Specific shear-dependent viscoelastic third-grade fluid model

A specific modified constitutive equation for a third-grade fluid is proposed so that the model be suitable for applications where shear-thinning or shear-thickening may occur. For that, we use the Cosserat theory approach reducing the exact three-dimensional equations to a system depending only on time and on a single spatial variable. This one-dimensional system is obtained by integrating the linear momentum equation over the cross-section of the tube, taking a velocity field approximation provided by the Cosserat theory. From this reduced system, we obtain the unsteady equations for the wall shear stress and mean pressure gradient depending on the volume flow rate, Womersley number, viscoelastic coefficient and flow index over a finite section of the tube geometry with constant circular cross-section.

Leaf water potential and sap flow as indicators of water stress in Crimson ‘seedless’ grapevines under different irrigation strategies

Vitis vinifera L. cv. Crimson Seedless is a late season red table grape developed in 1989, with a high market value and increasingly cultivated under protected environments to extend the availability of seedless table grapes into the late fall. The purpose of this work was to evaluate leaf water potential and sap flow as indicators of water stress in Crimson Seedless vines under standard and reduced irrigation strategy, consisting of 70 % of the standard irrigation depth. Additionally, two sub-treatments were applied, consisting of normal irrigation throughout the growing season and a short irrigation induced stress period between veraison and harvest. Leaf water potential measurements coherently signaled crop-available water variations caused by different irrigation treatments, suggesting that this plant-based method can be reliably used to identify water-stress conditions. The use of sap flow density data to establish a ratio based on a reference ‘well irrigated vine’ and less irrigated vines can potentially be used to signal differences in the transpiration rates, which may be suitable for improving irrigation management strategies while preventing undesirable levels of water stress. Although all four irrigation strategies resulted in the production of quality table grapes, significant differences (p ≤ 0.05) were found in both berry weight and sugar content between the standard irrigation and reduced irrigation treatments. Reduced irrigation increased slightly the average berry size as well as sugar content and technical maturity index. The 2-week irrigation stress period had a negative effect on these parameters.

Leaf water potential and sap flow as indicators of water stress in Crimson 'seedless' grapevines under different irrigation strategies

Abstract Vitis vinifera L. cv. Crimson Seedless is a late season red table grape developed in 1989, with a high market value and increasingly cultivated under protected environments to extend the availability of seedless table grapes into the late fall. The purpose of this work was to evaluate leaf water potential and sap flow as indicators of water stress in Crimson Seedless vines under standard and reduced irrigation strategy, consisting of 70 % of the standard irrigation depth. Additionally, two sub-treatments were applied, consisting of normal irrigation throughout the growing season and a short irrigation induced stress period between veraison and harvest. Leaf water potential measurements coherently signaled crop-available water variations caused by different irrigation treatments, suggesting that this plant-based method can be reliably used to identify water-stress conditions. The use of sap flow density data to establish a ratio based on a reference ‘well irrigated vine’ and less irrigated vines can potentially be used to signal differences in the transpiration rates, which may be suitable for improving irrigation management strategies while preventing undesirable levels of water stress. Although all four irrigation strategies resulted in the production of quality table grapes, significant differences (p ≤ 0.05) were found in both berry weight and sugar content between the standard irrigation and reduced irrigation treatments. Reduced irrigation increased slightly the average berry size as well as sugar content and technical maturity index. The 2-week irrigation stress period had a negative effect on these parameters.