AMER. ZOOL., 30:111-121 (1990)
Terrestrial Versus Aquatic Biology:
The Medium and Its Message1
MARK W. DENNY
Hopkins Marine Station of Stanford University, Pacific Grove, California 93950
pressure. The density of water varies by
only about 0.8% over the physiological
range of temperatures (Table 1). Note,
however, that the change in density is not
monotonic across this range—water
reaches a maximum density at 3.98CC. As
a result, ice floats, a phenomenon of considerable biological significance. For
instance, because ice floats, lakes freeze
from the top down rather than from the
bottom up. The initial layer of surface ice
decreases the intensity of wind-driven mixing and thereby decreases the rate at which
lakes lose heat, in the process providing a
temporal refuge for aquatic organisms. The
buoyancy of ice is also important to benthic
organisms (both in lakes and oceans). If ice
sank, these organisms would quickly be
encased in ice during the winter.
DENSITY
The density of water varies only slightly
At sea level and 20°C, the mass of a cubic as a function of pressure. This effect is dismeter of water is 1,000 kg, 830 times as cussed in some detail in a later section on
much as that of a cubic meter of air (1.2 bulk modulus, but it is worth noting here
kg). This difference in density (mass per vol- that the density of water increases by only
ume, p) is perhaps the most striking phys- 0.5% with each kilometer of depth. In conical difference between water and air. In trast, the density of air is strongly depenaddition to this sizable absolute difference, dent on both temperature and pressure.
the densities of the two fluids vary differ- The kinetic theory of gases asserts that the
ently with changes in temperature and density of a gas is directly proportional to
p/T, where p is the absolute pressure and
T is the absolute temperature (Feynman et
al., 1963). For air at one atmosphere of
' From the Symposium on Concepts of Adaptation in pressure, density decreases by about 13%
Aquatic Animals: Dn'ialionsfrom the Terrestrial Paradigm
over the range 0-40°C (Table 1).
presented at the Annual Meeting of the American
Atmospheric density, p, and pressure, p,
Society of Zoologists, 27-30 December 1988, at San
Francisco, California.
decrease exponentially with altitude at a
INTRODUCTION
Many of the basic attributes of an organism—size, shape, mode of locomotion,
reproductive strategy, means of obtaining
food, respiratory mechanism, sensory
capabilities—depend upon the fluid (air or
water) in which the organism lives. In this
article I examine some of the fundamental
physical properties of air and water and
explore how they have contributed to the
divergence of terrestrial and aquatic
organisms. It would be impractical to treat
in depth the intricacies of this topic in one
short essay. Instead, this article is limited
to a selected few examples; it deliberately
avoids the examples found in introductory
texts, and concentrates instead on cases that
provide new perspectives.
111
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SYNOPSIS. Many basic biological functions are constrained by the physical properties of
the fluids in which organisms live. Here 1 explore four selected examples in which physical
differences between air and water have contributed to the functional divergence of terrestrial and aquatic organisms. 1. Water is about 800 times as dense as air. As a result,
while the cost of locomotion is generally less for aquatic organisms, the hydrodynamic
forces they encounter are larger. 2. The combined effects of density and viscosity insure
that the capture of suspended particles is mechanically more effective on land than in
water. 3. The speed of sound is four times greater in water than in air, requiring aquatic
organisms to use higher frequency sounds in echolocation systems. 4. The resistivity of
air is 16 orders of magnitude larger than that of seawater, which might explain why
aquatic animals use electrical sensing organs to detect prey but terrestrial animals do not.
112
MARK W. DENNY
TABLE 1. The density of water and air at one atmosphere
pressure as a function of temperature.*
Temperature (°C)
Freshwater
Air
0
3.98
5
10
20
30
40
999.87
1.000
999.99
999.73
998.62
995.67
992.24
1.293
1.205
1.128
* Values given in kg/m'. Data taken from Chemical
Rubber Co. (1977) and Vogel (1981).
Psl
Psl
(1)
where the subscript 5/ denotes a value measured at sea level, z is altitude above sea
level, and zs is the scale height (the average
height of a gas molecule in the atmosphere). For air, the scale height is 8.43 km
(Chemical Rubber Co., 1977). Thus the
density and pressure at an altitude of 5.85
km are half those at sea level.
These differences in density between air
and water have multiple biological consequences, only a few of which are explored
here.
Cost of support
The weight of an object (as distinct from
its mass) depends on the difference in density between the object and the surrounding fluid. Weight = (p — Pj)Vg, where p is
the density of the object, pf is the density
of the medium, V is the object's volume,
and g is the acceleration of gravity (9.81
m/sec 2 ). The term (p — pj) is an object's
effective density. Most biological objects have
a density of 1,050-1,200 kg/m 3 and therefore have an effective density of 1,0491,199 kg/m 3 in air, 50-200 kg/m 3 in
freshwater, and 25-175 kg/m 3 in seawater. Wood has a density slightly less than
1,000 kg/m 3 , and therefore floats on water.
A few aquatic animals with carbonate skeletons have densities as high as 2,000 kg/
m3 and therefore have effective densities
in water nearly as high as those typical for
organisms in air.
Cost of transport
For an animal of a given weight, more
energy is expended to transport one kilogram of body mass one kilometer by walking or crawling than is expended by swimming (Schmidt-Nielsen, 1971). Flying is
more costly still. Although the physics that
accounts for this hierarchy of costs is complex, buoyancy again is an important contributing factor. A neutrally-buoyant fish
expends very little energy maintaining its
position against gravity—its primary transport cost comes in doing work on the water
as its moves. In contrast, terrestrial animals
that walk or crawl must maintain an upright
posture as they move. Because the body
lacks buoyant support from water, this posture requires the expenditure of energy.
Further, as an animal walks, its center of
mass typically goes through some vertical
oscillation, leading to an oscillation in gravitational potential energy. To a certain
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constant temperature according to the
Boltzmann relationship:
Because of the low density of air, objects
in air typically weigh 5-50 times more than
the same objects in water. As a result, the
requirements placed on terrestrial organisms by the need to resist gravity can be
more constraining than those on aquatic
organisms. Compare, for instance, a pine
tree and a kelp. Both plants can grow to
be 20-30 m in length, both have a canopy
of photosynthetic material arrayed near the
distal end of the plant, and both are constructed from materials with a density of
approximately 1,000 kg/m 3 . However,
because the pine lives in air, it must grow
and maintain a trunk approximately 0.5 m
in diameter, an expensive energy investment. The stipe of the kelp is likely to be
only one tenth the diameter of the pine's
trunk, with an investment in structural
material only 1% that of the pine.
While similar comparisons can be cited,
the differences in allocation to structural
material between terrestrial and aquatic
organisms are generally not this striking
despite the very large differences in their
effective density. This dearth of clear-cut
examples is likely due to structural requirements placed on organisms by other aspects
of the environment, especially by fluiddynamic forces.
THE MEDIUM AND ITS MESSAGE
113
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extent the kinetic energy gained during metabolized (carbohydrate, lipid, or prothe fall of the center of gravity can be tein).
applied towards returning the body to its
We first calculate the cost of transport
original position, but this reciprocal trad- for a salmon. The power of swimming at
ing of kinetic and gravitational potential cruising speed (defined by Schmidt-Nielenergy is never completely loss-free. As a sen, somewhat arbitrarily, as 75% of the
result, energy is expended in overcoming speed that can be maintained for 1 hr) is
gravitational forces that would not be
(2)
power = 7.37- 10- 5 M-° 084
expended if the animal were neutrally
buoyant. In this respect flying is worse than where power is measured in liters of O 2 /
walking—a large part of the energy kg/sec, M is body mass in kg, and the units
expended in flight is used simply to main- needed to relate mass to power have been
tain the animal's height above the ground. absorbed into the leading coefficient. The
Thus, without the benefit of being neu- speed at which the fish swims relative to
trally buoyant, terrestrial organisms spend the water is a function of its body mass and
much more energy in moving than do from data given by Brett (1965) can be
aquatic organisms.
calculated to be:
Note, however, that the cost of locoswimming velocity = 1.0M017 (3)
motion as outlined by Schmidt-Nielsen
(1971) refers to the cost of transport rel- where velocity is measured in m/sec. Thus
ative to a stationary medium. If the medium the effective cost of transport is
itself is moving in the direction in which
effective.
