The condition you are describing relates to a state often found in systems that are at equilibrium, particularly in the context of diffusion and transport. This state can be characterized by the following concepts:
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Dynamic Equilibrium: In a dynamic equilibrium, particles are continuously moving and interacting, but there is no net change in concentration over time for any of the components involved. For example, in a solution, molecules of solute may still move in and out of different regions, but the overall concentration throughout the solution remains constant.
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Steady-State Diffusion: In the case of steady-state diffusion, particles such as atoms or molecules are moving through a medium (e.g., gases, liquids, or solids) but the concentration gradient does not change over time. While particles continuously random walk through space, any influx of particles into a certain volume equals the outflux, leading to no overall change in concentration.
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Brownian Motion: This random movement of particles (such as colloidal particles in a fluid) is a physical phenomenon wherein particles move chaotically due to collisions with surrounding molecules. Despite this random movement, if the system is well-mixed and at equilibrium, the average concentration can remain constant.
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Concentration Gradient: Even if individual particles move randomly, if there is a concentration gradient present, particles will tend to move from areas of higher concentration to lower concentration, but in a fully mixed scenario (equilibrium), the overall concentration remains unchanged.
In summary, the continuous, random movement of particles without an overall change in concentration can be effectively described by the principles of dynamic equilibrium or steady-state diffusion.