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I am in the process of writing a model for the diffusion of a chemical in an aqueous medium. Typically, to do this, one would use the diffusion equation

$$\frac{\partial}{\partial t}U=\gamma \nabla ^2 U$$

where $U(\mathbf{x},t)$ is the concentration of the chemical at position $\mathbf{x}$ and time $t$, and $\gamma$ is a positive constant that represents the rate at which the spacial curvature of the concentration function is reduced.

The quirk in the model I am interested in producing is that I would like to include the half life of the chemical in my partial differential equation. To do this, I have concidered including a term to model the removal of the chemical from the system at a rate proportional to to the concentration of the chemical. This modified PDE looks like

$$\frac{\partial}{\partial t}U=\gamma \nabla ^2 U - \delta U$$

where $\delta$ is a positive constant between $0$ and $1$.

Is this a reasonable way of modeling chemical degradation? How would I go about determining the relation between the degradation rate $\delta$ and the half life $\lambda$ of the chemical?

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Your equations look about right (of course, depending on the degradation reaction – the form is correct if it is really a spontaneous decay). However, for dimensional reasons $\delta$ must have units of inverse time, so it cannot be a "number between 0 and 1", but is rather a positive inverse time.

To connect the half life and the decay rate you can consider the uniform case $U(x, t) = U(t)$, which makes $\Delta U = 0$, so you just end up with the equation: $$ \partial_t U(t) = - \delta U(t). $$ The solution of this equation is $U(t) = U(0) e^{-\delta t}$, so the half-life time $T_{\frac 1 2}$ is connected to the decay rate by: $$ e^{-\delta T_{\frac 1 2}} = \frac 1 2. $$

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