Modelling of simultaneous mass and heat transfer with chemical reaction using the Maxwell-Stefan theory II. Non-isothermal study

In Part I a general applicable model has been developed which calculates mass and heat transfer fluxes through a vapour/gas-liquid interface in case a reversible chemical reaction with associated heat effect takes place in the liquid phase. In this model the Maxwell-Stefan theory has been used to describe the mass transport. Also in Part I the isothermal absorption of a pure gas A in a solvent containing a reactive component B has been studied. In this paper the influence of thermal effects on the mass transfer rates is investigated, with special attention to the concentrated systems. The thermal effects arise as a consequence of enthalpy changes due to phase transitions and chemical reaction. Account is taken of the influence of temperature gradients on (i) the solubility of the gaseous component in the liquid phase, (ii) the chemical reaction rate and (iii) the mass transfer coefficients in the liquid phase. Numerical simulations show that, when compared to the corresponding isothermal case, the thermal effects can affect the mass transfer rates by as much as a factor of 30. In case of high Lewis numbers the numerically calculated mass transfer rates can very well be predicted from an approximate analytical expression, which has been presented in this paper. In most cases this is also a reasonable estimate of the mass transfer rate in case the Lewis number equals unity. In case of a second-order chemical reaction it was shown that thermal effects may change the maximum enhancement factor and consequently shift the absorption from the instantaneous regime to the pseudo-first-order regime. Further, it is concluded that there may exist non-isothermal gas-li1uid absorption systems where minor changes in parameters appearing in the heat balance, e.g. binary mass transfer coefficients, chemical reaction rate constant, Lé number or heat transfer coefficients, may result in drastically altered system behaviour. For situations in which thermal effects are significant, also the vaporization of the liquid mixture should be taken into account, especially when the calculated interface temperature is near or exceeds the boiling temperature of the liquid

Modelling of simultaneous mass and heat transfer with chemical reaction using the Maxwell-Stefan theory I. Model development and isothermal study

A general applicable model has been developed which can predict mass and heat transfer fluxes through a vapour/gas-liquid interface in case a reversible chemical reaction with associated heat effect takes place in the liquid phase. In this model the Maxwell-Stefan theory has been used to describe the transport of mass and heat. The description of the transfer rates has been based on the film model in which a well-mixed bulk and a stagnant zone are thought to exist. In this paper results obtained from the Maxwell-Stefan theory have been compared with the results obtained from the classical theory due to Fick. This has been done for isothermal absorption of a pure gas A in a solvent containing a reactive component B. Component A is allowed to react by a unimolecular chemical reaction or by a bimolecular chemical reaction with B to produce component C. Since the Maxwell-Stefan theory leads to implicit expressions for the absorption rates, approximate explicit expressions have been derived. In case of absorption with chemical reaction it turned out that the mass transfer rate could be formulated as the product of the mass flux for physical absorption and an enhancement factor. This enhancement factor possesses the same functional dependency in case Fick's law is used to describe the mass transfer process. The model which has been developed in this work is quite general and can be used for a rather general class of gas-liquid and vapour-liquid transfer processes. In this paper (Part I) only isothermal simulations will be reported to show the important features of the model for describing mass transfer with chemical reaction. In many processes such as distillation, reactive distillation and some absorption processes, heat effects may play an important additional role. In Part II non-isothermal processes will be studied to investigate the influence of heat effects on mass transfer rates

Aerated bunker discharge of fine dilating powders

The discharge rate of coarse powders (mean particle size 500 ¿m) from bunkers without aeration can be described by both empirical relations and theoretical models. In the case of small particles the discharge rate is largely overestimated. As the powder dilates during flow a negative pressure gradient develops near the hopper outlet, inducing an air flow into the hopper. This extra drag force decreases the discharge rate for fine particles. Aeration of the hopper through a porous cone section will create an opposite pressure gradient, and thereby increase the discharge rate. The aim of this investigation was to incorporate the dilation in an ad hoc way into the model of Altiner in order to improve its predictive power. To test the modified model we carried out experiments with a fluid catalytic cracking powder to study its discharge as a function of aeration. As the improved model needs a dilation parameter as input, the local bulk density was measured during flow at the outlet and at the bin/hopper junction using gamma-ray absorption. At the bin/hopper junction the bulk density was found to be independent of the discharge rate and equal to the bulk density at minimum fluidisation. At the outlet the bulk density goes through a maximum when the amount of aeration gas is increased. Without aeration gas a large dilation, i.e. a 15¿35% lower bulk density, was observed. With these data the model predictions improved from 600% overestimation error to 25¿90% underestimation for pure gravity discharge, and from 100% to 0¿20% error for aerated discharge. However, the bulk density at the outlet cannot be predicted from the powder compressibility, as it seems to depend on dilation at fluidisation

