quasisteady

Quasisteady, often written quasi-steady, describes a regime in dynamic systems where the evolution is slow enough that, at each instant, the internal state is approximately in a steady state despite ongoing change. It is used to justify simplifying assumptions that reduce time-dependent problems to a sequence of steady problems.

The key idea is a separation of timescales. If the system’s characteristic relaxation time, tau, is small compared with the timescale over which external conditions vary, T, such that T is much larger than tau, the system responds rapidly enough to appear steady as the external conditions change slowly. In practice, this allows setting time derivatives to zero or treating parameters as slowly varying, leading to a quasi-steady or quasi-static formulation.

Quasisteady methods are common in heat and mass transfer, chemical kinetics, electrochemistry, and fluid dynamics. Examples include heat conduction with slowly changing boundary temperatures, diffusion with slowly moving boundaries, and chemical reactors where fast internal equilibria adjust quickly to slow changes in feed or temperature. In circuit analysis with slowly varying inputs, currents or voltages may be treated as if in steady state at each moment.

Limitations arise when external forcing occurs on timescales comparable to or shorter than the system’s relaxation time, or when transient dynamics are essential. In these cases, the quasi-steady approximation can misrepresent behavior, and full time-dependent or transient analyses are required. Quasisteady is closely related to quasi-static concepts in thermodynamics and to the quasi-steady-state approximation used in chemical kinetics.