7.37- lO^Af"""
the animal wants to go, the effective cost
of moving from one point on the earth to
cost
Af>.i7 + c u r r e n t speed
another is less. This is unlikely to affect the
net cost for animals that crawl or walk
because the medium against which they By a similar method we can calculate the
push (the ground) seldom moves fast effective cost of transport for a bird. Again
enough to be of any consequence. But using values cited by Schmidt-Nielsen
ocean currents and atmospheric winds (1984):
could be used by swimming and flying anipower = 3.8-10-3Af-°03
(5)
mals, respectively, to substantially lower
speed = 14.6M020
(6)
their net transport cost. Using values available in the literature (Schmidt-Nielsen,
effective =
3.8-lQ-^M-" 03
1984), it is possible to calculate, for
(7)
instance, how fast the wind would have to
cost
14.6M020 + wind speed
blow in order for the net cost of transport
of a bird to be less than that of a fish.
These effective costs are plotted in Figure
The effective cost of transport (expressed 1 for the range of possible current and
as the liters of oxygen required to trans- wind speeds for an animal with a body mass
port one kilogram of body mass one meter of 1 kg. The wind must blow at about 40
relative to the ground) is equal to the power m/sec (90 mph) for the effective cost of
expended while moving at a constant speed flight to be less than that of swimming
relative to the medium (liters of O 2 / k g / through water with a current speed
sec) divided by the speed of the animal rel- between 0 and 10 cm/sec. Winds of this
ative to the ground (m/sec). This "ground velocity are certainly created in storms, but
speed" is the sum of the speed of the animal whether birds take advantage of them is
relative to the medium plus the speed of open to question. Perhaps more amenable
the medium relative to the ground. Note to transport are jet stream winds. These
that one liter of oxygen (at standard tem- high-velocity (30-140 m/sec) winds blow
perature and pressure) is the metabolic in predictable directions over the temperequivalent of approximately 20.9 kj, the ate regions of much of the globe, and could
exact value depending on what is being potentially be used for transport. Their
114
MARK W. DENNY
-3.2
-3.6
BIRD
-4.0
CJ
o
ITER
co
-4.4
-4.8
d
-5.2
i-
-5.6
o
8
-6.0
100
0.01
CURRENT OR WIND SPEED (M/S)
FIG. 1. The cost of transport from one point on the earth to another as a function of current or wind
velocity. Curves calculated for a bird and a salmon, each having a body mass of 1 kg.
main disadvantage is the fact that they
only occur at altitudes in excess of about
10,000 m.
Of course, the lower costs of transport
associated with currents and winds are only
realized when the current or wind blows
in the direction the animal wishes to travel.
Flying or swimming upstream increases the
cost of transport, and as the current or
wind approaches the intrinsic speed of the
animal, the cost tends toward infinity. For
instance, we can compare the effective cost
of transport between a bird flying in still
air and a salmon swimming upstream. For
water velocities greater than about 0.7
m/sec, the cost of transport is higher for
the fish.
sider a solid object moving relative to a
fluid.
Fluid directly in contact with a solid surface cannot slide along that surface. The
physical basis for this "no-slip" condition
is complicated and not entirely understood
(Khurana, 1988), but the phenomenon has
immense practical importance. Because of
the no-slip condition, any time a solid object
moves relative to a fluid, a velocity gradient
must result. As a consequence, any movement by the object is accompanied by a
force proportional to the surface area of
the object and to the viscosity of the fluid.
Therein lies an important set of differences
between water and air.
The dynamic viscosities of air, freshwater, and seawater are given in Table 2. Note
VISCOSITY
that at 20°C water is approximately 60 times
The dynamic viscosity of a fluid is defined more viscous than air. As a result, an object
as the ratio between the force per area (the of a given size experiences 60 times more
shear stress, r) imposed on the fluid and the viscous resistance in moving through water
at a certain speed than it does in moving
resulting velocity gradient:
through air. Note also that viscosity
V = r/(du/dz)
(8) depends on temperature for both air and
where z is distance measured at a right angle water, but in opposite directions for each.
to velocity. Stated another way, wherever Over the range 0-30°C the viscosity of air
a velocity gradient exists in a fluid, a shear increases by about 9%, while the viscosity
stress is exerted. The significance of this of water decreases by 45%. Thus the visstatement becomes evident when we con- cous component of the resistance to move-
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8
115
T H E MEDIUM AND ITS MESSAGE
FLUID-DYNAMIC FORCES
TABLE 2. The dynamic viscosity of air, freshwater, and
seawater (salinity 35%o) as a function of temperature.*
Freshwater
Air
ft)
0
5
10
15
20
25
30
40
kg/m/seclO"'
1.709
1.808
Seawater
kg/m/sec •10'
1.790
1.520
1.310
1.140
1.010
0.890
0.800
1.890
1.610
1.390
1.220
1.090
0.960
0.870
1.904
* Data taken from Chemical Rubber Co. (1977) and
Vogel (1981).
