Droplet Impacting a Cantilever: A Leaf-Raindrop System

Department of Mechanical and Industrial Engineering, University of Illinois at Chicago,Chicago, Illinois 60607, USA(Received 17 October 2014; revised manuscript received 12 March 2015; published 30 April 2015)Previousstudies showthat air pollution and wind erosion, which damage a leaf’sepicuticular wax layer,can change leaf surface properties from hydrophobic to hydrophilic. However, the dynamic response of adamaged leaf to a raindrop impact has not been investigated and could clarify the direct influence ofchanges in wettability on early leaf abscission. In this article, we investigate how leaves with differentsurface properties respond to falling raindrops, viewing this as a unique system of coupled elasticity anddrop dynamics. An elastic beam with tunable surface wettability properties is used as a simple leaf model.We find that wettable beams experience much higher torque and bending energy than nonwettable beams.This is because a drop sticks to a wettable beam, while a drop falls off a nonwettable beam. An analyticalmodel using momentum balance and simple cantilever beam theory quantifies the bending energy andtorque experienced by wettable and nonwettable beams. The results elucidate the potential damage causedby raindrops impacting a leaf as a function of its surface wettability and are correlated with environmentalfactors contributing to premature changes of leaf surface properties.

[1]  Rachel E. Pepper,et al.  Splashing on elastic membranes: The importance of early-time dynamics , 2007 .

[2]  T. Mansfield,et al.  Stomata and plant water relations: does air pollution create problems? , 1998, Environmental pollution.

[3]  Ilker S. Bayer,et al.  Water-Based Superhydrophobic Coatings for Nonwoven and Cellulosic Substrates , 2014 .

[4]  Lichao Gao,et al.  Contact angle hysteresis explained. , 2006, Langmuir : the ACS journal of surfaces and colloids.

[5]  R. Chazdon.  The Costs of Leaf Support in Understory Palms: Economy Versus Safety , 1986, The American Naturalist.

[6]  C. Tropea,et al.  Inertia dominated drop collisions. I. On the universal flow in the lamella , 2009 .

[7]  Karl J. Niklas,et al.  A mechanical perspective on foliage leaf form and function , 1999 .

[8]  R. Blossey.  Self-cleaning surfaces — virtual realities , 2003, Nature materials.

[9]  G. Tomlinson.  Air pollutants and forest decline. , 1983, Environmental science & technology.

[10]  R. Rioboo,et al.  Drop impact on soft surfaces: beyond the static contact angles. , 2010, Langmuir : the ACS journal of surfaces and colloids.

[11]  D. W. Bechert,et al.  Fluid Mechanics of Biological Surfaces and their Technological Application , 2000, Naturwissenschaften.

[12]  PV Biswas,et al.  HARNESSING RAINDROP ENERGY IN BANGLADESH , 2008 .

[13]  H. Hosaka,et al.  DAMPING CHARACTERISTICS OF BEAM-SHAPED MICRO-OSCILLATORS , 1995 .

[14]  Lei Xu.  Liquid drop splashing on smooth, rough, and textured surfaces. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  E. Baker,et al.  EROSION OF WAXES FROM LEAF SURFACES BY SIMULATED RAIN. , 1986, The New phytologist.

[16]  W. Barthlott,et al.  Purity of the sacred lotus, or escape from contamination in biological surfaces , 1997, Planta.

[17]  A. Leopold,et al.  The Nature of Leaf Abscission , 1964, The Quarterly Review of Biology.

[18]  Oliver Brand,et al.  Dimensional considerations in achieving large quality factors for resonant silicon cantilevers in air , 2009 .

[19]  D. Hu,et al.  Splash-cup plants accelerate raindrops to disperse seeds , 2013, Journal of The Royal Society Interface.

[20]  A. Yarin.  Drop Impact Dynamics: Splashing, Spreading, Receding, Bouncing ... , 2006 .

[21]  J. M. Bush,et al.  The fluid trampoline: droplets bouncing on a soap film , 2008, Journal of Fluid Mechanics.

[22]  W. Barthlott,et al.  Seasonal changes of leaf surface contamination in beech, oak, and ginkgo in relation to leaf micromorphology and wettability , 1998 .

[23]  T. Brakke,et al.  Seasonal variation in the structure and red reflectance of leaves from yellow poplar, Red Oak, and Red Maple , 1993 .

[24]  Xavier Boutillon,et al.  The force of impacting rain. , 2014, Soft matter.

[25]  D. Quéré.  Wetting and Roughness , 2008 .

[26]  T. Mansfield,et al.  Physiological disturbances in plants caused by air pollutants , 1990 .

[27]  L. Friberg.  [Air pollution]. , 1984, Svenska lakartidningen.

[28]  E. Villermaux,et al.  Single-drop fragmentation determines size distribution of raindrops , 2009 .

[29]  Ghislain Despesse,et al.  Harvesting raindrop energy: theory , 2008 .

[30]  G. S. Avery,,et al.  Leaf abscission and the so-called " abscission layer ". , 1950 .

[31]  Ghislain Despesse,et al.  Harvesting raindrop energy: experimental study , 2008 .

[32]  S. Huttunen,et al.  A review of the response of epicuticular wax of conifer needles to air pollution , 1990 .

[33]  L. Meirovitch,et al.  Fundamentals of Vibrations , 2000 .

[34]  M. Thomas.  Effects of air pollution on plants. , 1961, Monograph series. World Health Organization.

[35]  L. Bourouiba,et al.  Rain-induced ejection of pathogens from leaves: revisiting the hypothesis of splash-on-film using high-speed visualization. , 2014, Integrative and comparative biology.

[36]  J. Burkhardt,et al.  Particulate pollutants are capable to 'degrade' epicuticular waxes and to decrease the drought tolerance of Scots pine (Pinus sylvestris L.). , 2014, Environmental pollution.

[37]  C. Ulbrich,et al.  A Review of the Differential Reflectivity Technique of Measunng Rainfall , 1986, IEEE Transactions on Geoscience and Remote Sensing.

[38]  Dimos Poulikakos,et al.  Wetting effects on the spreading of a liquid droplet colliding with a flat surface: Experiment and modeling , 1995 .

[39]  J. Roberts,et al.  Cell Biology of Abscission , 1982 .

[40]  Marco Marengo,et al.  Understanding the drop impact phenomenon on soft PDMS substrates , 2012 .

[41]  F. Bussotti,et al.  Air pollution, forest condition and forest decline in Southern Europe: an overview. , 1998, Environmental pollution.

[42]  C. Megaridis,et al.  The fluid diode: tunable unidirectional flow through porous substrates. , 2014, ACS applied materials & interfaces.