ISSN print edition: 0366-6352 ISSN electronic edition: 1336-9075 Registr. No.: MK SR 9/7 Published monthly

Analytical solution of transport properties in the electrolyte of a li-ion battery

Abla Hamada, Afaf Djaraoui, Djamel Haddad, and Kafia Oulmi

Laboratory of Advanced Solutions in Process Engineering, Process Engineering Department, Faculty of Technology, University of Batna 2 Mostefa Ben Boulaid, Batna, Algeria

E-mail: a.hamada@univ-batna2.dz

Received: 30 May 2025  Accepted: 12 September 2025

Abstract:

This work presents an analytical solution to describe lithium-ion transport phenomena in the electrolyte of lithium-ion batteries. The study focuses on key parameters such as lithium-ion concentration, electric field distribution, and ionic flux under realistic discharge conditions. The governing transport equations were solved using the Laplace transform method, which offers explicit and tractable expressions for all target variables. The analysis considers real boundary conditions that reflect practical operation, enhancing the accuracy and applicability of the model. The time-dependent evolution of lithium-ion concentration was examined at different positions within the electrolyte, particularly near the anode and cathode interfaces, under a range of applied current values. The results reveal significant changes in concentration profiles with increasing current, showing stronger gradients and depletion zones near the anode, and corresponding accumulation at the cathode. The electric field and ionic flux were also derived and analyzed under the same current conditions, demonstrating how internal electric forces and ionic transport respond to variations in applied current. This analytical framework improves the understanding of lithium-ion battery behavior and provides a useful tool for predicting performance, reducing safety risks, and improving the design of more efficient and durable battery systems.

Keywords: Concentration profile; 1D model; Li-ion battery; Analytical solution; Laplace transform method

Full paper is available at www.springerlink.com.

DOI: 10.1007/s11696-025-04386-w

Chemical Papers 80 (1) 233–243 (2026)