic acid bacteria (LAB), e.g. from genera Lactobacillus, Streptococcus, Lactococcus or Leuconostoc. Based on their optimal growth temperature, these LAB can be either thermophilic (Lactobacillus and Streptococcus), characterized by an optimum temperature of around 42 °C, or mesophilic (Lactococcus and Leuconostoc), having an optimum temperature of around 26 °C (1,2).


Introduction
The key process in biotechnology used to obtain fermented (cultured) dairy products is lactic acid fermentation, a microaerophilic process consisting mainly in converting lactose to lactic acid (LA) in the presence of lactic acid bacteria (LAB), e.g. from genera Lactobacillus, Streptococcus, Lactococcus or Leuconostoc.Based on their optimal growth temperature, these LAB can be either thermophilic (Lactobacillus and Streptococcus), characterized by an optimum temperature of around 42 °C, or mesophilic (Lactococcus and Leuconostoc), having an optimum temperature of around 26 °C (1,2).
Many studies confi rm that the cell growth is inhibited by the accumulation of LA in the fermentation broth (3)(4)(5)(6)(7).
In order to avoid this inhibitory eff ect of the produced LA, various methods of LA removal from the broth during fermentation have been investigated, e.g.solvent extraction (8)(9)(10), electrodialysis (11)(12)(13), adsorption onto activated carbon (14) or molecular sieves (3), and retention onto anion exchange resins (4,6,7,(15)(16)(17)(18), each with its own limitations.The toxicity of organic solvents for the cells is an important disadvantage of solvent extraction.Electrodialysis implies high capital costs for large scale operation and it is not economically feasible.Generally, adsorption and ion exchange processes require a subsequent removal of the adsorbent or ion exchange particles from the system.Additional chemicals (salt solutions) are necessary to recover the LA from ion exchangers (3).
In situ LA removal from a characteristic fermentation medium (yoghurt) preparation by its retention onto hydrotalcite-type anionic clay has been studied in this paper.Yoghurt is commonly produced by the fermentation of full or skimmed milk in the presence of specifi c LAB in the following stages: (i) milk standardization, (ii) milk homogenization, (iii) heat treatment of standardized and homogenized milk, (iv) cooling to fermentation (incubation) temperature, (v) inoculation with starter culture, (vi) fermentation (incubation) and (vii) cooling (1,2,19).
Standardization stage involves an adjustment of milk total solid (fat, proteins, lactose and mineral ma er) content, whereas milk homogenization consists of fat globule disruption into smaller ones (1,(19)(20)(21).Conventional heat treatment of standardized and homogenized milk can be conducted at 80-85 °C for 30 min or at 90-95 °C for 5-10 min (1,2,19).The heat treatment mainly aims at destroying the unwanted microorganisms as well as at reducing the concentration of dissolved oxygen in order to assist the starter culture growth (2,19).A er its thermal processing, the milk is cooled to fermentation (incubation) temperature and is further inoculated with an individual or a mixed LAB starter culture.In the fermentation stage, the milk lactose is partially converted to LA (by means of LAB), resulting in a decrease in the pH and an aggregation of milk proteins forming a cross-linked gel network which has pores containing aqueous phase (whey) (19).When the yoghurt a ains the desired pH level, i.e. 4.1-4.7, it is quickly cooled, usually to 5-10 °C, and further stored at 2-5 °C in order to diminish the culture metabolic activity, otherwise some defects may occur, e.g.high acidity or distinct acetaldehyde fl avour (1,2,19).
A good quality yoghurt should have high viscosity and strength (fi rmness), characteristic fl avour, creamy texture, low whey separation (syneresis), and recommended values of pH and viable LAB.Rheological (viscosity and gel strength), sensory (fl avour, creaminess and whey separation) and microbial (viable LAB content) properties of yoghurt are infl uenced by the characteristics of starter culture (type and inoculation rate) and milk (composition, homogenization and heat treatment conditions) as well as by fermentation conditions (temperature and fi nal pH value).
Typically, a mixed starter culture of Streptococcus thermophilus (S. thermophilus) and Lactobacillus delbruekii ssp.bulgaricus (L.bulgaricus) is used in yoghurt production (1,2,(19)(20)(21)(22)(23)(24).A ratio of bacterial species of 1:1 and inoculation rates of 0.5-4 % (by mass) are recommended in order to obtain an optimal cell growth and good yoghurt properties (1,22,24).Due to a symbiotic relationship between bacterial species in the mixed culture, a higher growth rate and faster LA production in comparison with those of the individual cultures have been reported (1,2).Both species are thermophilic (S. thermophilus bacterium exhibits an optimal growth at 39 °C, L. bulgaricus at 45 °C, and mixed culture at 42-43 °C) and can convert homofermentatively the lactose into LA as a main product (1).Besides LA, the LAB yield low amounts of acetaldehyde, diacetyl, acetone, acetic acid, formic acid and other compounds contributing to characteristic yoghurt fl avour (1,(20)(21)(22)(23).From a physiological point of view, the fermentation process consists of two stages.In the fi rst stage, L. bulgaricus stimu-lates the growth of S. thermophilus, releasing short peptides and essential amino acids from casein, whereas in the second stage, S. thermophilus produces formic acid and carbon dioxide, which enhance the growth of L. bulgaricus (1,2,24).These LAB should be viable and abundant (the International Dairy Federation recommends a concentration of at least 10 7 colony-forming units (CFU) per g) in the fermented product in order to have benefi cial eff ects on digestive and immune system of consumers (2,21,23).
Milk processing has important eff ects on the yoghurt properties.Accordingly, an increase in gel viscosity and strength was observed at larger values of milk total solid content as well as a grainy texture and signifi cant syneresis at a high milk mineral ma er content (1,20).During conventional heat treatment of milk, an increase in gel viscosity and strength, a decrease in whey separation and faster gelation were reported at higher temperatures, i.e. 90-95 °C (1,2,19).
The incubation temperature, usually ranging from 38 to 48 °C, infl uences the cell growth, fermentation time and gel microstructure.Lower incubation temperatures (38-40 °C) lead to a lower cell growth rate, longer fermentation time and highly cross-linked protein network with small pores, yielding an increase in gel viscosity, strength and creaminess (smoothness) along with a decrease in whey separation (1,19).Final pH values between 4.1 and 4.7 are recommended in order to achieve appropriate cell growth and a good gel quality (1,2,(19)(20)(21)(22).A higher value of the fi nal pH (4.6-4.7),implying a shorter fermentation time, conduces to a less fi rm and viscous gel having a higher concentration of viable LAB and a more pronounced whey separation in comparison with a lower pH value (4.1-4.2) (1).A maximum number of viable cells at pH values ranging between 5.0 and 5.5 as well as a signifi cant decrease in their number at pH from 5.0-5.5 to 4.1-4.7 were reported (1,14).An addition of hydrotalcite-type anionic clay to the fermentation broth at pH=5.0-5.5, in order to retain some LA produced by lactose conversion, followed by a lactic acid fermentation stopping at pH=4.6-4.7 could promote the bacterial growth by reducing the LA concentration.This could result in an increase in gel strength, viscosity, creaminess and viable LAB number as well as in a decrease in whey separation.It was reported that a direct contact of an anion exchange resin with characteristic LAB of yoghurt preparation did not aff ect the cell activity (17).
The anionic clays consist of positively charged sheets of mixed metal hydroxides between which exchangeable anions and water molecules are located.Having diff raction pa erns very similar or identical to that of hydrotalcite, i.e.Mg 6 Al 2 (CO 3 )(OH) 16 •4H 2 O, they have also been referred to as hydrotalcites, hydrotalcite-like compounds or hydrotalcite-type anionic clays (25)(26)(27).Unlike the anion exchange resins, the anionic clays are less expensive and can be easily prepared in laboratory.Moreover, hydrotalcites are ingestible and widely used as antacid, antipepsin and gastric mucosa protection agents in the pharmaceutical industry (26,(28)(29)(30)(31)(32).Accordingly, due to their benefi cial health eff ects, they can be added to the fermented dairy product.
The retention of LA on porous anionic clay is strongly infl uenced by the contact conditions between the fermen-tation medium and clay particles.Ultrasonication is commonly applied as an effi cient technique to intensify the mass transfer in solid-liquid adsorption processes.Ultrasound cavitation can produce a turbulence in the liquid phase, leading to a decrease in the boundary layer (static liquid fi lm surrounding the adsorbent particle) thickness and an increase in the mass transfer rate (33,34).This paper focuses on modelling of batch fermentation of skimmed milk inoculated with LAB as well as on selection of favourable operation parameters to obtain a high yoghurt quality along with low energy and material expenses.Lactic acid fermentation was conducted in the presence of hydrotalcite-type anionic clay, with and without ultrasound fi eld, at diff erent operation temperatures and clay/milk ratios.