disturb the pattern offlowto a lesser extent
and have a lower drag. Except in a few
simple cases, it is not possible to predict
precisely on the basis of theory the effect
Pressure drag
of shape on drag, and the effect of shape
As fluid moves past an object, the pres- is taken into account by using an empirisure in the fluid is affected. In general the cally-determined "fudge factor," the drag
pressure is highest on the upstream face of coefficient, Cd. Note that Cd is a coefficient,
the object, and is lower around the sides not a constant; for a given shape it typically
and on the downstream face (Vogel, 1981). varies with size of the organism and with
The difference in pressure between the water velocity. These three factors can be
upstream and downstream faces results in combined multiplicatively to give an
a force, called pressure drag, tending to push expression for drag:
the object downstream.
drag = VzpfVtAfii
(9)
The magnitude of pressure drag is determined by three factors: (1) the dynamic pres- Due to the density difference between the
sure, (2) the area, Ap, projected in the direc- two media, drag in water is about 800 times
tion offlow,and (3) the shape of the object. that in air for an object of a given drag
The dynamic pressure is VapyM2, where u is coefficient and size at a given velocity.
the velocity of the fluid relative to the
object. This is the pressure the fluid would Lift
exert if it were brought to a complete halt
If the pattern of flow around an object
by the object, and it is directly proportional is such that the pressure on one of the latto the density of the medium. The pro- eral sides is greater than that on the oppojected area is the area over which the site side, a force is exerted on the object
upstream-downstream pressure difference at a right angle to the direction of flow.
acts. Note that the product of pressure and This lift behaves in much the same fashion
area is force. Shape affects drag by affect- as does drag. It is proportional to the
ing the pattern of flow. For example, bluff dynamic pressure and to the area over
bodies such as cylinders and broadside flat which the pressure difference acts. In this
plates, each oriented with its longest case, the relevant area is that projected
dimension perpendicular to flow, substan- perpendicularly to the direction of flow,
tially affect the pattern of flow in their the so-called "planform" area, Apl. As with
vicinity, resulting in a large upstream- drag, life also depends on the shape of the
downstream pressure difference and a large object, a factor that is taken into account
drag. In contrast, "streamlined" objects through an empirically-determined liftcoefIn addition to friction drag, there are
three other important fluid-dynamic forces.
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ment {thefriction drag) is about 10% higher
for a bird flying in the tropics than for the
same bird flying in the arctic. However,
the friction drag of a bird in flight is only
a minor fraction of the overall resistance
to movement (Alexander, 1982), and the
small change in viscosity with temperature
is unlikely to have had any major effect on
the flight mechanics of birds. In contrast,
the friction drag of a streamlined fish can
be a large fraction of the overall resistance
to movement (Webb, 1975). As a result, it
can be expected that fish have a considerably easier time moving about in tropical
than in arctic waters.
116
MARK W. DENNY
ficient, C,. Far from a solid boundary, objects
such as appropriately-oriented flat plates
and the special shapes known as airfoils
induce a large pressure difference across
their lateral faces and therefore experience large lifts. These shapes characterize
the wings of insects, bats and birds, and
the tails of fish and whales. Near a solid
boundary, the velocity gradient induced by
the no-slip condition can cause almost any
shape to experience lift. The overall
expression for lift is similar to that for drag:
In the case of a stationary object and an
accelerating fluid, the expression for the
acceleration reaction is different:
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acceleration reaction = (a + l)pfVa (12)
Because the object itself is not accelerating,
no force is imposed by the object's own
mass. However, the object occupies a space
that would otherwise be filled with accelerating fluid. As a result, the force due to
the motion of the fluid is greater than in
the case of a moving object in a stationary
fluid, hence the factor (a + 1).
lift = Vtp/u'AfjC,
(10)
In both cases described here, the accelAgain due to dependence on the density eration reaction is affected by the density
of the medium, lift is about 800 times of the fluid. For an object with a given
greater in water than in air for an object added mass coefficient and at a given relof a given lift coefficient and planform area ative acceleration, the acceleration reacat a given velocity.
tion is about 800 times larger in water than
in air.
