Reverse mass flow

In a binary mixture, diffusion coefficients are equal to each other for dissimilar molecules, and Fick s law can determine the molecular mass flows in an isotropic medium at isothermal and isobaric conditions. In a multicomponent diffusion, however, various interactions among the molecules may arise. Some of these interactions are (i) diffusion flows may vanish despite the nonvanishing driving force, which is known as the mass transfer barrier, (ii) diffusion of a component in a direction opposite to that indicated by its driving force leads to a phenomenon called the reverse mass flow, and (iii) diffusion of a component in the absence of its driving force, which is called the osmotic mass flow. 

The actual mass flow rates and speeds are corrected by factor ( /0/ ) and (l/ /0) respectively, reflecting variations in inlet temperature and pressure. The surge line joins different speed lines where the compressor s operation becomes unstable. A compressor is in surge when the main flow through a compressor reverses direction for short time intervals, during which the back... 

A reversible cycle with turbine expansion split into two steps (high pressure, HP, and low pressure, LP) is illustrated in the T, s diagram of Fig. 4.3. The mass flow through the heater is still unity and the temperature rises from T2 to Tt, = Tq hence the heat supplied (3b is unchanged, as is the overall isentropic temperature ratio (x). But cooling air of mass flow i//H is used at entry to the first HP turbine (of isentropic temperature ratio. xh) and additional cooling of mass flow is introduced subsequently into the LP turbine (of isentropic temperature ratio Xl)- The total cooling flow is then i/( = i/ h + >h.-... 

But this expansion through the LP turbine may be considered as two parallel expansions. The first is of mass flow (1 + from the temperature Tg to a temperature Tg (a continuation of the expansion of (1 + i/(h) from 5 to 9) and the second is of mass flow i/(l through a reversed compressor from state 7 to state 1 (which cancels out the... 

A simplified version of the model in Table IX, neglecting accumulation of mass and heat as well as dispersion and conduction in the gas phase, predicts dynamic performance of a laboratory S02 converter operating under periodic reversal of flow direction quite well. This is shown by Fig. 13 taken from Wu et al. (1996). Data show the temperature profiles in a 2-m bed of the Chinese S101 catalyst once a stationary cycling state is attained. One set of curves shows the temperature distribution just after switching direction and the second shows the distribution after a further 60 min. Simulated and experimental profiles are close. The surprising result is that the experimental maximum temperatures equal or exceed the simu-... 

In the Kirkendall effect, the difference in the fluxes of the two substitutional species requires a net flux of vacancies. The net vacancy flux requires continuous net vacancy generation on one side of the markers and vacancy destruction on the other side (mechanisms of vacancy generation are discussed in Section 11.4). Vacancy creation and destruction can occur by means of dislocation climb and is illustrated in Fig. 3.36 for edge dislocations. Vacancy destruction occurs when atoms from the extra planes associated with these dislocations fill the incoming vacancies and the extra planes shrink (i.e., the dislocations climb as on the left side in Fig. 3.36 toward which the marker is moving). Creation occurs by the reverse process, where the extra planes expand as atoms are added to them in order to form vacancies, as on the right side of Fig. 3.36. This contraction and expansion causes a mass flow that is revealed by the motion of embedded inert markers, as indicated in Fig. 3.3 [4]. 

It is well known that a flow-equilibrium must be treated by the methods of irreversible thermodynamics. In the case of the PDC-column, principally three flows have to be considered within the transport zone (1) the mass flow of the transported P-mer from the sol into the gel (2) the mass flow of this P-mer from the gel into the sol and (3) the flow of free energy from the column liquid into the gel layer required for the maintenance of the flow-equilibrium. If these flows and the corresponding potentials could be expressed analytically by means of molecular parameters, the flow-equilibrium 18) could be calculated by the usual methods 19). However, such a direct way would doubtless be very cumbersome because the system is very complicated (cf. above). These difficulties can be avoided in a purely phenomenological theory, based on perturbation calculus applied to the integrated transport Eq. (3 b) of the PDC-column in a reversible-thermodynamic equilibrium. 

It is well-known that the entropy production (150 is minimal in a flow-equilibrium where all mass-flow vanish, whereas the third flow of free energy remains 18,19). In the vicinity of the reversible-equilibrium, the relations... 

Consideration of Eqs. (29) and (32) shows that the mechanical energy equation involves only the recoverable or reversible work. In order to calculate this term on the average, however, it is necessary to compute the total work done W and subtract from it the part lost due to friction or the irreversible work F. If Eq. (60) is applied to steady flow in a pipe and divided by the mass flow rate, the following per unit mass form is obtained,... 

It will be seen from Fig. 9.30 that the buoyancy forces increase the velocity near the hotter wall (at Y = 1). Since the total mass flow rate is fixed, the increase in velocity near the hot wall is associated with a decrease in velocity near the cooler wall (at Y = 0). As the parameter GrjtRe increases, the velocity profiles become increasingly distorted and at high values of GrjIRe flow reversal can occur adjacent to the cooler wall, i.e., a downward flow can occur near the cooler wail. The condition under whjfch such a reverse flow occurs can be deduced by considering the shear... 

It is interesting to note that in the limit of rapid flow reversal the reverse flow reactor and the countercurrent fixed-bed reactor show completely similar temperature and conversion profiles [44]. This can be understood with the help of Fig. 25 With rapid flow reversal the catalyst temperature will remain constant due to the large heat capacity of the packing while the gas temperature will be below the catalyst temperature in the respective feed section and above in the exit section (Fig. 25B). This behavior is completely similar to that of a countercurrent fixed-bed reactor, where the catalyst is placed at the separating walls between the up and down flowing gas (Fig. 25C). It only has to be considered that instead of pushing the reacting gas for a short period in one and for another period in the other direction, now half of the mass flow will go per-... 

A stream of air at 10 baT and 800 K is mixed with another stream of air at 1 bar and 300 K i three times the mass flow rate. If this process is accomplished reversibly and adiabatically, what the temperature and pressure of the resulting air stream Assume air an ideal gas for whi/ CP = (7/2 )R. 

An operating parameter that must be considered in the context of reversibility is mass flow of analyte to the sensor. For reversible interactions where the response depends on an equilibrium distribution process, response is a function of analyte concentration and is independent of flow rate. This holds true provided the analyte concentration remains constant long enough for equilibrium to be attained higher rates of delivery of analyte to the sensor can result in more r id attainment of equilibrium but will not change the magnitude of the equilibrium response. 

The ability to capture the hot spot within the bed by flow reversal rehes on the large difference in the characteristic time for convective mass (flow) and conductive energy transport. Flow switching can be easily accomplished, as this occurs on a time-scale that is much shorter than the characteristic time of transit of a creeping hot spot to traverse the length of the reactor. 

A very important special case of the polytropic flow equation (5.25) is that describing a reversible, adiabatic expansion, where no heat is exchanged with the surroundings, i.e. an isentropic expansion. In this case, the ratio of specific heats, y, is substituted for n in the mass-flow equation ... 

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