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The hydrologic system
Published in Stephen A. Thompson, Hydrology for Water Management, 2017
The term dynamic equilibrium or steady state describes a certain condition of a system. Dynamic equilibrium is when a system, technically the ‘state’ of the system, does not change with time. In other words, a dynamic-equilibrium system is time-invariant, and inputs (I) to the system equal outputs (Q) from the system (Singh 1988). An important result of this condition is that the amount of the physical quantity in storage (S) remains constant. In most hydrologic systems, dynamic equilibrium usually obtains only when inputs and outputs are measured over sufficiently long periods of time so that short-term variations balance out. A simple way to visualize dynamic equilibrium is to imagine a lake with a stream flowing in and a stream flowing out. If you photograph this stream-lake system one day, and then photograph it say a week later, it might look the same in the two pictures (equilibrium), but tremendous quantities of mass and energy have passed through the system (dynamic) during that period. Dynamic equilibrium is easiest to understand, and is often useful as a first approximation of the operation of a complex system. In hydrologic analyses, time-invariance is called a steady condition, while a system that changes with time is non-steady. We’ll consider both time and space domains as a characteristic of hydrologic models in the next section.
Batch adsorption isotherm models applied in single and multicomponent adsorption systems – a review
Published in Journal of Dispersion Science and Technology, 2021
Beniah Obinna Isiuku, Paul C. Okonkwo, Chibuike Dickson Emeagwara
An adsorption isotherm is a plot that describes the phenomenon that controls the movement of adsorbate particles from the bulk phase to the porous solid adsorbent phase at constant pH and temperature.[7] Adsorption equilibrium is the state during adsorption at which the ratio of the concentration of the adsorbate in the adsorbent phase to that of the bulk phase is in dynamic equilibrium after contact between the two phases has been for a long time. It is also defined as the state of dynamic equilibrium when the rates of adsorption and desorption are equal. The relationship is expressed as a plot of the adsorbate concentration in the solid adsorbent phase (adsorption capacity) against the adsorbate concentration in the bulk phase.[12] Adsorbent physicochemical parameters coupled with basic thermodynamic presumptions give ideas about mechanism of adsorption, properties of adsorbent surface and the degree of affinity of the adsorbate to the adsorbent.[7] Many isotherms have been developed based on three approaches – kinetic consideration, thermodynamics and potential theory.[7] The first approach is kinetic; looks at adsorption equilibrium. The second approach which is thermodynamic provides a framework for the development of various isotherm models.[27,28] Potential theory, which is the third approach, gives major ideas on how to generate characteristic isotherm curves.[29] The various isotherm models that have been formulated include: