Dimensionless number Damkohler

From the above nondimensionalized boundary condition, we can define the dimensionless number, Damkohler number, as... 

Different kinetic dimensionless numbers These can also be used depending on the conditions of the process. The most important is the Damkohler number. 

Mathematicians have their names attached to theorems, lemmas and even conjectures naturalists have species and genera called after them physicists have their principles and chemists their reactions and reagents. Engineers can claim the dimensionless parameters, for they, who, in their function as designers, have often to work with units, appreciate more than anyone the conceptual beauty of the dimensionless number, invested as it is with full contextual meaning and magnitude. I submit that it would be more than appropriate to call this transfer parameter the Davidson number, for who has done more to elucidate the mechanism of this transfer process than John Davidson Damkohler has preempted the initial letters Da, but that is no matter, for transfer gives us Tr and we immediately think of Trinity and its present Vice-Master. 

Other factors limiting the overall rate can be external or internal mass transfer, or axial dispersion in a fixed-bed reactor. Pertinent dimensionless numbers are the Biot number Bi, the Damkohler number of the second kind Dan, or the Bodenstein number Bo (Eqs. (5.46)—(5.48)]. 

For reactions following an nth-order kinetic scheme, the reaction rate is often characterized by a dimensionless number the Damkohler criterion [14] ... 

Damkohler s original analysis [2] resulted in four dimensionless numbers which today are referred to as Damkohler numbers I through to IV and are given by... 

The power products formed with the aid of the dimensional matrix can be traced back to known, mostly named numbers (Re, Pr, Sc). The only new dimensionless number here is the Damkohler number, Da, which will be discussed later. The numbers obtained, together with the four anticipated trivial numbers, give the following dimensional-analytical framework ... 

G. Damkohler [113] used this possibility to develop Navier-Stockes differential equations of the mass and heat transfer for the case of an adiabatic reaction. Analytical solution of these differential equations is not possible. However, if they are made dimensionless, it becomes apparent that the pi-space is formed by the five dimensionless numbers listed below ... 

Although Damkohler traced numbers I to IV back to the above combinations of named dimensionless numbers known at that time, numbers I to IV have come to be known as the four Damkohler numbers Da to DaIV in chemical literature. We will not identify them in this way, instead we will only refer to the new, genuine reaction kinetic pi-number... 

From 7.136 it is clear that the concentration profile within the film depends on a dimensionless number, completely analogous to the Damkohler number (7.100) of Section 7.3.1.2 ... 

The Damkohler is a dimensionless number that can give us a quick estimate of the degree of conversion that can be achieved in continuous-flow reactions. The Damkdhler number is the ratio of the rate of reaction of A to the rate of convective transport of A at the entrance to the reactor. For first- and second-order ineversible reactions the Damkohler numbers are... 

The ratio of time constants for mixing and reaction defines the Damkohler number or the micro-mixing modulus, a dimensionless number shown in... 

Damkohler I number. A further dimensionless number is the Damkohler I number (Boucher and Alves 1959 Lassey and Blattner 1988 Bowman and Willett 1991 Lasaga... 

Answer The mass transfer Peclet number scales as Lpfr, and the interpellet Damkohler number scales as Lpp,. Therefore, PeMi = 150 and A mterpeiiet = 60. The other three dimensionless numbers are unaffected when the reactor length is doubled. 

Dimensionless numbers are introduced, with the Damkohler and Fourier numbers, by using the thickness of the sample, a characteristic time and the temperature difference which are considered as being characteristics of the process. 

The mass transfer in forced flow is trade-off between the attainable mass transfer time, t, and the energy input. The nonidentical geometries of the different devices complicate the direct comparison. Therefore, dimensionless numbers are used. The mass transfer performance is characterized by the ratio between the space time of the fluid and the characteristic mass transfer time. This ratio corresponds to the first Damkohler number for mass transfer. Whereas the porosity of a packed bed reactor is mostly in the order of 0.35 < < 0.45 depending on... 

