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| The '''Damköhler numbers''' ('''Da''') are [[dimensionless number]]s used in [[chemical engineering]] to relate the [[chemical reaction]] timescale ([[reaction rate]]) to the [[transport phenomena]] rate occurring in a system. It is named after German chemist [[Gerhard Damköhler]].
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| In its most commonly used form, the Damköhler number relates the reaction timescale to the [[convection]] times scale, [[flow rate]], through the [[reactor]] for continuous or [[Semibatch reactor|semibatch]] chemical processes:
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| : <math>\mathrm{Da} = \frac{ \text{reaction rate} }{ \text{convective mass transport rate} }</math>
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| <!--or as
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| : <math>\mathrm{Da} = \frac{ \text{characteristic fluid time} }{ \text{characteristic chemical reaction time} }</math> -->
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| In reacting systems that include interphase mass transport, the '''second Damköhler number''' ('''Da<sub>II</sub>''') is defined as the ratio of the chemical reaction rate to the mass transfer rate
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| : <math>\mathrm{Da}_{\mathrm{II}} = \frac{ \text{reaction rate} }{ \text{diffusive mass transfer rate} }</math>
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| Since the reaction timescale is determined by the reaction rate, the exact formula for the Damköhler number varies according to the raw law equation. For a general chemical reaction A → B of nth [[Order of reaction|order]], the Damköhler number for a convective flow system is defined as:
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| : <math>\mathrm{Da} = k C_0^{\ n-1}\tau</math>
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| where:
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| * ''k'' = [[chemical kinetics|kinetics]] [[reaction rate constant]]
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| * ''C''<sub>0</sub> = initial concentration
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| * ''n'' = [[reaction order]]
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| * <math>\tau</math> = mean [[residence time]] or '''space time'''
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| On the other hand, the second Damköhler number is defined as:
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| : <math>\mathrm{Da}_{\mathrm{II}} = \frac{k C_0^{n-1}}{k_g a}</math>
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| where
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| * ''k<sub>g</sub>'' is the global mass transport coefficient
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| * ''a'' is the interfacial area
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| The value of Da provides a quick estimate of the degree of [[Conversion (chemistry)|conversion]] that can be achieved. As a [[rule of thumb]], when Da is less than 0.1 a conversion of less than 10% is achieved,and when Da is greater than 10 a conversion of more than 90% is expected.<ref name="Fogler">{{cite book |last=Fogler |first=Scott |title=Elements of Chemical Reaction Engineering |location=Upper Saddle River, NJ |publisher=Pearson Education |year=2006 |edition=4th |isbn=0-13-047394-4 }}</ref>
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| ==References==
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| {{reflist}}
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| {{NonDimFluMech}}
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| {{DEFAULTSORT:Damkohler numbers}}
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| [[Category:Catalysis]]
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| [[Category:Chemical engineering]]
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| [[Category:Dimensionless numbers of chemistry]]
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| [[Category:Dimensionless numbers of fluid mechanics]] | |
| [[Category:Fluid dynamics]]
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