Biomimetic Groundwork for Thermal Exchange Structures Inspired by Plant Leaf Design
Abstract
:1. Introduction
1.1. Thermal Design Innovation and Biomimetics
1.2. Plant Structures, Leaf Exchange, and Thermodynamics
2. Materials and Methods
- Literature review and identification of botanical case studies pointing to a relation between leaf thermal function and morphology patterns—listed as leaf role models;
- Definition of leaf morphotypes and shape features of interest involved in such relations, presumed relevant for leaf exchange and plant thermal management, based on botany and transfer physics literature;
- Identification of thermal design features and hypotheses abstracted from the leaf literature review—listed as leaf-inspired design principles;
- Biology research addressing one instance of the reviewed case studies, that of sun–shade leaf dimorphism in oak trees. The experimental approach involved shape analysis of oak leaves with single-parameter metrics. This tested the suitability of basic geometrical parameters for differentiating sun and shade leaves (Section 2.1);
- Translation of a subset of design principles into a family of two-dimensional abstract geometries, reflecting leaf “morphotypes” and some results of the shape analysis of oak leaves. Paper models were used as leaf analogs in “proof-of-concept” evaporation tests, to observe and compare the evaporative transfer of these leaf-inspired geometries (Section 2.3).
2.1. Biology Research: Shape Analysis of Oak Leaves
2.2. Biomimetic Design Principles: Abstracted Leaf-Inspired Geometries
2.3. Proof-of-Concept Evaporation Study with Bio-Inspired Paper Models
3. Results
3.1. Biology Research Findings
3.1.1. Leaf Role Models for Evaporative Thermal Design
3.1.2. Quantifying Oak Leaf Dimorphism
3.2. Leaf-Inspired Design Principles
3.2.1. Geometrical Abstraction from Leaf Role Models
3.2.2. Leaf-Inspired Morphotypical Geometries
3.3. Proof-Of-Concept Evaporation Tests
4. Discussion
4.1. Mass Transfer Enhanced by Geometry Dissection
4.2. Biological and Biomimetic Significance
4.2.1. Heterophyllous Leaf Dissection
4.2.2. Sun–Shade Leaf Dimorphism
4.2.3. Marginal Teeth
4.2.4. Leaves from Temperate to Tropical Climates as Exchangers
4.2.5. The Multifactorial and Multifunctional Realm of Leaf Morphology
4.3. Applicability of Shape Parameters
4.3.1. Sun–Shade Leaf Morphology
4.3.2. Shape Parameters Relation to Evaporative Performance
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Leaf Shape Variation | Plant Case Studies, Reported Observations | References |
---|---|---|
Temporal variation: SEASONAL • summer vs. winter heterophylly | Southern coastal violet (Viola septemloba): Developed more lobed leaves in summer, which maintained lower leaf temperatures | [38] |
Spatial variation: GLOBAL • geographical trends • plant local adaptation | Geranium sanguineum: Leaves develop more elongated lobes in drier, continental habitats. | [45] |
Viburnum (Adoxaceae) clade: Leaves in warmer climates are more elongated and entire, overall. | [39] | |
LEAF • developing leaves • margin transpiration | Maple (Acer genus): Greater transpiration at the margins of young leaves; leaves grown in colder environments become more dissected, develop more numerous and larger marginal teeth. | [46,47] |
Elm (Ulmus genus): Leaf tissues with evaporative role develop prematurely at the margins of young leaves. | [43] | |
PLANT CANOPY • sun vs. shade leaf dimorphism | Oak (Quercus genus): Sun leaves have deeper lobes and greater transpiring capacity; transpiring sun leaves reach colder temperatures than shade leaves; sun leaf models in low wind convect heat better, more independently of orientation thanks to sinuses. | [40,48,49,50] |
Combined variation temporal and spatial: PLANT LIFETIME • heteroblasty • young vs. mature plants | Snowflake Aralia (Trevesia palmata): Sun leaves are more dissected; young plants have palmately lobed leaves, mature plants have pseudo-compound leaves. | [51] |
Mulberry (Morus genus): Lobes develop preferentially on leaves’ outer side; many-lobed leaves retain lower temperatures; young plants have more lobed leaves. | [44,52] |
Shape Parameter | Leaf Type | Mean | SD | Dif. | t ratio | Std Err Dif. | df | p | 95% CL Dif. | |
---|---|---|---|---|---|---|---|---|---|---|
Lower | Upper | |||||||||
Perimeter (cm) | SUN | 59 | 24 | 14 | 4.72 | 3.06 | 182.81 | <0.0001 | 8 | 20 |
SHADE | 45 | 19 | ||||||||
LDI (normalized perimeter) | SUN | 89 | 47 | 26 | 4.30 | 6.02 | 184.07 | <0.0001 | 14 | 38 |