Preparation and characterization of hydrotalcite-type anionic clay
For the synthesis of hydrotalcite-type anionic clay, coprecipitation method at low supersaturation and constant pH was selected, being the most frequently used method to prepare the anionic clays (25)(26)(27)(35)(36)(37)(38)(39).Solution A, consisting of 1 mol of Mg(NO 3 ) 2 •6H 2 O and 0.2 mol of Al(NO 3 ) 3 •9H 2 O dissolved in 700 mL of distilled water, and solution B, containing 3.5 mol of NaOH and 0.943 mol of Na 2 CO 3 in 1 L of distilled water, were prepared at 35 °C.All reagents were purchased from Sigma-Aldrich (Munich, Germany) and were used without further purifi cation.The solutions were mixed by dropwise addition of solution A to solution B under vigorous stirring, with the pH kept at about 10.A er precipitation completion, the slurry was aged at 65 °C for 18 h under continuous stirring.The precipitate was fi ltered, washed with distilled water to remove NaNO 3 and further dried at 100 °C for 18 h.Hydrotalcite-like compound synthesis was confi rmed by X-ray diff raction (XRD) analysis conducted on a Siemens D5000 X-ray Diff ractometer (Siemens, Munich, Germany) using Cu Kα radiation (λ=1.5406Å).Specifi c surface area, pore size distribution and mean pore diameter of hydrotalcite-type anionic clay were evaluated based on nitrogen adsorption/desorption isotherms at 77 K obtained by means of a Coulter SA 3100 surface area and pore size analyzer (Beckman Coulter, Krefeld, Germany) (36).

Yoghurt starter culture preparation
In order to prepare a yoghurt starter culture, low-fat (1.5 %) homogenized and high-temperature (85 °C) pasteurized milk was heated at 42 °C and inoculated with a lyophilized mixed starter culture (Chr.Hansen FD-DVS YC-X11 Yo-Flex, Chr.Hansen, Hørsholm, Denmark), containing the species S. thermophilus and L. bulgaricus.Inoculation was carried out according to the producer's recommendations.Lactic acid fermentation was performed at 42 °C until the pH value dropped to 4.6-4.7, the yoghurt was further cooled to 10 °C, and then stored at (4±1) °C.

Fermentation medium preparation
Low-fat (1.5 %) homogenized and high-temperature (85 °C) pasteurized milk, which was heated to the operation temperature and further inoculated with the yoghurt starter culture, was used as a fermentation medium.A milk volume of 0.40 L was vigorously mixed with 0.06 L of yoghurt and the mixture was poured into four heat-resistant glass beakers, each containing 0.1 L of milk and 0.015 L of yoghurt.The beakers were covered and then put into the experimental fermentation set-up.

Experimental set-up
The experimental set-up used to study the batch lactic acid fermentation consisted of a stainless steel ultrasonic bath (Retsch UR1, Haan, Germany), operated at an ultrasound frequency of 35 kHz, and a Thermo Haake B12 temperature-controlled circulating water bath (Thermo Electron, Karlsruhe, Germany), as shown in Fig. 1.The baths were coupled, ball valve was opened, circulating water bath was fi lled with water to a standard level, operational parameters (temperature and circulating pump fl ow rate) were set, circulating pump and heating were started.When the operation temperature value was obtained, four covered beakers containing the fermentation medium were put in a stainless steel basket and placed into the ultrasonic bath (1).Water continually circulated through the baths in order to maintain a constant temperature (±0.1 °C) during fermentation and water level in the ultrasonic bath was controlled by the ball valve.The pH values of the fermentation medium were measured by an InoLab pH Level 2 digital pH-meter (WTW, Weilheim in Oberbayern, Germany) with an accuracy of ±0.005 pH units.At a pH value of 5.0-5.1, when the LAB growth was considered optimal, various masses of anionic clay, namely 0.1, 0.5 and 0.75 g, were added to the fermentation medium in three beakers, under vigorous stirring conditions, i.e. 100 rpm for about 3 min using a Heidolph RZR 1 mechanical stirrer (Heidolph Instruments, Schwabach, Germany), obtaining a homogeneous and stable suspension.LA retention onto anionic clay was obtained with or without ultrasound fi eld (ultrasonic or static runs, respectively).Lactic acid fermentation was stopped at pH=4.6-4.7, the yoghurt was cooled to 10 °C, stored at (4±1) °C for 3 days and further analyzed.
The pH value of the fermentation medium was continuously recorded as a function of fermentation time, τ.Because the ratio between the concentration of LA and the total concentration of the other acids in the characteristic fermentation broth of yoghurt preparation is usually more than 9 (1), it was assumed that the contribution of the other acids to the titratable acidity as well as their retention onto the clay particles were negligible.The values of LA concentration in the liquid phase, γ LA , were estimated by a linear interpolation of γ LA,exp =f(pH) experimental data, where the values of γ LA,exp were determined by titration with 0.1 M NaOH in the presence of phenolphthalein indicator (36).

