2.1. THE PHYSICAL ENVIRONMENT
23
between the momentum (MBL) and diffusive boundary (DBL) layers is given
by
where Sc is the Schmidt number, which is the ratio of the diffusivity of
momentum to the diffusivity of the compound, gas, or ion in question. For
molecules that are relevant to photosynthesis and respiration, values of Sc
in seawater at 25°C are 797 for HC0 3 and 410 for O 2 , resulting in diffusive
boundary layers that are approximately 1/7 th to 1/10 th, respectively, as thick
as the momentum boundary layer.
Momentum and diffusive boundary layer characteristics are related to
the type and speed of fluid motion, the distance the fluid moves over the
surface, the surface roughness, and the steadiness of the flow (White 1994) .
Both types of boundary layers decrease as flow speed increases but how they
decrease depends on whether the flow is laminar or turbulent. Characteristics of the flow surrounding an object are related to the Reynolds number
Re (see (2.3)). Fluids with Re < 10 5 (over a smooth flat plate) usually are
laminar and become turbulent at Re > 5 . 10 5 • As a fluid flows steadily over
a surface, the boundary layer grows and its thickness is a function of the
local Re (Rex), defined as Uwx/v, where x is the distance downstream from
the leading edge of the surface and where Uw is the freestream flow speed.
The thickness of a boundary layer over a smooth flat surface is ::::: 5(Re x )- 0.5,
and in turbulent flow is > 0.37(Re x )-0.2. Laminar boundary layers become
turbulent when Rex> 10 5 - 10
6• Over smooth surfaces turbulent boundary
layers consist of a thin viscous sublayer adjacent to the surface, a transition
zone, and an outer region that is fully turbulent. In the presence of surface
roughness the viscous sublayer disappears. Unsteady flows (e.g. oscillatory)
introduce a temporal component to boundary layer formation and growth
and can result in the periodic disruption of established boundary layers
(White 1994). Allother things being equal, boundary layers (both momentum
and diffusive) will be thicker over organisms with smooth, bladelike shapes
compared with organisms whose surfaces have projections and/or arehack
highly branched.
Diffusive boundary layers may represent a significant resistance to the
flux of mass to and from the surfaces of benthic organisms. If the compound,
gas, or ion is taken up and used immediately in a metabolic process, then
diffusion across the boundary becomes the rate-limiting step and the process
is mass transfer limited (Bilger and Atkinson 1992) . In this case, the metabolic
rate should be a function of flow speed to either the 0.5 (laminar) or 0.8
(turbulent) power (Fig. 2.3).
DBL/ MBL = Sc-O .33
(2.11)
40
•
~ 30
•
c:r:
•
.::!
•
"0 20
•
•
~
~
•
10
0+--,.--,-----,----,----,---1
° 10 20 30 40 50 60
FlowSpeed
Fig. 2.3. Theoretical relationship between flow speed and the rate of
metabolism of mass transfer limited processes. Axisunits are arbitrary. The curve
fit represents a power function of the
form: MR = aFL b
MODELS OF MASS FLUX. To make analyses dimensionless, previous approaches to relate rates of mass transfer to fluid motion have used the
Sherwood number (Sh, Patterson et al. 1991) or the Stanton number (St,
Bilger and Atkinson 1992). Sh is defined as h m W / D m , where h.; is the mass
transfer coefficient, W is the characteristic dimension of the organism, and
D m is the coefficient of diffusion for the compound, gas, or ion. The mass
transfer coefficient is calculated from the metabolic rate per unit area divided
by the concentration gradient Cb - Co between the bulk fluid Cb and the wall
(Co, site of exchange). Sh represents the metabolic rate in a dimensionless
form and is the ratio of convection-assisted mass transfer to exchange by
23
between the momentum (MBL) and diffusive boundary (DBL) layers is given
by
where Sc is the Schmidt number, which is the ratio of the diffusivity of
momentum to the diffusivity of the compound, gas, or ion in question. For
molecules that are relevant to photosynthesis and respiration, values of Sc
in seawater at 25°C are 797 for HC0 3 and 410 for O 2 , resulting in diffusive
boundary layers that are approximately 1/7 th to 1/10 th, respectively, as thick
as the momentum boundary layer.
Momentum and diffusive boundary layer characteristics are related to
the type and speed of fluid motion, the distance the fluid moves over the
surface, the surface roughness, and the steadiness of the flow (White 1994) .
Both types of boundary layers decrease as flow speed increases but how they
decrease depends on whether the flow is laminar or turbulent. Characteristics of the flow surrounding an object are related to the Reynolds number
Re (see (2.3)). Fluids with Re < 10 5 (over a smooth flat plate) usually are
laminar and become turbulent at Re > 5 . 10 5 • As a fluid flows steadily over
a surface, the boundary layer grows and its thickness is a function of the
local Re (Rex), defined as Uwx/v, where x is the distance downstream from
the leading edge of the surface and where Uw is the freestream flow speed.
The thickness of a boundary layer over a smooth flat surface is ::::: 5(Re x )- 0.5,
and in turbulent flow is > 0.37(Re x )-0.2. Laminar boundary layers become
turbulent when Rex> 10 5 - 10
6• Over smooth surfaces turbulent boundary
layers consist of a thin viscous sublayer adjacent to the surface, a transition
zone, and an outer region that is fully turbulent. In the presence of surface
roughness the viscous sublayer disappears. Unsteady flows (e.g. oscillatory)
introduce a temporal component to boundary layer formation and growth
and can result in the periodic disruption of established boundary layers
(White 1994). Allother things being equal, boundary layers (both momentum
and diffusive) will be thicker over organisms with smooth, bladelike shapes
compared with organisms whose surfaces have projections and/or arehack
highly branched.
Diffusive boundary layers may represent a significant resistance to the
flux of mass to and from the surfaces of benthic organisms. If the compound,
gas, or ion is taken up and used immediately in a metabolic process, then
diffusion across the boundary becomes the rate-limiting step and the process
is mass transfer limited (Bilger and Atkinson 1992) . In this case, the metabolic
rate should be a function of flow speed to either the 0.5 (laminar) or 0.8
(turbulent) power (Fig. 2.3).
DBL/ MBL = Sc-O .33
(2.11)
40
•
~ 30
•
c:r:
•
.::!
•
"0 20
•
•
~
~
•
10
0+--,.--,-----,----,----,---1
° 10 20 30 40 50 60
FlowSpeed
Fig. 2.3. Theoretical relationship between flow speed and the rate of
metabolism of mass transfer limited processes. Axisunits are arbitrary. The curve
fit represents a power function of the
form: MR = aFL b
MODELS OF MASS FLUX. To make analyses dimensionless, previous approaches to relate rates of mass transfer to fluid motion have used the
Sherwood number (Sh, Patterson et al. 1991) or the Stanton number (St,
Bilger and Atkinson 1992). Sh is defined as h m W / D m , where h.; is the mass
transfer coefficient, W is the characteristic dimension of the organism, and
D m is the coefficient of diffusion for the compound, gas, or ion. The mass
transfer coefficient is calculated from the metabolic rate per unit area divided
by the concentration gradient Cb - Co between the bulk fluid Cb and the wall
(Co, site of exchange). Sh represents the metabolic rate in a dimensionless
form and is the ratio of convection-assisted mass transfer to exchange by