SHADE | 63 | 38 | ||||||||
Convexity | SUN | 0.55 | 0.15 | −0.08 | −3.75 | 0.02 | 203.46 | 0.0002 | −0.13 | −0.04 |
SHADE | 0.64 | 0.17 | ||||||||
Roundness | SUN | 0.60 | 0.08 | −0.04 | −3.28 | 0.01 | 186.64 | 0.001 | −0.07 | −0.02 |
SHADE | 0.64 | 0.10 |
Oak Species (Sample Size) | Parameter | Leaf Type | Mean | SD | Dif. | t Ratio | Std Err Dif. | df | p | 95% CL Dif. | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Lower | Upper | |||||||||||
Q. alba2 | ||||||||||||
Nsun = 21 | | LDI | SUN | 81 | 33 | 38 | 4.89 | 7.71 | 27.14 | <0.0001 | 22 | 54 |
SHADE | 43 | 15 | ||||||||||
Nsha = 26 | | Solidity | SUN | 0.68 | 0.12 | −0.13 | −4.53 | 0.03 | 28.45 | <0.0001 | −0.19 | −0.07 |
SHADE | 0.82 | 0.06 | ||||||||||
Q. macrocarpa2 | ||||||||||||
Nsun = 11 | | LDI | SUN | 127 | 43 | 55 | 3.61 | 15.19 | 16.80 | 0.0022 | 23 | 87 |
SHADE | 72 | 28 | ||||||||||
Nsha = 13 | | Solidity | SUN | 0.75 | 0.04 | −0.06 | −4.04 | 0.01 | 16.02 | 0.0009 | −0.09 | −0.02 |
SHADE | 0.80 | 0.02 | ||||||||||
Q. ellipsoidalis2 | ||||||||||||
Nsun = 7 | | LDI | SUN | 121 | 33 | 29 | 2.16 | 13.65 | 8.59 | 0.0609 | −2 | 61 |
SHADE | 91 | 23 | ||||||||||
Nsha = 16 | | Solidity | SUN | 0.46 | 0.06 | −0.12 | −4.17 | 0.03 | 11.79 | 0.0014 | −0.19 | −0.06 |
SHADE | 0.58 | 0.07 |
BIOLOGY Plant Role Model | ABSTRACTION Shape Features, Transfer Hypotheses | APPLICATION Transfer Regime |
---|---|---|
Viola septemloba Geranium sanguineum | • Elliptic lobation • Lobe elongation Elliptic lobes in two-dimensional exchangers enhance convection. Elliptic lobes of higher aspect ratio (elongated) enhance convection. | SENSIBLE HEAT convective cooling |
Viburnum genus | • Leaf blade elongation Shapes of high aspect ratio enhance convection. | |
Acer rubrum | • Toothed edges • Teeth proportions and shape Toothed edges, especially with proportionally large teeth, enhance vapor dissipation. | LATENT HEAT evaporation |
Ulmus genus | • Hierarchically toothed edges Hierarchical teeth enhance vapor dissipation. | |
Quercus genus | • Sinus profile in lobed shapes Sinuses of lobed shapes enhance orientation-independence of transfer in free convection, and inclination-independence under strong airflows. | HEAT and MASS TRANSFER evaporative cooling |
Trevesia palmata | • Compoundness • Fenestration A large surface dissected into semi-distinct, space-filling parts enhances transfer. | |
Morus genus | • Circular lobation • Convex teeth A hierarchical design of major obovate lobes and marginal curved teeth enhances transfer. |
Geometry (i.d. and Visual) | Abstract Design Features | Relative 1 Perimeter | LDI | Relative 1 Max. Inscribed Circle Diameter | Relative 1 Leff 2 (Effective Dimension) | Protrusion to Core Ratio | Convexity | Solidity | |
---|---|---|---|---|---|---|---|---|---|
C | | circular, control | 1 | 13 | 1 | 1 | 0 | 1 | 1 |
E | | ellipse, aspect ratio and elongation | 1.1 | 15 | 0.70 | 0.70 2 | 0 | 1 | 1 |
L | | “lobes”, few and large protrusions | 1.5 | 28 | 0.78 | 0.79 | 0.4 | 0.87 | 0.67 |
T | | marginal teeth, many small protrusions | 1.8 | 41 | 0.9 | 0.82 | 0.2 | 0.61 | 0.83 |
Characteristic Dimension | Shape | Evap. Flux Mean 1 (mg/min/cm2) | SD | Std Err | Relative2 Enhancement | df | F Ratio | p | |
---|---|---|---|---|---|---|---|---|---|
D = 5 cm | C | | 0.67 | 0.03 | 0.01 | - | 3 | 19.08 | <0.0001 |
E | | 0.69 | 0.02 | 0.01 | +4% | ||||
L | | 0.76 | 0.02 | 0.01 | +14% | ||||
T | | 0.76 | 0.01 | 0.01 | +14% | ||||
D = 10 cm | C | | 0.59 | 0.01 | 0.005 | - | 3 | 28.89 | <0.0001 |
E | | 0.59 | 0.01 | 0.005 | −1% | ||||
L | | 0.64 | 0.01 | 0.005 | +7% | ||||
T | | 0.63 | 0.01 | 0.005 | +6% |
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Rupp, A.I.K.S.; Gruber, P. Biomimetic Groundwork for Thermal Exchange Structures Inspired by Plant Leaf Design. Biomimetics 2019, 4, 75. https://doi.org/10.3390/biomimetics4040075
Rupp AIKS, Gruber P. Biomimetic Groundwork for Thermal Exchange Structures Inspired by Plant Leaf Design. Biomimetics. 2019; 4(4):75. https://doi.org/10.3390/biomimetics4040075
Chicago/Turabian StyleRupp, Ariana I. K. S., and Petra Gruber. 2019. "Biomimetic Groundwork for Thermal Exchange Structures Inspired by Plant Leaf Design" Biomimetics 4, no. 4: 75. https://doi.org/10.3390/biomimetics4040075
APA StyleRupp, A. I. K. S., & Gruber, P. (2019). Biomimetic Groundwork for Thermal Exchange Structures Inspired by Plant Leaf Design. Biomimetics, 4(4), 75. https://doi.org/10.3390/biomimetics4040075