Circulation Time Distribution Research Articles

Mixing state of xanthan gum solution in an aerated and agitated fermentor—Effects of impeller size on volumes of mixing regions and circulation time distribution

The effects of the impeller diameter and width on the volumes of the micromixing and macromixing regions, and on the circulation time distribution were investigated at various agitation speeds to formulate the relationships of them in emperical equations. A fermentor was a 10- l capacity, which was equipped with a turbine impeller with six flat balades and aerated at 1 vvm. It was found that the volumes of the micromixing and macromixing regions depended on the tip speed of the impeller, ND, and the discharging performance of the impeller, ND 2 W, respectively, in the xabthan gum solution with concentrations of 0.9, 1.8, 2.7, and 3.9%. Empirical equations were derived to estimate the volume of each mixing region from the impeller diameter, D, impeller width, W, agitation speed, N, and consistency coefficient of the xanthan gum solution. On the other hand, the circulation time distribution could be estimated empirically from only the impeller diameter and agitation speed, regardless of variation in the impeller width and consistency coefficient of the xanthan gum solution tested.

Mechanistic analysis of xanthan gum production in a stirred tank

The overall effect of agitation on xanthan gum production by Xanthomonas campestris ATCC13951 in a stirred vessel was mechanistically analyzed considering local variation of the specific production rate due to variation of shear stress in the vessel. The whole liquid volume in a fermentor was roughly divided into three regions; the micromixing region around the impeller with high shear stress, the macromixing region dominated by a circulating flow and the stagnant region. The value of the shear rate was first ascertained by experiments in order to obtain a picture of shear rate variation in a radial direction from the impeller, and the equivalence between the volumes of the high shear stress region and micromixing region was confirmed. The shear stress obtained using a correlation between the shear rate at the impeller tip and Reynolds number of Wichterle et al. was used as a representative of the shear stress in the micromixing region, and the shear stress estimated by use of an empirical correlation between the average shear rate in a fermentor and agitation speed derived by Metzner et al. was adopted as a representative of the shear stress in the macromixing region. The information about the circulation time distribution was also used to take into account oxygen deficiency during circulation of liquid elements in the macromixing region, considering that oxygen from the gas phase was supplied mainly in the high shear region. The calculated values of xanthan gum concentrations which were obtained by the proposed simulation method agreed well with the experimental data in the time course of xanthan gum production at various agitation speeds. Experimental results of the relationship between the overall specific production rate and ND ( N, agitation speed, and D, impeller diameter) was also verified by the proposed method.

Measuring the liquid circulation time in a large gas-liquid contractor by means of a radio pill. Part 2. Circulation time distribution

Measuring the liquid circulation time in a large gas-liquid contractor by means of a radio pill. Part 2. Circulation time distribution

Circulation time distribution and volume of mixing regions in highly viscous xanthan gum solution in a stirred vessel.

The distribution of circulation time of a tracer particle and the volume of mixing regions were investigated using a pseudoplastic solution at various concentrations of xanthan gum up to 4.6% in a stirred tank with a turbine impeller having six flat blades. When the relative frequency/N of each circulation time was plotted against Nθ (N, agitation speed; θ, circulation time) at various agitation speeds, the distribution curve for solutions of 1.8% (flow behavior index 0.12 and consistency coefficient 26.4 Pa•s0.12) or more xanthan gum shifted to the side of larger values of Nθ with increasing agitation speed, while distribution curves of the same shape were obtained in water or a diluted solution (0.9% xanthan gum). The mean circulation time also increased with increasing agitation speed. This phenomenon was confirmed by measuring the volumes of two mixing regions, the micromixing and the macromixing regions. These volumes increased with increases in the agitation speed, resulting in decreases of the stagnant region.

CONCENTRATION RESPONCES IN HIGH VISCOSITY LIQUID STIRRED TANKS

The mixing characteristics of high-viscosity liquid in stirred tanks were investigated from measurement of the concentration response curves by injecting tracer in the tanks, and it was confirmed, by comparing the results of the concentration response curves calculated from the circulation time distribution, that the circulation time distribution can be used to predict the concentration response curve that represents the mixing performance. The effect of diffusive mixing was found to be significant in the concentration response curve obtained experimentally, particularly in the case of paddle or turbine impellers in the range of Reynolds number less than 10. The characteristic values of mixing both observed and calculated showed a similar tendency and it was concluded that paddle and turbine impellers are preferable for mixing in the Reynolds number range greater than 20, and helical ribbon and helical screw impellers for less than 20. An attempt was made to correlate the parameters characterizing the circulation time distribution with operating conditions, and a method of estimating the characteristic values of mixing from the parameters of the circulation time distribution was obtained.

Circulation time distribution in a mixed charge

Circulation time distribution in a mixed charge

Mathematical analysis of circulatory mixing process.

The circulatory mixing process was analyzed as the time course of the dispersion of indicator after its injection into the heart. In simplified models, which had one or two lumped mixing chambers and circulatory pathways connected with them, it was suggested that the extent of dispersion could be evaluated by the variance of indicator distribution in the total circulating blood when the circulation time distributions between the chambers and the concentration curves in the chambers were known. The method of determining the circulation time distributions through the pulmonary, systemic and total circulations was derived and the actual distributions were obtained in dogs by indicator dilution techniques. With the use of these distributions, the time course of the circulatory mixing process was numerically calculated. The results showed that there was considerable difference in velocities of the process between the case of the right heart injection and the left heart injection of the indicator.

Circulation Time Distribution of Viscous Liquid in a Mixing Vessel

Circulation Time Distribution of Viscous Liquid in a Mixing Vessel

Comparison of the intravascular mixing and disappearance of radiosodium, radiopotassium and T-1824.

A method is presented utilizing the rapid intravenous injection of a dye-isotope mixture and rapid, serial arterial sampling which permits the determination of rates of disappearance of these materials from the vascular system. Since K + traverses capillary endothelial walls at about twice the rate of Na + it appears that these two ions, while being about the same size and having the same charge, are handled in different manners by the capillaries. Other variables obtainable from the T-1824 isotope time-concentration curves such as plasma volume, circulation time, cardiac output and isotope distribution volumes are also presented.