Physical limits and design principles for plant and fungal movements

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Original entry: Lidiya Mishchenko, APPHY 226, Spring 2009


Jan M. Skotheim and L. Mahadevan. Science 308, 2005(1308-1310) [[1]]


Scaling, classification, differential pressure, hydraulic motion


"The typical scales for plant and fungal movements vary over many orders of magnitude in time and length, but they are ultimately based on hydraulics and mechanics. We show that quantification of the length and time scales involved in plant and fungal motions leads to a natural classification, whose physical basis can be understood through an analysis of the mechanics of water transport through an elastic tissue. Our study also suggests a design principle for nonmuscular hydraulically actuated structures: Rapid actuation requires either small size or the enhancement of motion on large scales via elastic instabilities."

Classification of plant and fungal movement with the distance a fluid is transported (L) and the duration of the movement (tao). The dashed line separates movement limited by fluid transport (swelling and shrinking) and movement that uses elastic instabilites to go beyond this limit. The solid line represents the inertial limit on the movement.

Soft Matter Example

An important concept addressed in this paper is the concept of scaling laws. These kinds of order of magnitude calculations help classify phenomena in soft matter. For example, time scales differentiate between elastic (short time scales) and viscous (long time scales) materials.

This paper classifies fungal and plant movement together because they both posess cells that can sustain a large internal (turgor) pressure that they can utilize for growth and motion. Many of these concepts of pressure are relevant to capillarity and wetting.

Controlling differential pressures allows plants and fungi to move, which may be regulated passively (differential drying) or actively (osmotic pressure). The speed of actuation is limited by the rate of fluid transport. (Upper limits are a crucial consideration with scaling laws). Since the rate of fluid transport is determined by the distance a fluid is transported (L) and the duration of the movement (tao), movement of plants and fungi can be categorized with these two variables as shown in the figure.

The paper then continues to derive an equation for the characteritic time for the "diffusive equilibration of pressure" through porous elastic materials (like plant tissue). Relating viscocity, permeability of the tissue, length scale, and elastic modulus. Thought this is only approximate, it allows them to then classify fungal movement into movement that is limited by fluid transport alone, and movement that also includes storing energy with elastic instabilites, and their rapid release (which transcends this limit).

Finally, the paper finds and important physical limit to the motion of plants anf fungi. The time scale of the motion is limited by what they call "inertial time", which characterized the time for wave propagation in mechanical waves. This upper limit is also length scale dependent.

Thus, this paper gives a great example of scaling laws: considering physical limitations, sorting out relevant factors, and classification. But is also important from an engineering point of view: "the engineering of soft, nonmuscular hydraulically acutated systens for rapid movement requires either small size [since both time scales depend directly on L] or the enhancement of motion on large scales via elastic instabilities."