In order to obtain the (mixing-cup and surface) concentration and temperature profiles, the solution of Equations 8.52 and 8.55 requires the calculation of the dimensionless transfer coefficients Sh and Nw, which are in general functions of the Graetz parameters and of the Damkohler number. Correlations for these dimensionless numbers are available in the literature (e.g., Shah and London [39]), for several conditions regarding the degree of profile development, degree of hydrodynamic flow development, and boundary condition at the wall. These features are briefly discussed in the following. 

This mass transfer resistance and the reaction kinetics are usually compared using a dimensionless ratio, Damkohler number. Da, as in Equation 4.49. If Da is greater than unity, then the mass transfer resistance is significant and the reaction of the external diffusion is limited. On the other hand, when Da is less than unity, the reaction, in this case, is surface reaction limited. 

The first inequality characterizes recycle systems with reactant inventory control based on self-regulation. It occurs because the separation section does not allow the reactant to leave the process. Consequently, for given reactant feed flow rate Fq, large reactor volume V or fast kinetics k is necessary to consume the whole amount of reactant fed in the process, thus avoiding reactant accumulation. The above variables are conveniently grouped in the dimensionless plant Damkohler number introduced by Bildea et al. [14] for analysing the... 

We will use these characteristic times to define some dimensionless numbers, such as Damkohler number, Thiele modulus, and Hatta modulus. Here, we will give the broad definitions, and the true meanings will be clear as we move along the chapter ... 

Da mkohler number A dimensionless number. Da, used to relate the rate of a chemical reaction to certain phenomena that occur in the reaction. There are several types of num -bets that ate used whose defliution depends on whether the chemical reaction is related to momentum transfer or to heat transfer. For example, for an nth "order of reaction, the Damkohler number is ... 

The ratio of reaction and permeation rates is critical in designing an MR. Dimensionless numbers are important in parametric analysis of engineering problems. They allow comparison of two systems that are vastly different by combining the parameters of interest. Dimensionless numbers are used to simplify the meaning of the information in scaUng-up the reactor for real flow conditions and to determine the relative significance of the terms in the equations. The Damkohler number (Da) is the ratio of characteristic fluid motion or residence time to the reaction time, and the Peclet number (Pe) defines the ratio of transport rate by convection to diffusion or dispersion (Basile et al, 2008a Battersby et al., 2006 Moon and Park, 2000 Tosti et al., 2009). In the case of an MR, Da and Pe are defined in Equations [11.1] and [11.2]. 

In any circumstances, it can be expected that and (5x are algebraic functions of turbulence length scale and kinetic energy, as well as chemical and molecular quantities of the mixture. Of course, it is expedient to determine these in terms of relevant dimensionless quantities. The simplest possible formula, in the case of very fast chemistry, i.e., large Damkohler number Da = (Sl li)/ SiU ) and large Reynolds Re = ( Ij)/ (<5l Sl) and Peclet numbers, i.e., small Karlovitz number Ka = sjRej/Da will be Sj/Sl =f(u / Sl), but other ratios are also quite likely to play a role in the general case. 

The parameter term (k x) which is called Damkohler Number I, is dimensionless and is now the single governing parameter in the model. This results in a model simplification because originally the three parameters, x, k and Cao. all appeared in the model equation. 

In dimensionless terms, there is a critical value for S (Damkohler number) that makes ignition possible. From Equation (4.23), this qualitatively means that the reaction time must be smaller than the time needed for the diffusion of heat. The pulse of the spark energy must at least be longer than the reaction time. Also, the time for autoignition at a given temperature T is directly related to the reaction time according to Semenov (as reported in Reference [5]) by... 

From the boundary conditions, show the dimensionless parameters that the critical Damkohler number will depend on. 

For first order reaction in a porous slab this problem is solved in P7.03.16. Three dimensionless groups are involved in the representation of behavior when both external and internal diffusion are present, namely, the Thiele number, a Damkohler nunmber and a Biot number. Problem P7.03.16 also relates r)t to the common effectiveness based on the surface concentration,... 

The only two parameters appearing in eqn. (65) are the dispersion number, DjiiL, or inverse Peclet number, and the Damkohler number, or dimensionless rate group, t/jCa," - Solutions to eqn. (65) are therefore functions only of these two groups. If term (4) in eqn. (65) is absent, then... 

---