Acceleration reaction
Because fluid-dynamic forces are so
The fourth major fluid-dynamic force highly dependent on the density of the
does not depend on the relative velocity of fluid, we are left with the impression that
the fluid (as with lift and drag) but rather frictional and pressure drag, lift, and the
on how rapidly the velocity changes, in acceleration reaction are always much
other words on the fluid's acceleration rel- larger in water than in air. Is this indeed
ative to an object (Daniel, 1984). The force a justifiable generality? For example, given
an object experiences due to a relative an organism of a certain size, differences
acceleration between it and the surround- in lift and drag due to differences in density
ing fluid depends on whether the object is could be offset if the velocities typically
stationary and the fluid is accelerating, or encountered in air were roughly 8001/' ~
whether the fluid is stationary and the 28 times those encountered in water. But
object is accelerating. If the fluid is sta- this is unlikely to be the case. For instance,
tionary:
birds tend to fly at velocities only about ten
times greater than the speeds at which fish
acceleration reaction = pVa + apfVa (11) swim (Schmidt-Nielsen, 1984), implying
where a is the acceleration of the object that the lift and drag experienced by birds
relative to the stationary fluid and V is the are only about 35% of those experienced
volume of the object. pV is the mass of the by fish of a similar size. Storm winds may
object, so the first term in this equation reach velocities of 50 m/sec or so, but these
(pVa) is the force required to accelerate the velocities are only 5-10 times those that
object's mass. This force would operate benthic aquatic animals encounter in the
were the object in a fluid or not. The sec- surf zone of wave-swept shores or in mounond term in eq. 11 is similar to the first, tain streams, again nowhere near the facbut the mass that acts as if it is being accel- tor of 28 required to equalize forces in the
erated along with the object is a mass of two environments.
fluid rather than the mass of the object.
Similar reasoning applies to the accelThe magnitude of this added mass, relative eration reaction. Denny et al. (1985) have
to the mass of the fluid displaced by the shown that the acceleration reaction placed
object, is a, the added mass coefficient. Like on benthic organisms by breaking ocean
the lift and drag coefficients, a depends on waves can be used to explain why wavethe shape of the object. In general, objects swept organisms never get very large. The
that have a high drag coefficient have a same mechanical limitation to size could
high coefficient of added mass.
operate in terrestrial environments; but
THE MEDIUM AND ITS MESSAGE
117
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because the acceleration reaction in air is such as Webb (1975), Grace (1977), Vogel
(for stationary objects) only V800 as large as(1981), Alexander (1983), and Denny
that in water, organisms in air could be (1988).
about 800 times as large as those in the
PARTICLE CAPTURE
surf zone, all other factors being equal. The
factor most likely not to be equal would be
We now turn our attention to factors
the acceleration itself, but it is difficult to that determine the pattern in which a fluid
believe that aerial accelerations, even in flows. The precise trajectory followed by
gusty storm winds, could be sufficiently a parcel of fluid as it moves past an object
large to offset the effects of density. For depends on the size and shape of the object,
example, Denny et al. (1985) measured on the speed of the fluid relative to the
accelerations in the surf zone in excess of object, and on the viscosity and density of
400 m/sec 2 . Terrestrial plants and animals the fluid. For an object of a given shape,
are often an order of magnitude larger than these variables can be combined into a
those in the surf zone, and therefore would dimensionless number—the Reynolds
have to experience accelerations of 32,000 number, Re:
m/sec 2 if their size were to be limited by
Re = PfiiL/n
(13)
the same mechanism as that which applies
to intertidal organisms. It seems unlikely where u is the speed of the object relative
that accelerations of this tremendous mag- to the fluid (or of the fluid relative to the
nitude are ever present in air. In general, object) and L is a characteristic length of
then, it is indeed true that fluid-dynamic the object (here used as a measure of the
forces are larger in water than in air.
object's size). The numerator of this ratio
For some aspects of locomotion, how- is proportional to the inertial forces acting
ever, it is not the absolute magnitude of on afluidas itflowsaround an object. These
lift or drag that is important, but rather are the forces that give a fluid its tendency
their ratio. For example, as a fish swims to coast along in a given direction. In conthe oscillatory motion of its tail creates a trast, the denominator is the dynamic visforward-directed lift. If the fish is cruising cosity, a term proportional to the viscous
at a constant velocity, the average thrust forces acting on the fluid and therefore
provided by this lift is just equal to the total expressive of the tendency for the fluid to
drag. Changing the density of the fluid in come to a halt. It is this ratio of inertial to
which the fish swims would affect both lift viscous forces that determines the pattern
and drag to the same degree, and the abil- of flow around an object of a given shape,
ity of the fish to swim would not be altered. and it is for this reason that the Reynolds
In as much as thrust at a constant speed is number is a useful index of flow pattern.
