# Difference between revisions of "How aphids lose their marbles"

Wiki entry by Emily Gehrels, Fall 2012

Based on the article: Pike,N., Richards,D., Foster,W., and Mahadevan,L. (2002). How Aphids Lose their Marbles. Proc. R. Soc. Lond. B, vol. 269 no. 1497 pp. 1211-1215.

## Background

Aphids are a common species of insect that lives on and feeds off of plants. They have many natural predators in part because they have soft bodies and are not easily able to defend themselves. This is one of the reasons that many species of aphid have evolved to form plant galls and live within them for the duration of their lives. A plant gall is a growth that forms on a plant in the presence of certain parasites, such as aphids. Galls formed by aphids are hollow extensions of the plant that provide the aphids with a sheltered place to live while still providing them access to the nutrients of the plant off of which they live.

There are two major problems for insects living in such confined spaces. The first is that any liquid trapped in the space could easily drown them because of the dominance of surface forces in small-scale systems. The second is hygiene. Aphids have to eat a lot of plant sap to sustain themselves, and everything that they ingest must ultimately leave their bodies. This excrement is known as honeydew, and its presence in the gall must be carefully controlled to prevent both drowning and the development of pathogens that could harm the aphids.

The aphid has come up with a very clever way to deal with these problems. Aphids have special cells on the outsides of their bodies, which excrete a waxy powder that coats the inner surfaces of the plant gall. As soon as the honeydew leaves the aphid’s body it touches this powdery surface and is coated in a layer of wax that transforms the droplet into a liquid marble. These liquid marbles retain their sphere-like shape and do not wet any surface that they come in contact with.

Within groups of aphids there are specialized aphids, known as soldiers, which have certain extra defensive adaptations such as a hard exoskeleton or pincers. It has been found that in galling species, the soldiers are also responsible for removing the marbles of honeydew from the gall every day. The soldiers move the droplets by “kicking pushing, or walking on their surfaces.

The purpose of this paper is to examine the properties of the wax excreted by the aphids and study how it leads to the formation of liquid marbles and how these marbles are helpful to the aphids.

## Methods and Results

Galls found on black poplars made by the species “pemphigus spyrothecae” were collected in the UK. The galls were broken open and liquid marbles as well as aphids were collected from their interiors. The radii of 1000 liquid marbles were measured along with the circumferences of the anuses of 30 aphids. Liquid marbles were then centrifuged and purified to produce a sample of honeydew. The density of the honeydew was measured and the surface tension was found by measuring the height to which the honeydew rose in a capillary tube. The viscosity was determined by measuring the constant velocity at which a slug of honeydew fell through a capillary tube.

The properties of the aphid wax were measured in two configurations: i) wax that was taken, purified, and then smooshed down by hand into a thin layer and ii) wax as it is found inside a freshly collected portion of the inner gall. The wax powder that is deposited on the inside of the gall is made up of individual needles of wax with an average diameter of 12$\mu$m that overlap with an average spacing of 55$\mu$m to form a layer on the surface of the gall.

Firstly the contact angle of water on the wax in both of these configurations was measured. In the first (flattened wax) scenario the contact angle was measured to be 115 degrees, which displays the hydrophobic quality of the wax. However, when the textured wax surface was measured, the contact angle was found to be even higher at a value of 160 degrees. This means that the textured surface serves to increase the hydrophobicity of the wax layer. This remarkable effect is explained by the fact that for the water to go into the micron-scale gaps between the needles quite large capillary pressures (on the order not achievable by a simple water droplet) would be required. This means that the water droplet is only in contact with the surface at the tips of the needles that rise above the surface. The effective area of the water surface interface is in this way much decreased and everywhere else the drop is simply in contact with its own vapors.

This means that the honeydew droplets from the aphids are easily moved around the inner surface of the gall, and are able to therefore pick up more wax needles until the entire surface of the drop is coated. This led the authors of the paper to further explore the dynamics of these liquid droplets as they are moved around the surface of the gall. The average radius of the aphids; liquid marbles has been measured to be approximately 100 $\mu$m. They have found by calculations that these droplets move primarily by rolling, and not by sliding or shearing and that the droplets do not change shape as they are rolled due to the small velocities at which the aphids move them and the high ratio of viscous forces to surface tension forces. The speed at which the droplets can be moved for a given force has been calculated to be:

$V\cong \frac{F\kappa^-3}{\eta R^4}$