FACTORS DETERMINING VELOCITY OF FALL One effect of its molecular activity is that the air is viscous, i.e. it resists the movement of solid particles. A small particle liberated into the air from a resting position tends to fall with an acceleration due to gravity; however, the resistance of the air increases faster than the speed of fall, and a state of balance is soon reached in which the particle stops accelerating and continues to fall through the air at a constant terminal velocity.
The terminal velocity of smooth spheres with diameters of between about i µ* and roo µ is satisfactorily predicted by Stokes's law (for smaller particles Cunningham's correction becomes applicable, and larger par ticles have to be treated experimentally). Stokes's law can conveniently be given in the form: where, in C.G.S. units at ordinary surface temperature and pressure: = terminal velocity (velocity of sedimentation) in cm. per sec.; = density of sphere in gm. per cc. (water = 1 oo); p = density of medium (air = 1.27 x Ion gm. per cc.); g = acceleration of gravity (981 cm. per sec.-); = viscosity of medium (air at 18°C. = 1.8 x gm. per cm. sec.); r = radius of sphere in cm. (N.B. radius = diameter).
For a water droplet falling in air, vs = X cm. per sec., when the radius is expressed in microns (p.). A fog droplet of to w radius (zo µ diameter) has a calculated terminal velocity of 1•2 cm. per sec.
The pollens and spores with which we are concerned belong to the size-range where Stokes's law is valid, but they are seldom anything like smooth spheres. Stokes's law has given values of at least the right order, however, for spores whose terminal velocities have been measured experimentally. At first sight the pollen grains of some species of conifers appear to fall unexpectedly slowly, but these grains have conspicuous air sacs which greatly reduce the density of the individual particle.
The diameters of particles constituting the air-spora vary from approxi mately 1 E.c to too Ec or more for the largest pollens and spores (see Appendix I, p. zoo, Plates 5-7). Some spores are filamentous, perhaps one hundred times as long as wide. Although the densities of the spores of very few species have yet been measured, there are reasons for expecting them to be much less dense than mineral particles and indeed to resemble water droplets in density. The few determinations which have been made, relative to water = I, are as follows: The properties of spores are not invariable, but may alter with external conditions—sometimes enough to have a marked effect on their terminal velocity. For instance, the spores of the toadstool Amanitopsis vaginata were recorded by Buller (1922) as falling at 0.5 cm. per sec. when ob served immediately below the gill after liberation, but they became desic cated on continuing to fall through dry air and soon slowed down to one third of their original speed. Durham (1943) gave laboratory determina tionsof densities of pollens, and for some the probable outdoor values which are shown in parentheses: Ambrosia elatior, o•63 (0•55); A. bidentata, 0•56 (0.5o); Xanth unt commune, 0•52 (o•45); Iva .xanthifolia, o•79; Salsola pestifer, 1•0 (0.90); Acnida tamariscina, 1•o; Zea mays, 1.10 (Poo); Phleunt prateuse, 1.00 (0.90); Quercus imbricaria, 1•o4; Juglans nigra, 0.93; Abuts glutinosa, o•97; Fraxinus americana, 0.90.
Observed terminal velocities (vs) of spores and pollen grains are collected in Table I.
Two methods have been used for measuring terminal velocity. The simpler method is to time the fall over a short, measured distance in a small chamber of still air by direct observation with a horizontal micro scope. It was used in the pioneer work of Buller (1909), and by Yarwood & Hazen (194z). So far this method has been used only for small, slowly-. falling spores, because large ones travel too fast to be timed by direct observation. The method could no doubt be extended to fast-moving spores by photographing with a flash of known duration. The technique most generally used, however, has been to release spores or pollen at the top of a column of still air in a vertical cylinder and find the time they take to arrive at the bottom. This is the method used by Zeleny & McKee han (191o), McCubbin (1918), Ukkelberg (1933), Stepanov (1935), and \Veinhold (1955).