equal to drag, the same reasoning applies
At 20°C water is about 800 times denser
to flying insects, bats, and birds. However, than air and 60 times as viscous. As a result,
in the case of flying animals, the absolute the Reynolds number for an object of a
magnitude of lift is also important. If lift given size moving at a given velocity is about
is less than the animal's weight, the animal
15 times as high in water as in air. Thus
falls out of the sky. For this reason, vari- objects in air need to move 15 times as fast
ations in air density can affect flight. For as objects of the same size in water to
instance, Feinsinger et al. (1979) note that achieve the same general pattern of flow.
the foraging behavior of hummingbirds This difference can be important for those
varies with altitude in a fashion that can aspects of biological function that rely on
be explained by variations in air density— particular flow patterns. Here we explore
at high altitude the birds adopt a feeding a case in which the density and viscosity of
mode that minimizes their flight time.
the medium combine to affect the ability
The examples discussed here are but a of organisms to capture suspended partifew of the many in which fluid dynamics cles.
interacts with biology. The reader interRubenstein and Koehl (1977) note that
ested in further biological ramifications of many biological "filters" are different from
fluid-dynamic forces should consult sources sieves in that they can capture particles
118
MARK W. DENNY
Mesh
Element
FIG. 2. Schematic drawing of the trajectory taken
by a bit of fluid (solid line) and by a dense solid particle
(dashed line) as they move in the vicinity of one cylindrical element in a filtering mesh.
BULK MODULUS AND THE
SPEED OF SOUND
Closely tied to the differences in density
between air and water is a difference in
their bulk modulus, defined as the change
in pressure that must be exerted on a material to obtain a given fractional change in
density:
(P-Po)
(15)
- Po)/Po
(14) Here the subscript 0 designates quantities
measured before pressure is applied, and
B has the units of N/m 2 . The bulk modulus
where dp is the diameter of the particle, dc is the reciprocal of a material's compressis the diameter of the cylindrical mesh ele- ibility and, as we will see, is of interest
ment, and u is the velocity of the fluid rel- because it determines the speed of sound.
ative to the cylinder at a point well upstream
For air, the bulk modulus is predicted
of the filter. Inertial impaction is most by the kinetic theory of gases. It can be
effective when the "Reynolds number" of shown that under adiabatic conditions (i.e.,
a solid particle (pdpu/n), and therefore its no heat enters or leaves the system when
trajectory, is very different from that of the gas is compressed):
the fluid {pfdpu/ii). Because the effective
density of objects in air is 50-200 times
that in water, and because the viscosity of
(16)
water is 60 times that of air, the difference
m
in Reynolds numbers in eq. 14 is 3,000- where y is the ratio of the specific heat of
12,000 times greater in air than in water, the gas at constant pressure to its specific
bulk modulus, B =
index of
pdpu
inertial =
18<f,
impaction
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smaller than the distance between mesh
elements in the filter. One of the primary
mechanisms by which particles are captured by a filter is inertial impaction, as shown
in Figure 2. As fluid moves past a cylindrical mesh element, the streamlines bend
around the cylinder. If a particle traveling
with the fluid has the same density as the
fluid, it faithfully follows streamlines, and
only if it passes within one particle radius
of the mesh element will it contact the cylinder and be captured. However, if the
particle is denser than the medium, its inertia tends to keep it moving in a straight line
when the streamlines bend to pass around
the cylinder. In this fashion, the inertia of
the particle increases the probability that
it will be intercepted by a mesh element.
Rubenstein and Koehl (1977) provide an
index of the probability that a particle will
be captured by inertial impaction:
indicating that the capture of particles is
vastly more effective in air. This physical
effectiveness is often offset by the low concentration of suspended particles in air, and
for this reason aerial suspension feeding is
seldom practical. However, trees use this
mechanism to augment their water supply.
For example, the coast of California
receives little or no rain during the summer but is often inundated with fog.
