The Damköhler Number is defined as the ratio of which quantities, evaluated at the entrance?

The Damköhler Number is defined as the ratio of which quantities, evaluated at the entrance?

• A. Rate of diffusion of A to the rate of reaction of A
• B. Rate of reaction of A to the rate of convective transport of A
• C. Temperature difference to pressure difference
• D. Concentration of A to flow rate of the reactor

Answer: (B)

The essence is a comparison of time scales: how fast A reacts versus how quickly A is carried through the reactor by the flow. The Damköhler number expresses that ratio, using conditions at the inlet where the feed concentration is known. If A reacts quickly compared to how fast it is convected (Da large), most A is consumed near the entrance; if A is convected faster than it reacts (Da small), only a small portion reacts before being carried farther. For a simple first-order reaction, the inlet reaction rate is r_A,in = k C_A0, while the convective transport rate is tied to the flow delivering A, proportional to Q C_A0 (or, in terms of residence time τ = V/Q, Da ≈ k τ). This makes the Damköhler number the ratio of the rate of reaction to the rate of convective transport, evaluated at the entrance.

The essence is a comparison of time scales: how fast A reacts versus how quickly A is carried through the reactor by the flow. The Damköhler number expresses that ratio, using conditions at the inlet where the feed concentration is known. If A reacts quickly compared to how fast it is convected (Da large), most A is consumed near the entrance; if A is convected faster than it reacts (Da small), only a small portion reacts before being carried farther. For a simple first-order reaction, the inlet reaction rate is r_A,in = k C_A0, while the convective transport rate is tied to the flow delivering A, proportional to Q C_A0 (or, in terms of residence time τ = V/Q, Da ≈ k τ). This makes the Damköhler number the ratio of the rate of reaction to the rate of convective transport, evaluated at the entrance.