Effect of Temperature on the Solubility of CO₂ in Bread Dough

Abstract

Dough expansion during fermentation is caused by CO₂ production by yeast, and its transfer from liquid state in the dough liquor to gaseous phase in the gas cells. The liquid-gas equilibrium is controlled by the solubility of CO₂ in the dough and by the Henry coefficient. The solubility of CO₂ in bread dough was measured for different temperatures with a specific device based on the evolution of the pressure during fermentation at constant volume. The measurements range from 15 to 40°C. Data obtained was extrapolated to 0 and 50°C. Values were found between 1.6 × 10⁻⁵ and 5 × 10⁻⁶ g CO₂ kPa⁻¹ g⁻¹ LPD, at 0 and 50°C, respectively (LPD: Liquid Phase of Dough).

Keywords:

• Carbon dioxide solubility
• Fermentation
• Bread dough

INTRODUCTION

The solubility of carbon dioxide (CO₂) represents the total amount of carbonate species that can be dissolved in a solution.^[1] Two species of CO₂ must be considered: aqueous CO₂ (aq) which is a molecular form of dissolved CO₂, and carbonic acid H₂CO₃ resulting on the dissociation of CO₂ (Eq. 1).

(1)

This results in high CO₂ pressure and/or in low pH. Conventional measurements do not allow one to distinguish the two species easily.^[2] Most of the time, the result pools the two species in a bulk amount as indicated in Eq. (1), where , and are respectively the concentration of the molecular form, the carbonic acid and the two species together. The approximation of CO₂ solubility by CO₂ concentration is verified only in acid media.^[3] Near the neutrality, one must take in account the CO₂ dissociation in (Eq. 1), the dissociation in and in (Eqs. 2 and 3), and also the possible formation of carbonated complexes.

(2)

(3)

However, the concentration of these species remains negligible in comparison with the total concentration of carbonated species in solution. Near the neutrality, the concentration in can be done using solubility measurements with Eq. (4) Where is the total amount of carbonate species that can be dissolved in the solution, and is the apparent constant of the dissociation of CO₂ as presented in Eq. (2).

(4)

depends on the temperature T, the pressure P and the ionic power of the solution I. The dissociation as presented in Eq. (3) has a negligible role. Many authors studied the solubility of CO₂ in water. Table 1 presents the main studies on the subject. Table 1 shows almost all studies on solubility of CO₂ conducted at elevated pressures. CO₂ solubility in NaCl solutions was extensively investigated in broad pressure and temperature ranges. Table 2 shows experimental studies in literature on the solubility of CO₂ in NaCl solutions. The higher the NaCl concentration, the lower the CO₂ solubility.^[1] The presence of NaCl yields in a decrease of the partial pressure of water and results in a lower water vapor pressure in the gas phase.

TABLE 1 Experimental surveys carried out on aqueous solubility of CO₂ in water at high pressure (from^[1,^4])

Temperature (K)	Pressure (bar)	Reference
285.15–373.15	30–800	Weibe & Gaddy (1939, 1940)^[^5,^6^]
298.15–348.15	1–710	Weibe & Gaddy (1941)^[^7^]
374–393	30–700	Prutton & Savage (1945)^[^8^]
383.15–533.15	100–700	Takenouchi & Kennedy (1964)^[^9^]
323–473	200–3500	Toedheide & Franck (1963)^[^10^]
298–373	17–51	King & Coan (1971)^[^11^]
373–473	2–50	Zawisza & Malesinka (1981)^[^12^]
289–394	6.9–202.7	Gillespie & Wilson (1982)^[^13^]
289–533	6.9–202.7	Gillespie et al. (1984)^[^14^]
373–473	3.3–81.1	Müller et al. (1988)^[^15^]
353–471	21.1–102.1	Nighswander et al. (1989)^[^16^]
348–421	100–200	Sako et al. (1991)^[^17^]
299–298	60.8–243.2	King et al. (1992)^[^18^]
278–338	0.49–0.84	Zheng et al. (1997)^[^19^]
344	100–1000	Dhima et al. (1998)^[^20^]