Because fog particles have a density of
1,000 kg/m s , they can effectively impact
on the needles of conifers such as redwoods. The resulting "fog drip" adds substantially to the water available to these
trees (Kerfoot, 1968). Although the effectiveness of filtration is much lower in
aquatic environments, it still can be a viable
way to make a living because the concentration of available particles (detritus and
plankton) is relatively high in many aquatic
habitats. A wide variety of aquatic organisms capture suspended particles as their
only means of feeding.
T H E MEDIUM AND ITS MESSAGE
speed of sound, c = (B/po)v< (17)
Feynman^a/. (1963). Inserting eq. 16 into
eq. 17 we find that at atmospheric pressure
and 20°C the speed of sound in air is 346
m/sec. Under the same conditions the
speed of sound in water is 1,518 m/sec.
The wave length of a sound wave in a
given medium is equal to the ratio c/jwhere
/ i s the frequency of the sound (in Hertz)
and wave length is measured in meters.
Thus, for any given frequency, the wave
length in water is approximately four times
that in air, which can have biological consequences. For example, animals in both
air and water use sound to locate objects
in their environment. A pulse of sound is
emitted by the animal, who then listens for
the echo to be reflected back from the
object being located, often a prey item.
However, this scheme works only if the
prey is large enough to return a discrete
echo. The necessary size is determined by
the wave length of sound emitted by the
predator. If the length of the prey is at
least several wave lengths, sound is effectively reflected. If, instead, the prey is less
than a wave length long, sound tends to
diffract around it. To detect effectively
objects on the order of 1 cm in length,
sounds of a very high frequency must be
used. For example, bats use sounds on the
order of 30-80 kHz (wavelength 0.43-1.15
cm) in locating insect prey whose dimen-
sions are on the order of centimeters
(Wever, 1980). Aquatic animals must tune
their sonar systems to a higher frequency
than terrestrial animals if they are to be
able to detect objects of the same size, and
this indeed seems to be the case for whales,
which use clicks containing frequencies as
high as 50-200 kHz in their echolocation
systems (Wever, 1980).
ELECTRICAL RESISTIVITY
Perhaps the largest physical difference
between air and water is in electrical resistance. The electrical resistivity of dry air
at sea level is about 4-1013 flm (Chemical
Rubber Co., 1977). The resistivity of water
depends on its salinity, but for seawater it
is about 2.5-10" 3 Qm, some 16 orders of
magnitude less than that of air. This large
difference in resistivity might explain why
many animals in water can sense at a distance the electrical activity of other animals, while the ability to sense electrical
activity appears to be absent in terrestrial
organisms.
Consider the case shown in Figure 3. An
organism (the source) sits in the middle of
an infinite fluid of resistivity <£. The animal
has its center at the origin, and produces
an electrical current Is (as a by-product of
muscle contraction, for instance) that flows
from a point a distance V'LS to the right of
the origin, to a point a distance V'LS to the
left of the origin. The effective resistance
of the medium to this current can be shown
to be (J. Dairiki, personal communication):
resistance to
_ 3$
source current, Rt ~ 2irL
(18)
Because it takes energy to push a current
through a resistance, power, Ps, equal to
I?R, is expended by the source organism.
Thus for a given current, power expenditure increases directly with the resistance
of the medium. Solving for current in terms
of power we see that for a given power
expended by the source:
(19)
Is =
The electrical signal that can be detected
as a result of this activity depends on what
the electrical field is at a distance from the
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heat at constant volume (for air, 7 = 1 . 4 ) ,
R is the universal gas constant (8.314
J/mole/°K), T is the absolute temperature,
and m is the molecular weight of" the gas.
Note that m is usually measured in grams
(e.g., the average molecular weight of air
is 29 g/mole), but to be consistent with the
other units in the equation, m must be converted to kilograms (e.g., 0.029 kg/mole
for air). The higher the pressure and temperature, the higher the bulk modulus. At
one atmosphere of pressure and 20°C, the
bulk modulus of air is 1.42-105 N/m 2 .
At 20°C the bulk modulus of water is
2.1910 9 N/m 2 , 15,420 times that of air.
Thus, for most biological purposes water
may be considered to be incompressible.
Now the speed of sound (in m/sec) is a
function of bulk modulus:
119
M A R K W. D E N N Y
120
SOURCE
FIG. 3. Schematic drawing of a two-point source of
an electrical field and of a distant detector.
