Several investigators have giving terms to the phenomenon observed
that when there
constant flow with downstream pressure varying
(Holt’s experiment) as “flow regulator” (Robard, 1963; Holt, 1969).
While Permutt et al. (1962) attribute
to the “vascular waterfall”
suggesting flow may be independent of downstream pressure. Conrad’s
detailed account used the tunnel diode analogy and suggested “negative
impedance” between pressure drop across the collapsible tube and flow
Brower and Noordergaaf (1973) chose to consider the pressure drop
across the collapsible tube as a function of flow and the difference
between external pressure and downstream pressure as the primary
pressure-flow relationship in a collapsible vessel, viz:
They investigated this pressure drop (pl-p2) to flow relation
function of various parameters that are derived from the fluid and the
tube, i.e. elastic property of the vessel and its geometric dimension and
the fluid. The resulting simple relation shows flow,
as a function
the pressure drop, p1-p2, with pe-p2 as a parameter that
was gradedly varying (Fig 6.3.3).
This figure resembles that
transistor’s voltage-current relationship.
It can be seen here that the
“negative impedance” concept suggested by Conrad does not exist here.
Flow increases with pressure drop across the collapsible tube only within
certain regime. At low pressure drop and low pe-p2, the relationship is
more gradual and plateau is reached also gradually.
At high pressure
drop and high pe-p2, flow increases rapidly and reaching the plateau
much faster. The plateau region reflects increases in flow that is
independent of pressure drop Ap, across the collapsible vessel, pl-p2, and,
the difference between external pressure and downstream pressure, pe-p2.
In order to explain previous observations, Brower and Noordergraaf
973) expressed the relation in terms of all the governing factors: