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Spontaneous imbibition of liquids in glass-fiber wicks, where a liquid-front progresses during the wicknig process, is investigated experimentally and modeled using the concepts of single-phase flow in porous media. In order to have an accurate validation of the proposed model, a well-characterized glass-fiber wick and wicking liquid are used to plot the liquid-front of absorbed liquid as a function of time. The experimental outcomes are fcompared with predictions by the proposed analytical solution obtained by combining Darcy's law with the continuity equation and a capillary (suction) pressure formula imposed on the liquid front. The theoretical permeability and capillary-pressure formula used in the model are obtained by treating the wick as a bundle of parallel fibers. All properties of the wicking liquid and wick used in the experiments, including the porosity, permeability, viscosity, surface tension and contact angle, are measured independently. The proposed theoretical model is found to compare favorably with experiments without the use of any fitting parameters. Though more experiments are being done to further test the analytical model, by all indications, it has potential of becoming a powerful practical tool to predict wicking in industrial wicks manufactured from parallel tows of glass fiber.