TABLE 2 Experimental surveys carried out on aqueous solubility of CO₂ in NaCl solutions^[1]

Molality of
NaCl (mol.kg^−1 H2O)	Temperature (K)	Pressure (bar)	Reference
0–6	323–673	30–266	Drummond (1981)^[^21^]
0–2	445–603	16–93	Ellis & Golding (1963)^[^22^]
0–3	273–298	1	Harned & Davis (1943)^[^23^]
0–6	298–423	48	Malinin & Kurovskaya (1975)^[^24^]
0–4	298–348	48	Malinin & Savalyeva (1972)^[^25^]
0.1–4	273–313	1	Markham & Kobe (1941)^[^26^]
0–6	313–433	2–96	Rumpf et al. (1994)^[^27^]
0–10% of mass	353–473	1–100	Nighswander et al. (1989)^[^16^]
0–3	298	1	Onda et al. (1970)^[^28^]
0–4.3	423–523	100–1400	Takenouchi & Kennedy (1965)^[^29^]
0.49–5.096 (mol L^−1)	288–308	1	Yasunishi & Yoshida (1979)^[^30^]

In an aqueous solution, the apparent CO₂ concentration undergoes two successive dissociations (Eqs. 2 and 3). Their dissociations constants are given in Eqs. (5) and (6).

(5)

(6)

Patterson et al.^[31,^32] measured these constants in NaCl solution in a range of concentration from 0 to 5 mol L⁻¹ and in a range of temperature from 0 to 300°C under variable total pressure from (water saturation pressure) to . They used their measurements and data from literature for pure water and NaCl solutions (for ,^[23,^33–35] for .^[36–38] Portier^[1] used these results and found the following equations by least square method:

(7)

(8)

Chiotellis et al.^[39–40] showed the effect of temperature on the dissolved CO₂ concentration in the liquid phase of bread dough. Bloksma^[41] suggested that in the first steps of fermentation, most of the gas produced is dissolved in the liquid phase, whereas the gas penetration speed is low. The gas production rate measured by Bloksma was 2.5 × 10⁻⁵ kmol s⁻¹ m⁻³ LPD (m⁻³ Liquid Phase of Dough) for 2% of yeast at 27°C. At the same temperature, the saturation concentration of CO₂ in the liquid phase is 4.3 × 10⁻² kmol m⁻³ LPD. It was estimated that the saturation is reached after 50 min of fermentation. Bloksma took into account the variations in the solubility of CO₂ and water vapor pressure with temperature. The partial pressure of CO₂ in gaseous phase is related to concentration in the dough by Henry’s law as proposed in Eq. (9), where X_C is the concentration of CO₂ in the aqueous dough and K_H is Henry’s constant.

(9)

Solubility depends on temperature.^[42] The solubility of CO₂ decreases when temperature increases; thus K_H increases with temperature. It was assumed that the variation of K_H with temperature follows the Arrhenius relationship (Eq. 10) as proposed by Fan et al.^[43]

(10)

In Eq. (10) ΔH_c is the heat of solution of CO₂ in dough, and R the universal gas constant. K_H0 is the Henry’s law constant at the initial temperature T₀. Hibberd and Parker^[44] have reported that the Henry’s law constant K_H in a fermenting dough is 7.03 × 10⁷ Pa kg dough/kg CO₂ at a temperature of 27°C. Beyond 27°C, Fan et al.^[43] assumed that the temperature dependence of K_H in aqueous dough behaves in the same way as it did in water. They estimated the heat of solution of CO₂ from the literature data on the solubility of CO₂ in water;^[45] the value was 1.94 × 10⁴ J mol⁻¹.^[43]

