  The design of artificial microswimmers has generated significant research
interest in recent years, for promise in applications such as nanomotors and
targeted drug-delivery. However, many current designs suffer from a common
problem, namely the swimmers remain in the fluid indefinitely, posing risks of
clogging and damage. Inspired by recently proposed experimental designs, we
investigate mathematically the dynamics of degradable active particles. We
develop and compare two distinct chemical models for the decay of a swimmer,
taking into account the material composition and nature of the chemical or
enzymatic reaction at its surface. These include a model for dissolution
without a reaction, as well as models for a reacting swimmer studied in the
limit of large and small Damk\"ohler number. A new dimensionless parameter
emerges that allows the classification of colloids into ballistic and diffusive
type. Using this parameter, we perform an asymptotic analysis to derive
expressions for colloid lifetimes and their total mean-squared displacement
from release and validate these by numerical Monte Carlo simulations of the
associated Langevin dynamics. Supported by general scaling relationships, our
theoretical results provide new insight into the experimental applicability of
a wide range of designs for degradable active colloids.
