A　non-equilibrium　model　for　adsorption　process　of　single　ionic　species　onto　solid　adsorbent　has　been　proposed　within　the　framework　of　irreversible　thermodynamics.　Based　on　Ziegler’s　principle　of　maximal　rate　of　dissipation　and　combining　mass　balance　equation　of　ionic　species,　a　theoretical　formulation　of　general　description　for　non-equilibrium　adsorption　was　obtained.　Fatherly,　the　dispersion-type　energy　functions　included　two　Helmholtz　free　energy　and　one　dissipation　rate　density　were　constructed　by　complementary　error　function,　which　introduced　into　the　general　form　of　non-equilibrium　model　to　achieve　the　specific　form.　The　predicted　results　of　the　presented　model　were　compared　with　the　tested　kinetics　of　adsorption　processes　of　Pb2+　and　Cd2+　onto　Beidellite,　which　provided　a　better　agreement　with　the　experimental　data.　©　Springer　Nature　Singapore　Pte　Ltd.　2019.