Modelling of carrot tissue as a fluid-filled foam

Experimental values of the stiffness of carrot tissue were compared with the predictions from models of fluid-filled closed cell foams. Compared to an experimental value of 7 MPa for fresh carrot, predictions gave moduli in the range 2 to 33 MPa based on a compressible fluid, an isotonic state turgor pressure of 0.8 MPa, a cell wall modulus of 100 MPa and cell lengths from 54 to 3 times the wall thickness. The modulus was predicted to increase linearly with turgor pressure in agreement with experiment for turgor pressures up to about 1 MPa, whereafter the experimental modulus increased more sharply, reaching a value of 14 MPa at a turgor pressure of 2.1 MPa, closer to the predicted rate of increase in an earlier shell model. Predictions based on an incompressible fluid gave initial and equilibrium moduli of 14 and 2 MPa, respectively, in agreement with the experimental values at high and low levels of turgor, again assuming a cell wall modulus of 100 MPa but requiring small cells of length ratio less than three times their wall thickness.