Physical and microbiological analyses of yoghurt
Yoghurt mass, viscosity, syneresis and viable LAB concentration were measured a er 3 days of storage at (4±1) °C.Rheological tests were conducted using a Rheotest 2 rotary viscosimeter (MLW, Munich, Germany) equipped with coaxial cylinders.Yoghurt viscosity was determined at (4±0.1) °C for a shear rate ranging from 0.5 to 437 s -1 .Syneresis was estimated by transferring a yoghurt sample to a funnel covered with Whatman fi lter paper (Sigma-Aldrich).The funnel was placed on a conical fl ask and stored at (4±1) °C for 3 h.A erwards the mass of the separated whey was weighed and syneresis index, S (%), was calculated as whey mass (g) per 100 g of sample.
Viable LAB concentration was evaluated by enumeration on appropriate agar media in Petri dishes using standard procedures (1,(40)(41)(42).Accordingly, S. thermophilus was enumerated on M17 agar (Difco Laboratories, Detroit, MI, USA) a er aerobic incubation at 37 °C for 24 h and L. bulgaricus on MRS (De Man-Rogosa-Sharpe) agar with pH value adjusted to 5.2 (Difco Laboratories) a er anaerobic incubation at 45 °C for 72 h.

Characterization of hydrotalcite-type anionic clay
Anionic clay particles with a mean diameter of 0.006 cm and a density of 0.97 g/cm 3 were obtained by coprecipitation.A particle specifi c surface area of 3.6•10 5 cm 2 /g, a predominantly mesoporous structure of clay particle and a mean pore diameter of 12.5 nm were estimated based on nitrogen adsorption/desorption isotherms at 77 K.

Lactic acid fermentation
Characteristic experimental data of LA concentration in the liquid phase obtained under static and ultrasonic conditions, at various process temperatures and clay/milk ratios are depicted in Figs. 2 and 3.All experiments were triplicated and values of relative standard dispersions less than 5 % were obtained, indicating a good reproducibility.Final values of fermentation time, which are listed in Table 1 and shown in Fig. 4, decreased with the increase of operation temperature and the decrease of clay/milk ratio, and were higher in the presence of ultrasound fi eld.

Lactic acid fermentation in the absence of anionic clay
A linear variation of LA concentration in the liquid phase, γ LA , with fermentation time, τ, can be observed in the blank runs (R 0 =0 g/L); consequently the LA generation rate, v g , can be considered constant in time.Data present-ed in Fig. 5 show this linear dependency as well as the values of v g , estimated as line slope, for static and ultrasonic blank runs conducted at t 2 =43 °C, i.e. 0.0172 and   0.0159 g/(L•min).Values of v g , which are listed in Table 1 and shown in Fig. 6, slightly increased with the increase of operation temperature and were lower in the presence of ultrasound fi eld.A decrease in LA generation rate in ultrasonic runs can be a consequence of cell disruption caused by cavitation (33).

