wellmmixed

Wellmixed or well-mixed is a term used in physics, chemistry, biology, and related fields to describe a system in which all constituents are uniformly distributed at any given time. Under a well-mixed assumption, properties such as concentration, temperature, and chemical composition are spatially homogeneous, so they do not vary with position within the system.

In chemical engineering and reactor theory, a well-mixed reactor (often called a continuously stirred tank reactor, or CSTR) is modeled as having instantaneous homogenization of its contents. This leads to a set of ordinary differential equations that describe the time evolution of species concentrations, rather than partial differential equations that would be required to account for spatial gradients. The well-mixed assumption is contrasted with plug-flow or diffusion-limited models, where spatial variation is essential.

In stochastic chemical kinetics and population biology, well-mixed models assume that reactions occur with probabilities determined only by the current counts or concentrations, independent of location. This enables the use of stochastic simulation algorithms, such as the Gillespie algorithm, and supports deterministic rate equations in large populations. The assumption simplifies analysis but may break down in large volumes, highly heterogeneous media, or systems with slow mixing.

In ecology and population genetics, a well-mixed population refers to a situation where individuals interact and mate with equal probability across the entire population, effectively ignoring spatial structure. This leads to panmictic assumptions and standard Hardy–Weinberg expectations in genetic models.

Limitations of the well-mixed assumption arise when mixing is incomplete, diffusion is slow, or spatial structure influences dynamics, necessitating spatially explicit or reaction-diffusion approaches.