Carbon dioxide solubility is an important parameter needed for the understanding and the modelling of the fermentation of bread dough. During shaping and moulding, high pressure is applied on dough and an amount of CO₂ is lost from the bubbles through the solution while the pressure is decreasing. Thus, moulding can not eliminate all gas and it remains a significant gas volume in the dough. It is also of interest to know the solubility of CO₂ at baking temperature. During the baking step, temperature rises resulting in a vaporisation of the CO₂ dissolved in the liquid phase of the dough. At the same time, increases quickly and the gas bubbles volume increases.^[41–46] Fan et al.^[43] concluded that the solubility of CO₂ in aqueous dough during baking is responsible for the early oven rise of dough whereas vapor makes a significant contribution to the later expansion. Alcoholic compounds produced during fermentation remain dissolved in the dough at lower temperature. They also contribute to the oven rise during baking. Finally, the crumb porosity can reach 0.79 and the crust porosity 0.71.^[46]

The objective of this work was to measure the solubility of CO₂ in bread dough over a large temperature domain. One constrains lies in the fact that yeast activity is reduced at lower temperature and becomes very high at higher temperature. Therefore, experiments were carried out in a limited domain and results were extrapolated to a larger temperature domain using the Arrhenius model.

THEORY

Theoretical development proposed by Hibberd and Parker has been used to determine the solubility of CO2.^[44] Let’s consider unit mass of dough of total volume V, of which V_d is the volume of the continuous dough phase. The volume of the gas is therefore V – V_d. The gas in the bubbles is a mixture of carbon dioxide generated during fermentation, components of air entrained during mixing, and water vapor. The gas is considered to be in equilibrium with the gas dissolved in the continuous dough phase.

From the perfect gas law, the mass of CO₂ in the gaseous phase, is given in terms of its partial pressure, P_c by Eq. (11),

(11)

where M_c is the molecular weight of CO₂ in g mol⁻¹. Assuming that the solubility of CO₂ in the continuous dough phase follows Henry’s law, the mass of carbon dioxide dissolved in the dough, is given by Eq. (12):

(12)

where K_c is the solubility constant of the carbon dioxide in mass per unit mass of dough per unit pressure. The total mass, m_c, of CO₂ in unit mass of dough is therefore,

(13)

(14)

where

(15)

V_c may be considered as the equivalent volume of the carbon dioxide dissolved in unit mass of dough. Similar equations can be derived for each of the components of the entrapped air. During the first steps of fermentation, the dough becomes saturated in CO₂. Then, the rate of production of CO₂ will correspond either to an increase of the pressure in the gas cell in the case of constant volume or to an increase of volume in the case of constant pressure. The experimental setup was designed to perform experiments at constant volume. The time derivative of Eq. (14) gives:

(16)

The partial pressure of the carbon dioxide is equal to P, the total pressure in the bubbles decreased by the partial pressure of the dry air P_a and by the partial pressure of the water vapor P_v:

(17)

The bubbles volume and the quantity of dry air and of water vapor are constant, and thus the partial pressures of the dry air and of the water vapor, so that

(18)

The pressure in the bubbles P is the sum of the atmospheric pressure P_atm, of the external pressure P_e exerted by the experimental device, and of the pressure exerted by the dough on the bubbles, P_d.

(19)

The atmospheric pressure is constant, and the pressure exerted by the dough changes slowly so that

(20)

Thus,

(21)

which can still be written

(22)

During proofing, is constant during a long time. If the volume V is changed from time to time (V_d remains constant), and that the pressure P_e is logged, as many points are obtained than values of volume are chosen. Then V_c is got from the slope of the straight line define by Eq. (22), and K_c is deduced then from Eq. (15).

MATERIALS AND METHODS

Doughs were prepared base on the recipe proposed in Table 3. Ingredients were mixed in a Diosna SP24 laboratory mixer with 2 min slow speed and 7 min fast speed. Flour properties are indicated in Table 4 (crop 2007 – Moulin Soufflet, Pornic, France). The dough was placed in a cylindrical flask (2.5-cm inner diameter) with a mobile piston. The piston was contacted on a force sensor to log the pressure that develops during fermentation in function of time.