Diffusion Coefficients and Viscosities of CO2 + H2O, CO2 + CH3OH, NH3 + H2O, and NH3 + CH3OH Liquid Mixtures

To evaluate quantitatively the results of gas-liquid absorption experiments, accurate liquid-phase diffusion coefficients and viscosities are needed. In this paper experimental values of these quantities will be reported for the binary systems carbon dioxide + water, carbon dioxide + methanol, ammonia + water, and ammonia + methanol. The diffusion coefficients have been measured using the Taylor-Aris dispersion method, and the viscosities have been measured with a falling ball viscometer at temperatures from 293 to 333 K. The ammonia mole fraction ranged from 0 to 0.312. The results have been correlated using Arrhenius-type equations and have been compared with literature data, where available. Furthermore, the measured diffusion coefficients are compared with values predicted by the modified Stokes-Einstein equation and the Wilke-Chang equation

Extended quantum conditional entropy and quantum uncertainty inequalities

Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum. Recently these inequalities have been generalized to the tensor product of several Hilbert spaces and we show here how their derivations can be shortened to a few lines and how they can be generalized. All the recently derived uncertainty relations utilize the strong subadditivity (SSA) theorem; our contribution relies on directly utilizing the proof technique of the original derivation of SSA.Comment: 4 page

Dietary restriction and fasting arrest B and T cell development and increase mature B and T cell numbers in bone marrow

Dietary restriction (DR) delays ageing and extends life span. Both long- and short-term DR, as well as short-term fasting provide robust protection against many "neuronal and surgery related damaging phenomena" such as Parkinson's disease and ischemia-reperfusion injury. The exact mechanism behind this phenomenon has not yet been elucidated. Its antiinflammatory actions prompted us to thoroughly investigate the consequences of DR and fasting on B and T cell compartments in primary and secondary lymphoid organs of male C57Bl/6 mice. In BM we found that DR and fasting cause a decrease in the total B cell population and arrest early B cell development, while increasing the number of recirculating mature B cells. In the fasting group, a significant reduction in peripheral B cell counts was observed in both spleen and mesenteric lymph nodes (mLN). Thymopoiesis was arrested significantly at double negative DN2 stage due to fasting, whereas DR resulted in a partial arrest of thymocyte development at the DN4 stage. Mature CD3+ T cell populations were increased in BM and decreased in both spleen and mLN. Thus, DR arrests B cell development in the BM but increases the number of recirculating mature B cells. DR also arrests maturation of T cells in thymus, resulting in depletion of mature T cells from spleen and mLN while recruiting them to the BM. The functional relevance in relation to protection against organ damage needs to be determined

Pre-B Cell Receptor Signaling Induces Immunoglobulin κ Locus Accessibility by Functional Redistribution of Enhancer-Mediated Chromatin Interactions

During B cell development, the precursor B cell receptor (pre-BCR) checkpoint is thought to increase immunoglobulin κ light chain (Igκ) locus accessibility to the V(D)J recombinase. Accordingly, pre-B cells lacking the pre-BCR signaling molecules Btk or Slp65 showed reduced germline Vκ transcription. To investigate whether pre-BCR signaling modulates Vκ accessibility through enhancer-mediated Igκ locus topology, we performed chromosome conformation capture and sequencing analyses. These revealed that already in pro-B cells the κ enhancers robustly interact with the ∼3.2 Mb Vκ region and its flanking sequences. Analyses in wild-type, Btk, and Slp65 single- and double-deficient pre-B cells demonstrated that pre-BCR signaling reduces interactions of both enhancers with Igκ locus flanking sequences and increases interactions of the 3′κ enhancer with Vκ genes. Remarkably, pre-BCR signaling does not significantly affect interactions between the intronic enhancer and Vκ genes, which are already robust in pro-B cells. Both enhancers interact most frequently with highly used Vκ genes, which are often marked by transcription factor E2a. We conclude that the κ enhancers interact with the Vκ region already in pro-B cells and that pre-BCR signaling induces accessibility through a functional redistribution of long-range chromatin interactions within the Vκ region, whereby the two enhancers play distinct roles