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Mechanical properties and impedance model for the branching network of the sapping system in the leaf of Hydrangea Macrophylla

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Abstract

An electrical analogue model has been developed based on main leaf hydraulics characteristics and intrinsic geometry. The simulations show good qualitative agreements with specialized literature reports. The constant-phase behavior and the variation with ambient temperature of the frequency response of the leaf impedance are assessed by means of simulation studies.

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Abbreviations

δ :

Womersley parameter = \(R\sqrt{\omega \rho /\mu}\)

ε0′,ε10′:

phase angles of the complex form of Bessel functions of the first kind and orders 0, respectively 1 (rad)

μ :

dynamic viscosity (kg/m⋅s)

θ :

circular coordinate

ρ :

sap density (kg/m3)

ω :

circular frequency (rad/s)

c x :

capacity per distance unit (l⋅m/kPa)

c * :

the complex velocity of wave propagation

f :

frequency (Hz)

g x :

conductance per distance unit (l⋅m/kPa)

i :

imaginary unit\({}=\sqrt{-1}\)

l x :

inductance per distance unit (kPa⋅m⋅s2/l)

p :

pressure (kPa)

q :

flow (l/s)

r :

radial coordinate

r x :

resistance per distance unit (kPa⋅m⋅s/l)

t :

time (s)

u,v,w:

velocity components in the radial, circular, and axial directions, respectively

z :

axial coordinate

y :

ratio of radial position to radius=r/R

C e :

compliance (l/kPa)

J :

Bessel function

ℓ :

airway length (m)

L e :

inertance (kPa⋅s2/l)

M :

modulus for pressure gradient (kPa)

M0′,M10′:

modulus of the complex form of Bessel functions of rank 1 and orders 0, respectively 1

P :

pressure (kPa)

Q :

flow (l/s)

R e :

resistance (kPa⋅s/l)

R :

airway inner radius (m)

Z :

impedance (kPa⋅s/l)

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Authors and Affiliations

  1. Department of Electrical Energy, Systems and Automation, Ghent University, Technologiepark 913, B9052, Gent, Belgium

    Clara Ionescu

  2. Department of Electrical Engineering, Institute of Engineering of Porto, Porto, Portugal

    J. Tenreiro Machado

Authors
  1. Clara Ionescu
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  2. J. Tenreiro Machado
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Correspondence to Clara Ionescu.

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Ionescu, C., Tenreiro Machado, J. Mechanical properties and impedance model for the branching network of the sapping system in the leaf of Hydrangea Macrophylla . Nonlinear Dyn 60, 207–216 (2010). https://doi.org/10.1007/s11071-009-9590-0

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