TABLE 3 Dough formula

Ingredient	(% w/w flour basis)
Flour	100
Water	58
Yeast	5
Salt	2
Improver	1

TABLE 4 Analysis results for the flour (Moulin Soufflet, Pornic, France)

Moisture content (%)	13.72
Ash content (%)	0.53
Protein content on dry matter (%)	10.58
Zeleny	38
Falling number (sec)	402
Alveograph – Pm	60
Alveograph – L	97
Alveograph – Pm/L	0.62
Alveograph – W	183
Farinograph A water absorption (%)	52.9
Farinograph B development time (min)	1.7
Farinograph C dough stability (min)	5.4
Farinograph D dough strength (BU)	85
Farinograph E softening number (BU)	84

The sample was 5 g of dough. It was placed in the cylinder which walls were previously lubricated with a film of sun flower oil. The installation of the sample must be done carefully to avoid the trapping of air between the dough and the walls of the cylinder. The piston is then pressed down firmly, forcing the air above the dough to escape through the upper exhaust hole (Fig. 1).

FIGURE 1 Schematic diagram of instrument used to make pressure-volume measurements on dough.

The cylinder containing the dough was then placed between a rigid plate and the force sensor. The distance between the plate and the sensor was fixed to a mechanical setup made of two plateau and two screws. During the experiment, volume of the dough sample varied by screwing the nuts more or less. Pressure rise of the dough was monitored for period of around 20 to 30 min. The nuts were unscrewed to reduce the pressure to zero resulting in an expansion of the dough. The dough is compressed again but to a volume greater than the previous one. A novel pressure rise was monitored with a new porosity of the dough. During an experiment, the pressure variation was recorded for 4 different volumes. With a least square method, V_c and its standard deviation are deduced from Eq. (12). Then with Eq. (12), K_c and its standard deviation are calculated.

The temperature of the sample was controlled by circulating water from a thermostated bath through the jacket surrounding the cylinder (Fig. 2). The volume of the sample, as placed in the cylinder, includes gas bubbles entrained during mixing. Knowing the density of the degassed dough it was possible to determine the volume of gas from the effective density of a sample determined at the time of installation in the cylinder. The total volume of gas at any stage of fermentation was taken as the sum of the volume of these bubbles entrained during mixing and the change in volume as calculated from the change in height of the cylinder.

FIGURE 2 Scheme of the cell used to make the fermentation at constant volume.

RESULTS AND DISCUSSION

Figure 3 shows the evolution of pressure for different volumes V_i of the dough. Pressure increases in a uniform way in the first 30 min. The pressure increase for V₁, V₂, V₃ and V₄ is attributed to carbon dioxide, which diffuses from the liquid phase of the dough to bubbles. On Fig. 4, for selected temperatures, are placed the points , and the corresponding regression lines. The absolute values of the different slopes correspond to the equivalent volumes V_c (ml of CO₂ g⁻¹ of dough). V_c decreases with temperature because of the decrease of CO₂ solubility. As , one can deduce from values of V_c the values of K_c. Data of K_c in function of 1/T are shown in Fig. 5. Assuming that the solubility is following an Arrhenius model, a logarithm function should fit data obtained and presented in Fig. 5. This was indeed the case, as shown in Fig. 6. Equation (23) was obtained.

(23)

FIGURE 3 External pressure evolution for different dough density at 20°C for 30 g of dough.

FIGURE 4 Evolution of vs. during fermentation at constant volume for selected temperatures.

FIGURE 5 Experimental values and Arrhenius law modelling for Solubility constant of CO₂ in bread dough.

FIGURE 6 Solubility (K_c) of CO₂ in bread dough using the Arrhenius model presented in Eq. (23) for temperature between 0 and 50°C.