Lactic acid fermentation in the presence of anionic clay
Experimental results of batch lactic acid fermentation dynamics obtained under various operation conditions in the presence of anionic clay (Figs. 2 and 3) highlight that the LA concentration in the liquid phase, γ LA , has a linear variation in time from initial pH=6.0-6.1 (γ LA,0 =2.272-2.430g/L) to pH=5.0-5.1 (γ LA =4.745-4.993g/L), when the anionic clay is added and, in ultrasonic runs, when the ultrasonic bath is started.A er the clay addition, γ LA decreases with fermentation time until the clay reaches the saturation state, when LA concentration in the liquid phase obtains a minimum value, γ LA,min .The γ LA decreases more sharply and γ LA,min values are lower at higher values of clay/milk ratio.Moreover, γ LA,min values, which are listed in Table 1 and shown in Fig. 7, are lower in ultrasonic runs.A er the clay saturation, γ LA increases with fermentation time until pH=4.6-4.7 (γ LA =5.801-5.935g/L), when the fermentation process is stopped.
Considering that a maximum cell number was obtained at pH=5.0-5.5 (γ LA =3.753-4.993g/L), this period of maximum cell growth, estimated using Eq. 1, lasted about 70-80 min at R 0 =0 g/L, 80-100 min at R 1 =1 g/L, 110-130 min at R 2 =5 g/L and 120-150 min at R 3 =7.5 g/L, as shown in Table 1.Moreover, tabulated data emphasize that Δτ max values are slightly higher in ultrasonic runs performed in the presence of anionic clay than in static runs.Accordingly, the viable LAB number could be larger in the yoghurt containing anionic clay which was prepared under ultrasonic operation conditions.

Modelling of lactic acid fermentation accompanied by LA retention onto anionic clay
To describe the retention process of species from the liquid phase onto the adsorbent or ion exchange particles, simple or complex models can be selected, depending on the simplifying assumptions, equations and restrictions considered (3,4,6,7,18).
The model adopted to predict the species (LA) retention onto hydrotalcite-type anionic clay particles in batch operation is based on the following simplifying assumptions: (i) anionic clay particles have a predominately mesoporous structure, spherical shape, same size (r P =0.003 cm) and are surrounded by a static liquid fi lm (boundary layer), (ii) mesopore mean diameter (12.5 nm) is much larger than LA molecule size (0.62 nm), (iii) pore diff usion resistance is negligible (fi ne adsorbent particles with large pores), (iv) species mass transfer in the fi lm occurs by ordinary molecular diff usion in a planar medium (δ»r P ) and a quasi-stationary state, (v) the species concentrations at the particle-liquid fi lm interface are estimated by an interphase equilibrium relationship, (vi) the external solution is perfectly mixed, and (vii) the system operates under isothermal conditions.
The mean diameter of LA molecule, d LA , was estimated applying Eq. 2, where M LA is LA molecular mass (M LA =90 g/mol), ρ LA is LA density (ρ LA =1209 g/L) and N A is Avogadro's number (N A =6.023•10 23 mol -1 ).
Characteristic equations and restrictions of the retention process of molecular species (LA) from the liquid phase onto anionic clay particles consist of conservation equation in the liquid phase (Eq.3), conservation in the solid phase (Eq.4), diff usion in the liquid fi lm (Eq.5), equilibrium relationship at the particle-liquid fi lm interface (Eq.6), initial conditions (Eq.7) and boundary conditions (Eq. 8).
Combining Eqs.3-6, respectively, the following independent equation system was obtained: Characteristic parameters of model equations and restrictions are as follows: species concentration in the liquid phase, γ LA (g/cm 3 ); species concentration at the particle-liquid fi lm interface γ i LA (g/cm 3 ); minimum species concentration in the liquid phase in the presence of anionic clay, γ LA,min (g/cm 3 ); species diff usion coeffi cient in the liquid fi lm, D LA (cm 2 /s); species mass fl ux, J LA (g/ (cm 2 •s)); species mass transfer coeffi cient in the liquid fi lm, k LA (cm/s); species distribution coeffi cient, K d,LA (g/cm 3 ); solid mass, m S (g); particle number, n P ; radial distance, r d (cm); clay particle radius, r P =0.003 cm; species concentration in the solid phase, s LA (g/g); equilibrium (saturation) species concentration in the solid phase, s LA,eq (g/g); species generation rate, v g (g/(cm 3 •s)); solution volume, V (cm 3 ); solid volume, V S (cm 3 ); liquid fi lm thickness, δ (cm); particle density, ρ P =0.97 g/cm 3 ; fermentation time, τ (s).
The equation and restriction system in Eqs.7-10 was solved by the fourth order Runge-Ku a method.The species generation rate, v g , was estimated based on the experimental data obtained in the blank runs and the distribution coeffi cient was determined in a previous work, i.e.K d,LA =0.06 g/cm 3 (38).The species mass transfer coeffi cient in the liquid fi lm, k LA , was calculated from the experimental data by the least squares method, by minimizing the objective function: Based on Eqs. 9 and 10 and considering that the anionic clay is added to the fermentation medium at pH=5.0-5.1 (γ LA,add =4.745-4.993g/L), as well as that the fermentation process is stopped at pH=4.6-4.7 (γ LA,stop =5.801-5.935g/L), the equation system describing the batch fermentation kinetics in the presence of anionic clay can be wri en as: ( ) Characteristic curves of batch lactic fermentation dynamics, γ LA (τ), predicted by the equation system in Eq. 12 are shown in Figs. 2 and 3. A good agreement between experimental and simulated data was observed (root mean squared errors were less than 0.07).
The infl uence of experimental variables on the equilibrium (saturation) species concentration in the solid phase, s LA,eq, and the species mass transfer coeffi cient in the liquid fi lm, k LA , is summarized in Table 1 ultrasonic runs, they increase with the increase of operation temperature and decrease with the increase of clay/ milk ratio.Moreover, values obtained for s LA,eq (0.171-0.383 g/g) and for k LA (0.0018 to 0.0077 cm/min) are in agreement with data reported in the literature referring to batch lactic acid fermentation in the presence of anion exchangers, e.g.0.342-0.417g/g and 0.0073 cm/min, respectively (6,7,18).

