Yutaka Tada

Experimental study on miscible viscous fingering involving viscosity changes induced by variations in chemical species concentrations due to chemical reactions

When a reactive and miscible less-viscous liquid displaces a more-viscous liquid in a Hele-Shaw cell, reactive miscible viscous fingering takes place. We succeed in showing experimentally how a reactive miscible viscous fingering pattern in a radial Hele-Shaw cell changes when the viscosity of the more-viscous liquid is varied owing to variation in chemical species concentration induced by an instantaneous chemical reaction. This is done by making use of a polymer solutions dependence of viscosity on pH. When the viscosity is increased by the chemical reaction, the shielding effect is suppressed and the fingers are widened. As a result, the ratio of the area occupied by the fingering pattern in a circle whose radius is the length of the longest finger is larger in the reactive case than in the non-reactive case. When the viscosity is decreased by the chemical reaction, in contrast, the shielding effect is enhanced and the fingers are narrowed. These lead to the area ratio being smaller in the reactive case than in the non-reactive case. A physical model to explain this change in the fingering pattern caused by the chemical reaction is proposed.

Power Consumption and Mixing Time in an Agitated Vessel with Double Impeller

Power consumption in a non-baffled agitated vessel with a double impeller was measured over a wide range of Reynolds number from laminar to turbulent flow regions. The power correlation for the double impeller was derived from the modification of the power correlation for a single impeller proposed by the authors. The power consumption in a baffled vessel was only measured in the turbulent flow region. The power consumption for the double impeller has the maximum value, which was almost twice the power consumption for the single impeller at larger ratio of impeller clearance to liquid depth than 0.35, and it took the minimum value at the impeller clearance ratio of 0.18–0.25. Mixing time in a baffled vessel with some types of double impeller was measured in the turbulent flow region using the decolorization method of sodium thiosulfate and iodine reaction. The minimum mixing time was observed at 0.1–0.2 of the ratio of impeller clearance to liquid depth for the two-stage paddle system, and 0.5–0.7 for the double impellers constructed with the pitched blade paddle. The relationship of mixing time to power consumption for the double impeller system coincided with that for a single impeller at the impeller clearance taking the minimum mixing time.

Effects of moderate Damköhler number on miscible viscous fingering involving viscosity decrease due to a chemical reaction

We have succeeded in experimentally investigating the effects of a moderate Damkohler number, Da (defined as the ratio between a characteristic time of fluid motion and that of a chemical reaction), for various Peclet numbers, Pe , on miscible viscous fingering involving a decrease in the viscosity of the displaced liquid due to a chemical reaction in Hele-Shaw cells. We achieved this by using a chemical reaction between a polymer solution and metal ions. Main analysis has been done for the radial fingering. In the range of Pe employed here, the fingering patterns without the reaction ( Da = 0) were independent of Pe . The fingering patterns with the reaction depended on the single parameter, Da , and the area occupied by the fingering pattern near the injection hole increased with Da in the range of Da employed here. The ratio of the area occupied by the fingering pattern within the circle radius of which is the length of longest finger to the area of the circle increased with Da in the range of Da employed here. This result is opposite to that of Nagatsu et al . ( J. Fluid Mech ., vol. 571, 2007, p. 475), in which the area was decreased by the reaction decreasing the viscosity involving significantly high Da . Experiments in the linear geometry show that the shape of a single finger also depended on the single parameter, Da , and the finger width increased near the base with Da . This result is also opposite to that in the previous case in which the width of a single finger was considered to be decreased by the reaction. These results, interestingly, show that the effects of the decrease in the displaced liquids viscosity due to chemical reaction on the fingering pattern for moderate Da are opposite to those for significantly high Da . A mechanism for the opposite effects on the fingering pattern depending on Da is discussed.

Correlation of Power Consumption for Several Kinds of Mixing Impellers

The authors reviewed the correlations of power consumption in unbaffled and baffled agitated vessels with several kinds of impellers, which were developed in a wide range of Reynolds numbers from laminar to turbulent flow regions. The power correlations were based on Kamei and Hiraokas expressions for paddle and pitched paddle impellers. The calculated correlation values agreed well with experimental ones, and the correlations will be developed the other types of impellers.

Performance of a shaking vessel-type bioreactor with a current pole

The performance of a shaking vessel-type bioreactor with a current pole at its central axis was examined experimentally with respect to particle dispersion, power consumption, and solid-liquid mass transfer coefficient. The current pole improved the particle dispersion without an increase in power consumption and reduced the critical circulating frequency for complete suspension. The mass transfer coefficient with a current pole had the same value as that without a current pole above the critical circulating frequency for complete suspension. The shaking vessel-type bioreactor with a current pole was thus very suitable for the mass production of regenerated plantlets from fragmented horseradish hairy roots.

Miscible viscous fingering involving viscosity changes of the displacing fluid by chemical reactions

In our previous study, we experimentally studied the effects of changes in the viscosity of the displaced more-viscous liquid by instantaneous reactions on miscible viscous fingering pattern [Y. Nagatsu, K. Matsuda, Y. Kato, and Y. Tada, “Experimental study on miscible viscous fingering involving viscosity changes induced by variations in chemical species concentrations due to chemical reactions,” J. Fluid Mech. 571, 475 (2007)]. In the present study, experiments have been performed on the miscible viscous fingering involving changes in the viscosity of the displacing less-viscous liquid by instantaneous reactions in a radial Hele-Shaw cell. We have found that the shielding effect is suppressed and the fingers are widened when the viscosity is increased. As a result, the reaction makes the fingering pattern denser. In contrast, the shielding effect is enhanced, and the fingers are narrowed when the viscosity is decreased. As a result, the reaction makes the fingering pattern less dense. These results are ...

Miscible viscous fingering involving viscosity increase by a chemical reaction with moderate Damköhler number

In our previous study, we experimentally studied the effects of increased or decreased viscosity of the more-viscous liquid caused by chemical reactions at a very high Damkohler number, Da (defined as the ratio between a characteristic time of fluid motion and that of a chemical reaction), on miscible viscous fingering [Y. Nagatsu et al., “Experimental study on miscible viscous fingering involving viscosity changes induced by variations in chemical species concentrations due to chemical reactions,” J. Fluid Mech. 571, 475 (2007)]. In another study, we experimentally studied the effects of decreased viscosity caused by chemical reaction at a moderate Da on the fingering [Y. Nagatsu et al., “Effects of moderate Damkohler number on miscible viscous fingering involving viscosity decrease due to a chemical reaction,” J. Fluid Mech. 625, 97 (2009)]. In the present study, we investigated the effects of increased viscosity caused by chemical reaction at a moderate Da on the fingering in a radial Hele-Shaw cell. W...

Mixing Properties of Unsymmetrical Molten Salts Based on the Law of Corresponding States

The law of corresponding states of molten salt mixtures that include unsymmetrical salts was developed. The corresponding states equations for the thermodynamic and transport properties were obtained by expanding the Helmholtz free energy and the transport properties in terms of differences of the pair potential parameters, difference of the ionic size, and difference of the ionic mass. The effect of valences on the properties was accounted for by the products of cation and anion valences in the corresponding states equations. Equations for the mixing molar volume, surface tension, electrical conductivity, and viscosity were derived from the corresponding states equations. The estimated mixing properties satisfactorily agreed with the observed ones.