Turgor is the driving force of plant growth, making possible for roots to overcome soil resistance or for stems to counteract gravity. Maintaining a constant growth rate while avoiding the cell content dilution, which would progressively stop the inward water flux, imposes the production or import of osmolytes in proportion to the increase of volume. We coin this phenomenon stationary osmoregulation. The article explores the quantitative consequences of this hypothesis on the interaction of a cylindrical cell growing axially against an obstacle.

An instantaneous axial compression of a pressurized cylindrical cell generates a force and a pressure jump which both decrease toward a lower value once water has flowed out of the cell to reach the water potential equilibrium. In a first part, the article derives analytical formula for these force and over-pressure both before and after relaxation. In a second part, we describe how the coupling of the Lockhart's growth law with the stationary osmoregulation hypothesis predicts a transient slowdown in growth due to contact before a re-acceleration in growth. We finally compare these predictions with the output of an elastic growth model which ignores the osmotic origin of growth: models only match in the early phase of contact for high stiffness obstacle.