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            <title xml:lang="en">Continuum mechanics at nanoscale. A tool to study trees' watering and recovery</title>
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            <idno type="stamp" n="EC-MARSEILLE">Ecole Centrale de Marseille</idno>
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            <idno type="stamp" n="M2P2">Mécanique Modélisation et Procédés Propres</idno>
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            <note type="commentary">The paper is a review and overlap of my different papers about the watering of  trees as a mathematical development of my paper in The Journal of Theoretical Biology. These results are presented together with new researches: transfer of liquid water and vapour between xylem microtubes, an explanation of ultrasounds generated in the watering network considered as sound pipes, numerical calculations of flows in thin liquid films and of Poiseuille flows in xylem microtubes, an estimation of the velocity for the ascent of crude sap and of the recovery time of trees during the spring period.</note>
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                <term xml:lang="en"> liquid-nanofilm</term>
                <term xml:lang="en">Disjoining pressure</term>
                <term xml:lang="en"> tree watering</term>
                <term xml:lang="en"> tree recovery</term>
                <term xml:lang="en"> cohesion-tension theory.</term>
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              <p>The cohesion-tension theory expounds the crude sap ascent thanks to the negative pressure generated by evaporation of water from leaves. Nevertheless, trees pose multiple challenges and seem to live in unphysical conditions: the negative pressure increases cavitation; it is possible to obtain a water equilibrium between connected parts where one is at a positive pressure and the other one is at negative pressure; no theory is able to satisfactorily account for the refilling of vessels after embolism events.A theoretical form of our paper in the Journal of Theoretical Biology is proposed together with new results: a continuum mechanics model of the disjoining pressure concept refers to the Derjaguin School of physical chemistry. A comparison between liquid behaviour both in tight-filled microtubes and in liquid thin-films is offered when the pressure is negative in liquid bulks and is positive in liquid thin-films and vapour bulks. In embolized xylem microtubes, when the air-vapour pocket pressure is greater than the air-vapour bulk pressure, a refilling flow occurs between the air-vapour domains to empty the air-vapour pockets although the liquid-bulk pressure remains negative. The model has a limit of validity taking the maximal size of trees into account. These results drop inkling that the disjoining pressure is an efficient tool to study biological liquids in contact with substrates at a nanoscale range.</p>
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