The values of solubility obtained are expressed as g of Liquid Phase of Dough (g LPD). Values were between 1.6 × 10⁻⁵ and 5 × 10⁻⁶ g CO₂ kPa⁻¹ g⁻¹ LPD, at 0 and 50°C, respectively. The values of the solubility were expressed per g of liquid phase of dough rather than per g of dough as did by Hibberd and Parker,^[44] because the solubility of the CO₂ depends principally of the liquid phase, and because the water content in bread dough vary with the manufacturer.^[47]

Hibberd and Parker found a solubility constant value equal to 1.45 × 10⁻⁵ g CO₂ kPa⁻¹ g⁻¹ dough at 27°C.^[44] In the same units the value found in this work is equal to 1.64 × 10⁻⁶ g CO₂ kPa⁻¹ g⁻¹ dough at 30°C, i.e., a ratio of about 10. The difference may be explained by the fact that data proposed by Hibberd on dough recipe and flour moisture were not very accurate. Also, the recipe they used contained shortening. Shortening may affect the size distribution of gas cells in the dough, which should be more numerous and smaller than without any shortening. Also, the water content of the dough of Hibberd and Parker is unknown, and it can be a major cause of difference. Another point is that considering the solubility per gram of liquid phase of dough is a first approach. Ideally, the solubility should be calculated per gram of free water (freezable water) in the dough, even though the fact that CO₂ dissolved only in the free water phase may be discussed. In our case, specific experiments showed that for the recipe used, the amount of free water obtained by calorimetry was 60.5% (results not shown). Applying this factor to our results would make that the solubility at 30°C would be 2.76 × 10⁻⁶ g CO₂ kPa⁻¹ g⁻¹ free water vs. 1.67 × 10⁻⁶ g CO₂ kPa⁻¹ g⁻¹ LPD. In addition, one can observe that our data obtained at different temperatures show a great degree of coherence as expected by the Arrhenius model. No other explanation of observation can be proposed to explain the difference. There are very few data available in the literature to propose any further discussion on the results.

CONCLUSION

A method for measuring the CO₂ solubility in bread dough during fermentation was developed. The solubility of CO₂ was determined in the bread dough for temperatures between 15 and 35°C and data have been extrapolated from 0 to 50°C using an Arrhenius model. The model that has been obtained can be very useful to study the behaviour of bread dough in the case of fermentation at different temperature values or in the case of dough ripening at temperature for which the yeast is no more active. These results give a new insight in dough fermentation. Further studies such as studying the impact of recipe, degree of starch damage, dough hydration could be very useful in better understanding of the interaction between the dough liquor and the solubilisation of CO₂ in this very specific liquid domain.

ACKNOWLEDGMENTS

Thanks to Christophe Couedel and Luc Guihard for technical support.

FUNDING

This study has been carried out with financial support from the Commission of the European Communities, FP6, Thematic Area “Food quality and safety,” FOOD-2006-36302 EU-FRESHBAKE. It does not necessarily reflect its views and in no way anticipates the Commission’s future policy in this area. Partial financial support has also been obtained from AISQAL national project (Région Pays de Loire).

NOMENCLATURE

I	=	Ionic strength (mol L−1)
Kc	=	Solubility constant of carbon dioxide (g CO2 kPa−1 g−1 LPD)
KH	=	Henry’s law constant (Pa kg dough/kg CO2)
	=	Dissociation constant for the first dissociation of CO2
	=	Dissociation constant for the second dissociation of CO2
m	=	Mass (g)
M	=	Molar mass (g mol−1)
P	=	Pressure (Pa)
	=	Saturation pressure of water (Pa)
	=	Total concentration of CO2 at saturation (mol L−1)
R	=	Perfect gas constant = 8.314 J mol−1 K−1
t	=	Time (s)
T	=	Temperature (K)
V	=	Volume (ml g−1 of dough)
ΔHc	=	Heat of solution of CO2 (J mol−1)
[]	=	Molarity (mol L−1)
Subscripts	=
a	=	Air
atm	=	Atmosphere
c	=	Carbon dioxide
d	=	Dough
e	=	External
v	=	Vapor
0	=	Initial
	=	Number of volume values during a proofing experiment

Additional information

Funding

This study has been carried out with financial support from the Commission of the European Communities, FP6, Thematic Area “Food quality and safety,” FOOD-2006-36302 EU-FRESHBAKE. It does not necessarily reflect its views and in no way anticipates the Commission’s future policy in this area. Partial financial support has also been obtained from AISQAL national project (Région Pays de Loire).