Yoghurt characterization
Hourly production, P (g/h), expressed as a ratio between the yoghurt mass and fi nal fermentation time; dynamic viscosity, η (Pa•s); syneresis index, S (%); and viable LAB number, N (CFU/g) of the yoghurt produced by lactic acid fermentation are shown in Figs.10-13.Depicted data, which are consistent with values reported in other studies (1,(40)(41)(42)(43), reveal a low viscosity and a signifi cant syneresis of the product yielded at the highest temperature (t 3 =48 °C), as well as a low production and a pronounced syneresis of the yoghurt obtained at the highest clay/milk ratio (R 3 =7.5 g/L).Moreover, a grainy structure of the yoghurt samples was observed at the highest levels of t and R. Taking into account these aspects along with the heating and clay expenses, it can be concluded that the fermentation at the highest temperature and clay/milk ratio is unfavourable.In order to achieve a high yoghurt LAB concentration, the fermentation in the presence of anionic clay is more advantageous, as shown in Fig. 13.Consequently, from the experiments conducted under various operation conditions and summarized in Table 1 (runs 1-24), only eight runs are favourable for obtaining a high yoghurt quality at low cost, namely those characterized by the following values of operational variables: ν=0 and 35 kHz, t=38 and 43 °C and R=1 and 5 g/L (runs 2, 3, 6, 7, 14, 15, 18 and 19).The best yoghurt quality, characterized by maximum values of dynamic viscosity (η=0.155Pa•s) and viable LAB concentration (N=1.58•10 7CFU/g), minimum syneresis index (S=22.37%) and a creamy coagulum, was obtained at ν 2 =35 kHz, t 2 =43 °C and R 2 =5 g/L.

Statistical analysis of the data
Final fermentation time, τ f ; minimum species concentration in the liquid phase in the presence of anionic clay, γ LA,min ; equilibrium (saturation) species concentration in the solid phase, s LA,eq ; species mass transfer coeffi cient in the liquid fi lm, k LA ; hourly yoghurt production, P; and yoghurt properties, i.e. dynamic viscosity, η; syneresis index, S; and viable LAB number, N, were selected as process--dependent variables (responses).These variables can be linked to the process-independent variables (factors), namely ultrasound frequency, ν; operation temperature, t; and clay/milk ratio, R, with adequate regression equations.Factor and response values for an experimental set consisting of favourable runs to obtain a high yoghurt quality at low cost (runs 2, 3, 6, 7, 14, 15, 18 and 19 in Table 1) are given in Table 2. Values of dimensionless factors were calculated depending on those of natural factors with the following equations:  /24/ According to Eqs. 17 and 18, fi nal values of fermentation time, τ f , are lower and minimum lactic acid concentration in the liquid phase, γ LA,min , is higher in static operation mode (inferior level of ultrasound frequency, x 1 ) at higher temperature, x 2 , and lower clay/milk ratio, x 3 .The values of τ f and γ LA,min depend on individual factors as well as on their double and triple interactions.Eqs.19 and 20 emphasize that equilibrium (saturation) species concentration in the solid phase, s LA,eq , and species mass transfer coeffi cient in the liquid fi lm, k LA , are higher in ultrasound operation mode (higher level of x 1 ), higher level of x 2 and lower level of x 3 .The values of s LA,eq and k LA depend signifi cantly on x 1 and x 3 factors as well as on the interaction of these factors, x 1 x 3 .Yoghurt production, P, is be er at lower levels of x 1 and x 3 , at higher level of x 2 , and it is infl uenced by all process factors and their interactions (Eq.21).Yoghurt viscosity, η, and viable LAB number, N, are higher and syneresis index, S, is lower at higher levels of all process factors (Eqs.[22][23][24].The η and N depend only on individual factors, whereas S is infl uenced by individual factors and their interactions.

