50
3 Mechanical Aspects of Biosystems
about nitrogen bubble formation in decompression sickness, see Sect. 9.18.) More
details about bubbles is contained in the Appendix D.
The shape of a hanging drop of blood plasma, urine, or cerebrospinal fluid can
be used to determine the fluid’s surface tension. This value is of interest in medicine
since the surface tension of these fluids is affected by various pathologies. The
‘pendant hanging method’ is the following: The drop is allowed to hang and form a
pendant shape. Optical instruments determine the droplet’s shape, including the radii
of curvature at various levels in the droplet. Then a computer is used to solve for
the surface tension, using two equations: (1) The Young-Laplace relation Eq. (3.12)
and (2) The net zero force condition on a segment of the droplet from its base to a
given height z:
2πrσ cos φ = ρgV (z) + πr
2 p ,
(3.13)
where r is the radius of the droplet at height z, φ is the angle between the surface
tangent at height z and the vertical axis, ρ is the density of the fluid, and V (z) is the
volume of the droplet up to the height z.
3.4.4 Capillary Action
‘Capillary action’ is the movement of a liquid caused by adhesion to a hydrophilic
contacting material. If the molecules of a liquid adhere to the surface of a material
with an effective binding energy greater than that within the bulk of the liquid, the
liquid ‘wets’ the material. This is the case for water and glass, because hydrogen
bonding can occur between the water molecules and silicon dioxide, and because
the water molecules can embed into the spaces between the molecules of the glass
surface. Glass surfaces therefore are hydrophilic. In contrast, mercury does not wet
glass.
If a solid material adheres to one fluid greater than another, and is placed across
the boundary layer between these two immiscible fluids under the influence of
gravity, a ‘meniscus’ (crescent shape) will form at the boundary between the fluids
due to the contact forces between the fluids and the solid. Water placed in a vertical
tube with a hydrophilic interior surface will rise in the tube until the weight of the
column of water balances the force adhesion and surface tension σ holding the liquid
at a given height. If we assume that the meniscus that forms has a contact angle of θ
with the tube wall, then the two forces will balance when 2πrσ cos θ = ρ ghπ r 2 ,
where r is the tube inner radius, and h the height of the liquid of density ρ. This
gives h = 2σ cos θ/ρgr.
Because water is the medium of life, the hydrophobic and hydrophilic behavior
of biomolecular surfaces is often related to the function of the surface. Plants take
advantage of capillary-like adhesive forces to raise water from the soil (which itself
holds water by adhesive forces) against the force of gravity. An upwardly-directed
gradient of water pressure at the top of a plant or tree is generated by
3 Mechanical Aspects of Biosystems
about nitrogen bubble formation in decompression sickness, see Sect. 9.18.) More
details about bubbles is contained in the Appendix D.
The shape of a hanging drop of blood plasma, urine, or cerebrospinal fluid can
be used to determine the fluid’s surface tension. This value is of interest in medicine
since the surface tension of these fluids is affected by various pathologies. The
‘pendant hanging method’ is the following: The drop is allowed to hang and form a
pendant shape. Optical instruments determine the droplet’s shape, including the radii
of curvature at various levels in the droplet. Then a computer is used to solve for
the surface tension, using two equations: (1) The Young-Laplace relation Eq. (3.12)
and (2) The net zero force condition on a segment of the droplet from its base to a
given height z:
2πrσ cos φ = ρgV (z) + πr
2 p ,
(3.13)
where r is the radius of the droplet at height z, φ is the angle between the surface
tangent at height z and the vertical axis, ρ is the density of the fluid, and V (z) is the
volume of the droplet up to the height z.
3.4.4 Capillary Action
‘Capillary action’ is the movement of a liquid caused by adhesion to a hydrophilic
contacting material. If the molecules of a liquid adhere to the surface of a material
with an effective binding energy greater than that within the bulk of the liquid, the
liquid ‘wets’ the material. This is the case for water and glass, because hydrogen
bonding can occur between the water molecules and silicon dioxide, and because
the water molecules can embed into the spaces between the molecules of the glass
surface. Glass surfaces therefore are hydrophilic. In contrast, mercury does not wet
glass.
If a solid material adheres to one fluid greater than another, and is placed across
the boundary layer between these two immiscible fluids under the influence of
gravity, a ‘meniscus’ (crescent shape) will form at the boundary between the fluids
due to the contact forces between the fluids and the solid. Water placed in a vertical
tube with a hydrophilic interior surface will rise in the tube until the weight of the
column of water balances the force adhesion and surface tension σ holding the liquid
at a given height. If we assume that the meniscus that forms has a contact angle of θ
with the tube wall, then the two forces will balance when 2πrσ cos θ = ρ ghπ r 2 ,
where r is the tube inner radius, and h the height of the liquid of density ρ. This
gives h = 2σ cos θ/ρgr.
Because water is the medium of life, the hydrophobic and hydrophilic behavior
of biomolecular surfaces is often related to the function of the surface. Plants take
advantage of capillary-like adhesive forces to raise water from the soil (which itself
holds water by adhesive forces) against the force of gravity. An upwardly-directed
gradient of water pressure at the top of a plant or tree is generated by