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Locomo n in viscoelas fluids: pusher puller snowman

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39 pages
Locomo?n?in? viscoelas? ?fluids:? pusher,?puller?&?snowman? Lailai?Zhu?and?Luca?Brandt? Linné?Flow?Centre,?KTH?Mechanics,?? Stockholm,?Sweden? Eric?Lauga?and?On?Shun?Pak? Department?of?Mechanical?and?Aerospace?Engineering,?? University?of?California?San?Diego,?La?Jolla?CA,?USA?

  • ?of?micro?organisms? change?in?visco?elas??fluids?

  • locomo?n?in? viscoelas?

  • eric?lauga?and?on?shun?pak? department?of?mechanical?and?aerospace?engineering

  • lailai?zhu?and?luca?brandt? linné?flow?centre

  • ?can? we?use?this

  • ?thrust?comes?from?rear??part?of?the?body?? posi?e? ?


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Locomo on
in
 viscoelas c 
fluids:

pusher,
puller
&
snowman

Lailai
Zhu
and
Luca
Brandt

Linné
Flow
Centre,
KTH
Mechanics,


Stockholm,
Sweden

Eric
Lauga
and
On
Shun
Pak

Department
of
Mechanical
and
Aerospace
Engineering,


University
of
California
San
Diego,
La
Jolla
CA,
USA
Outline

•  How
does
locomo on 
of
micro‐organisms

change
in
visco‐elas c
fluids
?

•  What
can
swim
only
in
visco‐elas c
fluids?
Can

we
use
this?
Introduc on

•  Study
locomo on
in
biologically
relevant
non‐Newtonian
fluids

•  Spheroid
axisymmetric
squirmer
driven
by


tangen al
velocity
(envelope
method) 

α
u = sin(θ)+ sin(2θ)θ
2
α∈ [−5,5]•  Consider

steady
cilia
bea ng
with

•  Nega ve
 α:
pusher.
Thrust
comes
from
rear

part
of
the
body


Posi ve
 α:
puller.
Thrust
comes
from
front
part
of
the
body


Introduc on:
locomo on
in
polymeric
fluids


•  Lauga
(2007)
and
Fu
et
al.
(2009)
analy cal
work
on
waving
sheet/filament


•  Teran
et
al.
(2010),
numerical
study
of
finite
length
filament

•  Experiments
with
C.
Elegans
by
Shen
et
al.
(2011)

•  Zhu
et
al.
(2011),
Neutral
swimmer
by
tangen al
surface
deforma on 
Introduc on

•  Study
locomo on
in
biologically
relevant
non‐Newtonian
fluids

•  Spheroid
axisymmetric
squirmer
driven
by


tangen al
velocity
(envelope
method)

α
u = sin(θ)+ sin(2θ)θ
2
α∈ [−5,5]•  Consider

steady
cilia
bea ng
with

•  Nega ve
 α:
pusher.
Thrust
comes
from
rear

part
of
the
body


Posi ve
 α:
puller.
Thrust
cfront
part
of
the
body


α
Tangen al
velocity u = sin(θ)+ sin(2θ)θ
2
Neutral
Pusher Puller
swimmer
Swimming


direc on
Nega ve
 α:
pusher.
Thrust
comes
from
rear

part
of
the
body


Posi ve
 α:
puller.
Thrust
cfront
part
of
the
body



Model
and
assump on

•  Steady
locomo on

•  Axisymmetric
Stokes
flow
(size
of
the
cell
is
small
enough
)

•  No
Brownian
effect
(size
of
the
cell
is
large
enough

)

Numerical
method

•  Finite
Element
Discre za on 
DEVSS‐G

•  Streamline‐upwind/Petrov‐
Galerkin
(SUPG)
method


for
the
convec ve
term
in
the
cons tu ve
equa on
Polymeric
fluid
dynamics

Stokes
flow
and
Giesekus
model
for
the
cons tu ve

Mobility factor equa on

α =0.2m20=−∇p+β∇ u+∇ ·τp
∇ ·u=0
Weissemberg
number
Viscosity
ra o

µ µs p
β = =1−
µ µResults

• 
Integral
quan es:
swimming
speed,
power
and
efficiency 


Efficiency
is
defined
as
the
ra o
between
the
work
rate
necessary
to
pull
a
sphere/

ellipsoid
at
the
swimmer
speed
in
the
same
fluid
and
the
swimming
power
P


• 
Flow
visualiza on:
streamlines
and
polymer
stretching
Pusher
vs.
puller

 
Dissipa ng
ring
vor ces