Conclusions
Characteristic lactic acid fermentation kinetics of yoghurt production was studied in the presence of hydrotalcite-type anionic clay particles under static and ultrasonic operation conditions.The anionic clay particles retained the LA produced in the fermentation medium and reduced its inhibitory eff ect on the LAB growth, whereas the ultrasonic fi eld intensifi ed the LA retention process by decreasing the boundary layer thickness and increasing the mass transfer rate.
A hydrotalcite-type anionic clay was synthesized by coprecipitation and further characterized by adsorption/ desorption isotherms at 77 K in order to determine its specifi c surface area (3.6•10 5 cm 2 /g), pore size distribution (predominantly mesoporous structure) and mean pore diameter (12.5 nm).Lactic acid fermentation experiments were performed using as fermentation medium low-fat (1.5 %) pasteurized milk inoculated with a yoghurt starter culture.The anionic clay was added to the fermentation medium at pH=5.0-5.1, when the LAB growth was considered optimal, and LA retention onto anionic clay particles was obtained with and without ultrasound fi eld.The experimental study was conducted under static and ultrasonic conditions (at ν=0 and 35 kHz), at three operation temperatures (t=38, 43 and 48 °C) and four clay/milk ratios (R=0, 1, 5 and 7.5 g/L).Twenty four experimental curves describing the variation of LA concentration in the liquid phase, γ LA , with fermentation time, τ, were obtained.It was concluded that the fi nal fermentation time, τ f , was lower in static runs and decreased with the increase of t and the decrease of R. A physical and microbiological analyses of the fermented product highlighted that only eight experimental runs (ν=0 and 35 kHz, t=38 and 43 °C and R=1 and 5 g/L) were favourable for preparation of a high quality yoghurt at low cost.The best yoghurt quality, characterized by maximum viscosity and viable LAB number, minimum syneresis index and creamy coagulum, was obtained at ν=35 kHz, t=43 °C and R=5 g/L.Due to a high content of viable LAB and to the presence of clay with antacid properties, this product can have signifi cant health benefi ts.
A mathematical model, assuming a perfect mixing of fermentation medium and mass transfer resistance concentrated in a static liquid fi lm around the anionic clay particle, was selected to describe the lactic acid fermentation accompanied by LA retention onto clay particles.By solving the model equations depending on experimental data, i.e. γ LA =γ LA (ν, t, R, τ), the equilibrium (saturation) LA concentration in the solid phase, s LA,eq , and the LA mass transfer coeffi cient in the liquid fi lm, k LA , were estimated under various operation conditions.Values obtained for s LA,eq (0.171-0.383 g/g) and k LA (0.0018-0.0077 cm/min), in a good agreement with data reported in the related literature, were higher in ultrasonic runs, with higher values of t and lower values of R.
A statistical analysis of the data based on a 2 3 factorial experiment was performed for the runs selected as favourable.Regression equations linking the process responses to their factors were established and commented.

Table 1 .
Infl uence of experimental variables on fermentation process kinetics R=m(clay)/V(milk); τ f =fi nal fermentation time; Δτ max =period of maximum cell growth; v g =lactic acid (LA) generation rate; γ LA,min =minimum LA concentration in the liquid phase in the presence of anionic clay; s LA,eq =equilibrium LA concentration in the solid phase; k LA =mass transfer coeffi cient in the liquid fi lm . Bars in Figs.8 and 9highlight that the values of s LA,eq and k LA are larger in

Table 2 .
Experimentation matrix f =fi nal fermentation time; γ LA,min =minimum lactic acid (LA) concentration in the liquid phase in the presence of anionic clay; s LA,eq = equilibrium LA concentration in the solid phase; k LA =mass transfer coeffi cient in the liquid fi lm; P=hourly yoghurt production; η=yoghurt dynamic viscosity; S=syneresis index; N=viable LAB number•10 -2