McCubbin and Ukkelberg report results of similar type. The number of wheat-rust spores reaching the bottom of the tube in successive inter vals of time showed a negative skew distribution. Ukkelberg was able to show that part of this skewness was due to the presence of clumps of spores which fell faster than single units. It is also clear that, with both uredospores and aecidiospores of rust fungi, a large number of single spores fall very slowly. Measurements are needed to test whether, within one species, the single spores arriving first at the bottom are larger than those arriving at the end of the experiment. Another possibility is that small eddies may have hastened the fall of some spores and retarded that of others. A more serious defect of the method is that a vertical circulation of air by convection in the cylinder might bias the results by introducing a systematic acceleration or retardation of fall. 'Phis drawback could be overcome by establishing a small temperature difference between the top and bottom of the column, so that the stratified air would be stabilized as in a `temperature inversion'. A thermostat may produce artefacts from convection currents set up by rhythmic temperature changes. Buller (1909) emphasized the difficulty of reducing air to anything like stillness, even in closed beakers.
In air, spores gain or lose water rapidly and the effect of spore hydra tion on terminal velocity, noted earlier by Buller, is evidently complex. Weinhold (1955) showed that with uredospores of Pucciuia graminis tritici, changes in volume and weight occurred within 3 minutes of transfer to air of different temperature and humidity. Wcinhold reported that, contrary to expectation, spores stored at 5 per cent relative humidity fell at cm. per sec., in spite of being smaller and less dense than spores stored at 8o per cent relative humidity, which fell at 1. cm. per sec. Increasing the humidity of air through which the spores fell increased the terminal velocity, which was: 103, 1•22, i•23, and i•54 cm. per sec. at relative humidities of 24, 45, 52, and 8o per cent, respectively. With increasing temperature, terminal velocity decreased from 1•o6 cm. per sec. at 23.4°C. to o•94 cm. per sec. at 399°C.
We still lack observations on the rate of fall of highly elongated fungus spores found in such genera as Ophiobolus, Epichloe, Geoglossum, and Cordyceps, whose unusual shape makes Stokes's law inapplicable. Falck (1927) calculated terminal velocities for a number of species with approxi mately elliptical spores on the assumption that the expected velocity = v,/ /(a/b), where is the fall velocity of a spherical particle of the same volume, and a and b are axes of the ellipse. McCubbin stressed our lack of observations on asymmetrical spores, and provisionally suggested a method of calculating terminal velocity on the assumption that surface drag accounts for most of the retardation. He showed that observed terminal velocities of most spherical and oval spores fitted the as consisting of an intercalated cylinder (length = lµ) between two axial cones (each of axial length = being again in mm. per sec.
During fall in still air, an asymmetrical particle will assume a charac teristic orientation. Hydrodynamical theory requires that the orientation assumed will be that in which the resistance of the air to the motion of the particle is greatest. This phenomenon can be observed with the naked eye if minute airborne particles of fibre are watched in a beam of light in a still, darkened room.
We know very little as yet about spore orientation. Buller (1909) observed that some slightly elongated spores tend to fall with their long axis horizontal, as is to be expected for dynamical reasons. Sometimes factors other than shape seem to influence the orientation of an asymmetric spore. When Yarwood & Hazen (1942) watched the smooth conidia of Erysiphe graminis, measuring 32 zo during fall in vertical glass tubes 7 mm. in diameter, they saw that half of the spores fell with the long axis horizontal and the other half with it vertical. This might indicate an uneven distribution of materials of different density in the cell contents; but, more likely, the vertical position was due to drag at the wall boundary, because if the tube is made even narrower, all the spores fall vertically. The present author has seen the filamentous ascospores of Cordyceps gracilis similarly oriented whilst being carried up by convection currents beside a vertical glass surface. Further, while watching the tailed spores of the puffball, Bovista plumbea, falling in a small chamber on the stage of a horizontal microscope, the tail was seen to trail behind the spherical spore. In Chapter VI it will be indicated that spores tend to be deposited with characteristic orientation on a surface.
Stokes's law holds for smooth spheres. Few pollens or spores are spheres, but a large proportion of them are microscopically smooth. Others, when highly magnified, are seen to possess warts, spines or other projections, or even to be pitted. These roughnesses would be expected to increase friction during movement through air and to retard fall, but we have as yet no experimental evidence of this.
Viewed over the whole range of spore and pollen size of, say, 4 to 100µ diameter, and of terminal velocities of from o•o5 to io cm. per sec., it is clear that Stokes's law gives a good idea of terminal velocity in still air, but that asymmetry and surface roughness may play a part as yet unmeasured.