Diffusion-controlled Shrinkage and Growth of an Air Bubble Entrained in Water and in Wheat Flour Particles

Shimiya, Yoko; Yano, Toshimasa

doi:10.1080/00021369.1987.10868309

Cited by 6 publications

(10 citation statements)

References 3 publications

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“…Large bubbles never stop growing; this means C * never reaches C ¥ . As bubbles grow, C * increases initially (it must do, as CO 2 is entering the bubble), then it decreases again later (again, it must do, as C * is proportional to P CO2 b , which decreases at large diameter as diameter increases, according to equation (12)). Therefore, as bubbles grow, C * and P CO 2 b pass through a maximum.…”

Section: Calculation Of the Critical Bubble Sizementioning

confidence: 99%

“…So the initial bubble size for which this maximum corresponds to C * = C ¥ is the critical bubble size; this is the bubble size which is just small enough for C * to reach C ¥ and stop growing. This can be calculated by differentiating equation (12) and setting the differential to zero, and solving to ® nd the diameter at which the partial pressure of CO 2 is at a maximum. From this C * max can be calculated; the critical bubble size occurs when C * max and C ¥ are equal.…”

Section: Calculation Of the Critical Bubble Sizementioning

confidence: 99%

See 1 more Smart Citation

Proving of Bread Dough: Modelling the Growth of Individual Bubbles

Shah¹,

Campbell²,

McKee³

et al. 1998

Food and Bioproducts Processing

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roving of bread dough was modelled using classical one-component diffusion theory, to describe the rate of growth of bubbles surrounded by liquid dough containing dissolved carbon dioxide. The resulting differential equation was integrated numerically to predict the effect of initial bubble size and system parameters (carbon dioxide concentration, surface tension at the bubble interface, temperature) on bubble growth. Two situations exist, potentially; the dough could be either supersaturated or subsaturated with carbon dioxide. When the dough is supersaturated, the model predicts a critical bubble size above which bubbles grow inde® nitely, while below the critical bubble size bubbles reach a limiting size and stop growing. The critical bubble size decreases with increasing carbon dioxide concentration and increases with increasing surface tension. Below saturation, all bubbles reach an upper size limit proportional to their initial size. The ® nal bubble size increases with carbon dioxide concentration and decreases with increasing surface tension. Higher temperatures increase the rate of bubble growth and reduce the critical bubble size for supersaturated doughs, by increasing the value of Henry' s Law constant. Higher temperatures also increase the ® nal bubble size for subsaturated systems. The model could be extended to include yeast kinetics and entire bubble size distributions, to develop a full simulation of the proving operation.

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Section: Calculation Of the Critical Bubble Sizementioning

confidence: 99%

Section: Calculation Of the Critical Bubble Sizementioning

confidence: 99%

Proving of Bread Dough: Modelling the Growth of Individual Bubbles

Shah¹,

Campbell²,

McKee³

et al. 1998

Food and Bioproducts Processing

View full text Add to dashboard Cite

show abstract

“…If air is lost, the bubble shrinks, and if air is gained, the bubble grows. For such a change in bubble size, the following equation was successfully applied (Epstein & Plesset, 1950;Shimiya & Yano, 1987; Kumagai et a/., 1991), in which the air transfer rate is Calculation of the change of bubble-size distribution For the calculation of the time course of the bubble-size distribution at a constant temperature, Eq. ( I ) was numerically integrated using Runge Kutta's method.…”

Section: Theoreticalmentioning

confidence: 99%

“…Recently, Shimiya and Yano (1987) analyzed the time courses of shrinkage and expansion of an isolated bubble existing in water, showing that the time courses of the shrinkage under a constant temperature and the expansion under a temperature rise were successfully predicted by the theory of Epstein and Plesset (1950). Kumagai et a/.…”

mentioning

confidence: 99%

Diffusion-Controlled Change in Bubbles Impregnated in Viscous Solutions.

Sugiyama¹,

Yano

1997

FSTI

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The applicabilities of Epstein and Plesset's theory and Lemlich's theory to the change in bubble-size distribution under a constant temperature were studied on bubbles impregnated in homogeneous viscous solutions. The numerical calculation based on Epstein and Plesset's theory that took into account the change in the dissolved air concentration in the surrounding solution agreed well with the measured results, while Epstein and Plesset's theory, which assumed the dissolved air concentration in the surrounding solution to be constant, and Lemlich's theory, did not fit the measured results.

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“…5) at 19°C. Some large bubbles didn't shrink but grew, absorbing air released from smaller shrinking bubbles.…”

mentioning

confidence: 99%

Rates of shrinkage and growth of air bubbles entrained in wheat flour dough.

Shimiya

Yano²

1988

Agricultural and Biological Chemistry

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The rates of shrinkage at constant temperature, and growth under a temperature rise below 100°C, of bubbles entrained in wheat flour dough were analyzed and compared with those of a bubble in water. The rate of shrinkage of bubbles in flour dough was controlled by the diffusion of dissolved air from the surface of bubbles to the bulk of flour dough. The apparent diffusion coefficient of the dissolved air in wheat flour dough with the water fraction of 0.49 calculated from the shrinkage of bubbles, was (3.2±1.5)x 10~nm2/sec (19°C), and (6.4±2.0)x 10"11m2/sec (42°C). However, the growth behavior of bubbles in flour dough under a temperature rise was very different from that predicted from the diffusion theory. The critical radius of bubbles to grow was larger than that estimated from the diffusion theory. The mechanism of growth of bubbles in wheat flour dough, which was different from that of a bubble in water, is a subject that needs to be clarified.

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Diffusion-controlled Shrinkage and Growth of an Air Bubble Entrained in Water and in Wheat Flour Particles

Cited by 6 publications

References 3 publications

Proving of Bread Dough: Modelling the Growth of Individual Bubbles

Proving of Bread Dough: Modelling the Growth of Individual Bubbles

Diffusion-Controlled Change in Bubbles Impregnated in Viscous Solutions.

Rates of shrinkage and growth of air bubbles entrained in wheat flour dough.

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