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Water Transport Through Plant Cells and Cell Walls: Theoretical Development¹

ABSTRACT

An increasing body of experimental evidence indicates that cell walls constitute an important pathway for water movement through plant tissues. Therefore, the present paper develops a mathematical description of water transport which allows for a water flux in the cell walls that does not necessarily traverse the cell membranes. The result is two coupled diffusion equations, one describing flow in the cell wall pathway and the other describing flow in the parallel cell to cell pathway. Using a resistance-capacitance network analogy, the various parameters in the governing equations are identified as per cell resistances to water flow and per cell water capacities in and between the two parallel pathways.

The theory is applied to a hypothetical water transport process in a sheet of plant tissue. A general closed-form solution to the governing equations is obtained in the form of two double Fourier series, and realistic values are obtained from the literature for the various parameters. The theory predicts tentatively that water flows in the cell to cell and cell wall pathways will be comparable in magnitude and highly coupled, with each cell remaining in local equilibrium with the wall material external to its membrane. In this case, the overall transport process can be described by a single diffusion equation which is derived along with an expression for the free energy diffusivity of the combined pathways. The results of this study are in agreement with and bring together several past experimental studies by showing that a significant portion of the water flux traversing a plant tissue can occur in the cell wall pathway with the overall flow process still obeying simple diffusion kinetics. Whenever this occurs, the mathematical treatment of water transport in plant tissue will be simplified considerably.

¹ Contribution of the Civil Engineering Department and the Mathematics Department, Auburn University, Auburn, Ala. 36830.

² Assistant Professor of Civil Engineering and Professor of Mathematics, respectively, Auburn University.

Received for publication February 4, 1974. Accepted for publication April 9, 1974.

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