Nonlinear Dynamics

, Volume 60, Issue 1, pp 207–216

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

Original Paper

DOI: 10.1007/s11071-009-9590-0

Cite this article as:
Ionescu, C. & Tenreiro Machado, J. Nonlinear Dyn (2010) 60: 207. doi:10.1007/s11071-009-9590-0

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.

Keywords

Fractal Impedance Constant-phase behavior Power-law Leaf Frequency domain Hydraulics Mechanics 

Nomenclature

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)

cx

capacity per distance unit (l⋅m/kPa)

c*

the complex velocity of wave propagation

f

frequency (Hz)

gx

conductance per distance unit (l⋅m/kPa)

i

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

lx

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

p

pressure (kPa)

q

flow (l/s)

r

radial coordinate

rx

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

Ce

compliance (l/kPa)

J

Bessel function

airway length (m)

Le

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)

Re

resistance (kPa⋅s/l)

R

airway inner radius (m)

Z

impedance (kPa⋅s/l)

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Electrical Energy, Systems and AutomationGhent UniversityGentBelgium
  2. 2.Department of Electrical EngineeringInstitute of Engineering of PortoPortoPortugal