1 +_j*_T
source. The precise nature of the electrical
field is a complicated function of distance
and direction relative to the x axis, but for
radial distances that are large compared to
Ls, a reasonable approximation can be calculated for a steady (DC) current:
•[{cos20 + (sin0cos0)2]*
(20)
where \ES\ is the strength of the field at
distance r from the origin, and 0 is the angle
measured from the positive x axis (see Fig.
3). For a given current produced, the electrical field increases in proportion to the
resistivity of the medium. If we substitute
eq. 19 into eq. 20 to express current in
terms of power, we see that for a given
power output of the source, the magnitude
of the electrical field at a distance r from
the origin increases as the square root of
the resistivity of the medium. Because air
is about 1016 times more resistive than seawater, this would imply that the field
strength produced by an organism expending a given power would be 108 times as
strong in air as in water at any given distance.
Why then do aquatic organisms use electrical sensing while terrestrial organisms
2irLdRd\
•[{cos 2 0-(l/3)} 2
+ {sin0cos0}2]*
(21)
This equation can be simplified in two specific situations. First consider the case in
which the internal resistance of the detector is equal to the resistance that would
exist if the detecting points were only connected by the medium itself, 3$/(2icLd). In
this case, the impedance of the detector is
optimally matched to the medium, providing the largest available signal:
16r6
•[{cos 2 0-(l/3)F
{sin0cos0}2f
(22)
In other words, when the resistance of the
detector is matched to that of the medium
(and assuming that Ld is similar in magnitude to Ls), the power available to the
detector is on the order of (Ld/r)6.
If water is the medium, this sort of
impedance matching is feasible—for
example if Ld is a few centimeters, the
internal resistance need only be on the
order of a few ohms. In contrast, it would
be nearly impossible for a terrestrial organism to match the resistance of its detector
to that of air. If Ld is a few centimeters, the
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do not? The answer appears when we calculate the power available to a detecting
organism. For simplicity I assume that this
organism detects the electrical signal by
extending two point conductors into the
medium a distance Ld apart, the two points
being connected internally by a resistance
Rd (Fig. 3). The line connecting these two
points is assumed to lie parallel to the electrical field. The electrical power generated
in this detecting circuit by the field from
the source organism is assumed to be the
available signal. It can be shown that the
power available to the detector, Pd, relative
to that expended by the source animal is
DETECTOR
THE MEDIUM AND ITS MESSAGE
required detector resistance is on the order
of 1015fi!
Eq. 21 can also be simplified if Rd <i 3"i>/
(2irLd), such as might occur in air. In this
case, eq. 21 reduces to
P.
•[{cos 2 0-(l/3)} 2
+ {sinflcosfl}2]'7'
(23)
POSTSCRIPT
Only a few physical properties have been
presented here, and the biological examples described are mere hors d'oeuvres in
the potential feast of comparisons between
terrestrial and aquatic environments. For
lack of space I cannot discuss why rates of
transport by diffusion are 10,000 times
faster on land than in aquatic environments or explore the biological consequences of the difference in refractive index
between air and water. The physics of the
interface between air and water—surface
tension, capillary waves, gravity waves,
etc.—have also not been mentioned. The
list goes on and on. I hope, however, that
the information and ideas presented here
will stimulate others to search through the
Handbook of Chemistry and Physics (Chemical
Rubber Co., 1977) for clues to interesting
biological phenomena.
ACKNOWLEDGMENTS
I thank Jeff Dairiki for deriving the
equations relating to electrical signal
detection and an "anonymous" reviewer
for helpful suggestions. Preparation of this
manuscript was made possible by NSF
Grant OCE-8716688.
REFERENCES
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If Ld and Ls are of similar magnitude, the
detectable power is proportional to (RdLd/
$)(Ld/r)6, which is smaller than the value
cited above for a well-matched detector by
the ratio of RdLd to <£. For example, at a
given source power and at a given distance,
if the internal resistance in the detector of
a terrestrial organism is as high as 106 ohms
and Ld is 10 cm, the detected power in air
would only be one hundred-millionth that
detected by a well-matched detector in
water. It is thus not surprising that terrestrial organisms do not routinely sense the
electrical activity of those around them.
This analysis is not meant to belittle the
capabilities of aquatic organisms in detecting electrical signals. Even if the resistance
of the detector is optimally matched to the
medium, the detectable signal still decreases
very rapidly with distance from the source
organism (proportional to 1/r6), and the
electrical sensing organs of fish and other
aquatic animals must be very sensitive.
121
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