suction feeding in the carnivorous plantappliedmath.ucmerced.edu/sites/appliedmath...bladderwort...
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Suction feeding in the carnivorous plant bladderwort (Utricularia)
lessons from
the smallest and fastest suction feeders
Ulrike Müller California State University
Fresno
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Bladderwort (Utricularia inflata)
© Makoto Honda
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Bladderwort traps
*Vincent et al, Proc. Roy. Soc. B (2011); ‡Poppinga et al., AoB Plants (2016); © Vicent (left), Wikipedia (right)
underwater traps length 0.5 to 8 mm ‡
(Utricularia aurea)(Utricularia australis)
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U. bisquamata
U. sandersonii
U. gibba
U. heterosepala
> 200 species | trap sizes: 0.5 to 8 mm Poppinga et al., AoB Plants (2016)
U. livida
U. graminifolia
U. longifolia
U. livida? U. australis
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China & Holzman, PNAS (2014)
sucking while small – does size limit performance?
Bladderwort gape ~200 µm
peak flow near mouth 1 m/s
Fish larvagape ~200 µmpeak flow near mouth 1 mm/s
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QuestionSmall suction feeders: what’s the fluid mechanics?
How do small suction feeders overcome the relatively large viscous forces?
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HypothesisBladderwort operate within
inviscid (inertial) flow,
which lowers the relative contribution of friction
and increases flow speed.
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Predictionsfrom fluid dynamic models
1. inviscid flow model
2. viscous flow model
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Analytical model of inviscid vs viscous flow outside the trap*
x : axial coordinatexm : axial position of mouth planeum : fluid velocity at mouth planed : gape diameterud/2 : fluid velocity at ½ gape
xm
x
d
*Sampson, Proc R Soc London A 1891; ‡ Muller et al., J Theor Biol 1982
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flow visualization | experimental setup
recordingat up to50 000 frames/s
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Bladderwort operate ininviscid (inertial) flow,which lowers the contribution of friction
and increases flow speed. PIV data (n = 15 events)
creeping flow model*
inviscid
model‡
*Sampson, Proc R Soc London A 1891; ‡ Muller et al., J Theor Biol 1982
maximum acceleration: 5000 g
maximum flow speed: 5 m/s
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Conclusionbladderwort trap
flow is inviscid
can generate fast flowsdespite their small size
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Question 2How do bladderwort traps keep the flow inviscid?
What do bladderwort differently from larval fish?
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HypothesesBladderwort operate within
H1: undeveloped flow or H0: developed inertial flow,
which lowers the relative contribution of friction
and increases flow speed.
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❶ inertial flow → large pressure: >10 kPa
❷ start-up effect → brief event: < 1 ms
❸ entrance effect → short channel: <200 µm
What enables bladderwort to generate effectively inviscid suction flows?
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what causes the effectively inviscid flow in bladderwort traps?
❶ high pressure
pressure: 15 kPa 5 kPa 1 kPa 0.2 kPaflow speed @1ms: 4.8 m/s 2.5m/s 1.0 m/s 0.3 m/s
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-10
-8
-6
-4
-2
0
-3 -2 -1 0 1 2 3
what causes the effectively inviscid flow in bladderwort traps?
steady
❷ start-up effect
50 µs
distance (gapes)
pre
ssure
(kPa) start-up effect:
• lowers ΔP inside the mouth ‘funnel’
• does not change performance in front of mouth
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what causes the effectively inviscid flow in bladderwort traps?
0
10
20
30
0 0.05 0.1 0.15 0.2
volu
metr
ic f
low
rate
(m
m3/s
)
time (ms)
❸ entrance effect• 1:1 L:D funnel has
monotonically increasing flow
• a shorter funnel speeds up the onset, has transient peak
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what causes the effectively inviscid flow in bladderwort traps?
0
10
20
30
0 0.05 0.1 0.15 0.2
volu
metr
ic f
low
rate
(m
m3/s
)
time (ms)
❸ entrance effect• 1:1 L:D funnel shows
monotonically increasing flow with plateau after 0.15 ms
• a shorter funnel speeds up the onset of fast flow
• experimental data (●) suggest that funnel is functionally very short
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How to avoid viscous effects?
❶high pressure, ❷start-up, ❸entrance effect
τ = 10 msreach max P
τ = 1 msreach max P
τ = 0.03 msreach max P
τ = 0.1 msreach max P
0.00001 0.0001 0.001 0.01 0.1
0.001
0.01
0.1
1
10
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How to avoid viscous effects?❶high pressure ❷start-up ❸entrance effect
fast flow:
fast onset:
()
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Conclusion 2bladderwort traps generate
inviscid flow byH0: generating high pressureH1: sucking thru a very short throatH1: a fast onset of flow (start-up effect)
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Thank you | collaborators | funding
Gen Li (Chiba University)
Janneke Schwaner (University of Idaho)
Johan van Leeuwen & Kees Voesenek (Wageningen University)
Roi Holzman (Tel Aviv University)
Otto Berg (Fresno State University)
NSF BIO-IOS # 1352130