Acoustophoretic trapping of particles by bubbles in microfluidics

Acous opho e ic apping o
pa icles by bubbles in
mic ofluidics
I zia González
1
*, Manuel Candil
1
and Jon Luzu iaga
1
,
2
1
Labo a o y o ul asonic esona o s Resul , Ins i u e o Physical echnologies and In o ma ion ITEFI, Consejo
Supe io de In es igaciones Cien íficas CSIC, Mad id, Spain,
2
Signaling Lab, Depa men o Cell Biology and
His ology, Facul y o Medicine and Nu sing, Uni e si y o he Basque Coun y (UPV/EHU), Leioa, Spain
We p esen in his pape a simple me hod o p oduce s a egic acous ic pa icle
cap u e si es in mic ofluidic channels in a con olled way. Ai bubbles a e
in e mi en ly injec ed in o a mic o-capilla y wi h ec angula c oss sec ion du ing
aflow mo ion o liquid suspensions con aining mic on-sized pa icles o pa icles o
c ea e bubble-defined “mic o-gaps”wi h size close o 200 µm and sphe oidal
geome y. The es ablishmen o a 3D s anding acous ic wa e inside he capilla y
a a equency close o 1 MHz p oduces di e en adia ion o ces on solid pa icles
and bubbles, and acous ic s eaming a ound he bubble. While he sample flows, pa
o he pa icles collec along he acous ic p essu e node es ablished nea he cen al
axis and con inue ci cula ing aligned h ough he capilla y un il eaching he end,
whe e a e eleased en iched. Meanwhile, he bubble a els e y as owa d
posi ions o maximum p essu e ampli ude beside he channel wall, d i en by
Bje kness o ces, and a ach o i , emaining immo able du ing he acous ic
ac ua ion. Some pa icles adhe e o i s memb ane apped by he acous ic
s eaming gene a ed a ound he oscilla ing bubble. Changes o equency we e
applied o analyze he influence o his pa ame e on he bubble dynamics, which
shows a comple e s abili y once a ached o he channel wall. Only inc easing he
flow mo ion induces he bubble displacemen s. Once eached he open ai a he
end o he capilla y, he bubble disappea s eleasing he apped pa icles sepa a ed
om hei ini ial hos suspension wi h a pu i y deg ee. The de ice p esen s a e y
simple geome y and a low-cos ab ica ion.
KEYWORDS
mic ofluidics, acous ofluidics, apping, pa icles, bubbles. lab-on-a-chip, acous ic weeze s
1 In oduc ion
Se e al applica ions in mic ofluidic pla o ms such as LOC e e o anspo samples om
one loca ion o ano he while keeping he sample in ac .
Mic opa icles as well as biological ma e ial can be apped and manipula ed in
mic ofluidics using di e se echnologies, such as spi al channeliza ions [1–8], channels
including con ac ion/expansion ese oi s o an alignmen o cells, mic opilla s
[9–12],mic o-scale o ices [13,14], mic on-sized gaps, se pen ine channels o memb ane-
based mic ofil e s [15–17] wi h po e diame e s. Pa icles and cells can be handled by
ul asounds, which induce acous opho e ic mo ions [18–21].
The physics o oscilla ing bubbles allows di e se applica ions in mic ofluidics. An
oscilla ing bubble can ac as weeze o mic o-sized objec s manipula ion, like biological
cells. A bubble can be assumed as a so memb ane able o ib a e unde he ac ion o ex e nal
exci a ion. The esponse o a bubble can be linea o non-linea depending upon he ampli ude
o he ib a ion [22].
OPEN ACCESS
EDITED BY
Han Zhang,
Ins i u e o Acous ics (CAS), China
REVIEWED BY
Se gey Gu ba o ,
Lobache sky S a e Uni e si y o Nizhny
No go od, Russia
Mohd Ridzuan Ahmad,
Uni e si y Technology Malaysia, Malaysia
*CORRESPONDENCE
I zia González,
[email p o ec ed]
SPECIALTY SECTION
This a icle was submi ed o Physical
Acous ics and Ul asonics,
a sec ion o he jou nal
F on ie s in Physics
RECEIVED 05 Oc obe 2022
ACCEPTED 10 Janua y 2023
PUBLISHED 26 Janua y 2023
CITATION
González I, Candil M and Luzu iaga J
(2023), Acous opho e ic apping o
pa icles by bubbles in mic ofluidics.
F on . Phys. 11:1062433.
doi: 10.3389/ phy.2023.1062433
COPYRIGHT
© 2023 González, Candil and Luzu iaga.
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unde he e ms o he C ea i e Commons
A ibu ion License (CC BY). The use,
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o ums is pe mi ed, p o ided he o iginal
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his jou nal is ci ed, in acco dance wi h
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which does no comply wi h hese e ms.
F on ie s in Physics on ie sin.o g01
TYPE B ie Resea ch Repo
PUBLISHED 26 Janua y 2023
DOI 10.3389/ phy.2023.1062433
Bubbles also can be manipula ed in fluids by acous ic fields, named
Acous ofluidics: hey can be d i en owa d ce ain zones o acous ic
equilib ium and apped [23,24]. The mo ion o a sphe ical bubble
unde he ac ion o a con inuously oscilla ing p essu e field can be
defined by he Rayleigh–Plesse Eq. 1.
Acco ding o classical heo y [25], bubbles subjec o an acous ic
s anding wa e field ga he a ei he p essu e nodes o p essu e an inodes
depending on whe he hei undamen al esonance equencies a e below
o abo e he d i ing equency. In 1955, Yosioka, Kawasima and Hi ano
s udied he acous ic adia ion p essu e on bubbles [26]. In 1968, Elle
de i ed an exp ession o he o ce expe ienced by a bubble in a s anding
acous ic wa e. La e , he and C um s udied in 1970 he ins abili y o
mo ion o a pulsa ing bubble in a sound field [27]. In 1993, Wa anabe and
Y. Kuki a analyzed he ansla ional and adial mo ions o a bubble in an
acous ic s anding wa e field [28]. They showed ha a sphe ical bubble,
no unde going shape dis o ions, can also execu e i egula ansla ional
mo ionsinas andingwa efield on he condi ion ha i s adial pulsa ions
a e igo ous enough.
In mic ofluidics, acous ic s eaming can gene a e o ici y and
hen flow mixing wi h go e ning iscous o ces [29]. Bu , al e na i ely,
he p esence o bubbles in hese mic ofluidic geome ies exci ed a
hei esonan equencies can gene a e in ense s eaming in he
su ounding liquid associa ed o he ib a ion induced on he gas/
liquid in e ace o he bubbles [1]. Bubble-a ound mic os eaming is
he gene a ion o o ex flows which a ise a ound oscilla ing
ul asound mic obubbles in mic ofluidics. The ib a ion o
sphe ical and fla ened mic ofluidic bubbles can p oduce in ense
mic os eaming when exci ed by ul asound nea esonance.
In 2007, Manasseh and Ooi [30]confi med expe imen ally some hing
obse ed p e iously by Ma mo an and Hilgen eld [31]wi hnea ly
sphe ical bubbles a ached o a wall wi h a fini e con ac angle: a s ong
mic os eaming o bubbles exci ed a equencies nea esonance, wi h
o ici y a ec ing pa icle ajec o ies a dis ances beyond 10 bubble adii.
Longue -Higgins [32] explained in 1998 ha in ense long- ange o ici y
esul s om he combina ion o wo modes o ib a ion oscilla ing ou o
phase. These wo modes a e in hei case he main olume mode and he
o-and- o ansla ion o he bubble cen e o mass wi h espec o he
solid su ace. This heo y comple edbyDoiniko andBouakaz[
33]in
2010, was de eloped o eely oscilla ing sphe ical bubbles.
Mekki Be ada e al analysed in 2016 he mic os eaming flow
a ound an isola ed bubble and ound a sho - ange mic os eaming
a ound i [34]. To s udy eely oscilla ing bubbles in s eady condi ions,
hey confined bubbles be ween he wo walls o a silicone
mic ochannel and ancho ed hem on mic opi s.
La ge ampli udes o ib a ion a e ob ained when he exci a ion
equency co esponds o a pe ime e ha is a mul iple o he Fa aday
wa eleng h.
S eaming mainly occu s in he bulk due o iscous a enua ion. In
a second mechanism, obse ed e en in low-dissipa ion fluids,
s eaming akes i s o igin nea bounda ies whe e eloci y g adien s
a e he s onges and can d i e fluid ci cula ions up o he bulk [35];
Hol sma k e al. [36].
These fixed bubbles can be used o ap and deli e a pa icle o cell
o a desi ed loca ion as acous ic weeze s. Bu hey can p omo e also
o ma ion o s able clus e s o a la e desi ed deli e y. In he p esen
wo k, we desc ibe expe imen al obse a ions o he e ec s on pa icles
induced by mic os eaming de eloped a ound and inside semi-
fla ened bubbles acous ically d i en owa d a wall o a mic ofluidic
channel by he ac ion o a s anding wa e.
2 Me hods and ma e ials
2.1 Theo e ical p inciple o ope a ion
2.1.1 Radia ion o ce exe ed on small pa icles
Pa icles o pa icles in suspension exposed o acous ic wa es
expe ience en ainmen e ec s associa ed o a non-linea in e ac ion
be ween he inciden wa e and ha one sca e ed by each pa icle,
which gene a es an acous ic adia ion o ce ac ing on hem. Fo a
pa icle in a s anding wa e much smalle han he acous ic wa eleng h
λ,wi hdensi yρ
p
, comp essibili y β
p
and a olume V
p
, his o ce can be
exp essed as [37]:
FRad −
πP2
0Vpβ0
2λφρ,β

sin 2kx
() (1)
whe e φ5ρp−2ρ0
2ρp+ρ0
−βp
β0is he acous ic con as ac o , P
0
he inciden
wa e p essu e ampli ude, ρ
0
and β
0
he densi y and comp essibili y
coe ficien s o he fluid espec i ely, and “x” he dis ance om he
pa icle o he nea es node o p essu e in he s anding wa e.
Acco ding o his equa ion, he pa icles collec in pa allel bands
pe pendicula o he sound wa e di ec ion, sepa a ed by a hal
wa eleng h dis ance (λ/2). The sign o φindica es he mo ion o
he pa icles ei he owa d he nodes (φ>0) o o he an inodes in he
s anding wa e (φ<0).
The eloci y o a pa icle mo ing owa ds a p essu e node a
dis ance x om i can be ob ained by equa ing he a e age ul asonic
o ce ac ing o mo e pa icles in o hands wi h S oke’s d ag o ce om
he quiescen liquid, FDx −6πηRpupz, neglec ing ine ial e ec s o
mic ome e -sized sphe ical pa icles:
uxP2
0Vpβl
12ληRp
φρ
p,ρl,ρβp,βl

sin 2kx
() (2)
F om i , he pa icle ajec o y can be de i ed as:
x
()1
ka c an an kx 0
()()
e4φ
3kRp
()
2Eac
η

(3)
wi h he acous ic ene gy densi y: Eac p2
0
4ρ0·c2
0.
We can also calcula e he ime i akes a pa icle o mo e om any
ini ial posi ion z (0) o any final posi ion z ( ):
3η
4ΦkR2
c

Eac
ln an k ·x
()[]
an k ·x0
()[]
 (4)
On he o he hand, he shea a e o a liquid sample flowing in a
mic ofluidic channel wi h ec angula c oss-sec ion (wid h ~ wand
dep h ~ h) is es ima ed [38,39] as:
]shea 32Qsample
πd3
h
32 w+h
()
3 low
πh2w2(5)
Being s
sample
he flow a e o he sample Qsample  olume
S· low and
d
h
he hyd aulic diame e o he ec angula channel, defined as d
h
=2 wh/
(w+h).Pa abolic p ofiles a e desc ibed in Mic ofluidic flow mo ion, as
shown in Figu es 1A, B shows a nume ical p edic ion o acous opho e ic
ajec o ies o h ee sphe ical pa icles de i ed in Ma lab om h ee
di e en posi ions in a s anding wa e while flowing along he channel
om le o igh (y-axis) in a lamina flow condi ions (S okes egime).
The shea o ces a e a iable wi hin he capilla y c oss sec ion wi h
he flow pa abolic p ofile, p o iding a complex con ibu ion o he
acous ic adia ion o ce on he pa icles.
F on ie s in Physics on ie sin.o g02
González e al. 10.3389/ phy.2023.1062433
2.1.2 Mo ion o a bubble in a s anding wa e
The equa ions o mo ion in he ansla ional and he adial
di ec ions a e e-de i ed he e using he Lag angian o malism. A
gas bubble unde goes olume and ansla ional oscilla ions in an ideal
incomp essible liquid. Using he sphe ical coo dina es ( ,θ,ε)
o igina ed a he mo ing cen e o he bubble, he bounda y
condi ions a he su ace o he bubble can be w i en as
δϕ
δ 
_
R+_
xcos θa R
() (6)
whe e ϕis he eloci y po en ial, R ( ) and x ( ) a e he ime dependen
adius and posi ion o he cen e o he bubble, espec i ely, and he
o e do deno es he ime de i a i e [40,41]. The eloci y po en ial,
which mus sa is y he Laplace equa ion.
Δϕ= 0, can be ep esen ed as
ϕa
()
+
_
b
()
2cos θ(7)
Subs i u ing Eq. 7in o Eq. 6, we ob ain a ( ) = R_R
2
and b ( ) = x_R
3
/
2 espec i ely. The Lag angian unc ion o he sys em akes he o m:
L2ρR3_
R2+
_
x2
6

+4
3πR3psc +xFex (8)
whe e p
sc
is hesca e edp essu ea hesu aceo hebubble,V=4πR
3
/3
is he ime- a ying olume o he bubble, and F
ex
e e s o ex e nal o ces
on he bubble, such as he p ima y Bje knes o ce o iscous d ag.
I is known ha a single bubble in a s a iona y acous ic field is
a ac ed o epulsed a he p essu e node o an inode. The o ce ha ac s
on his single bubble is he p ima y Bje knes o ce [22,25]isdefined as:
FB−
4πR3∇pA
3(9)
whe e ∇pa ep esen s he g adien o p essu e. The kine ic ene gy To
he sys em is de e mined by he kine ic ene gy o he su ounding
liquid [42]. Fo low ampli ude ib a ions, a bubble o adius Rwill
esona e a a unique equency, , gi en by [43]:

1
4ρlπ2R23kP
0+2σ
R

−2σ
R

(10)
whe e ρis he densi y, σis he su ace ension, kis he poly opic
exponen o he gas and Po is he hyd os a ic p essu e and he
subsc ip ldeno es liquid. This equa ion is no applicable o
highe ampli udes since he bubbles s a o oscilla e wi h ha monics.
A pa icle mo ing nea a ib a ing liquid-gas in e ace will
expe ience he ‘S okes D ag o ce’F
D ag
along he s eamline. This
o ce is gene a ed by ela i e mo ion be ween an objec and he fluid in
which i is imme sed [44]:
FD ag 6πηRpUp(11)
whe e η ep esen s he dynamic iscosi y, R
p
he pa icle adius and U
p
e e s o he ela i e eloci y be ween he pa icle pand i s su ounding
fluid. A second-o de -adia ion o ce, known as he Bje knes o ce, is
gene a ed o ac on a pa icle expe iences nea an oscilla ing bubble [22]. I
is gene a ed because o a sca e ing e ec o he incoming ul asonic wa es
om he liquid–gas in e ace. This o ce ends o come ou o he cen e o
he bubble and a ec s he pa icles ha a e p esen wi hin he flow field. I
is gene ally assumed ha he pa icles abso b his sca e ed adia ion
acqui ing pa o he momen um ans e ed [45].
F ad 4πR3
pR4
d5ω2ξ2ρl−ρp
ρl+2ρp
⎛
⎝⎞
⎠(12)
whe e d ep esen s he cen e - o-cen e sepa a ion be ween he bubble
and he pa icle; ωdeno es he angula equency and ξ ep esen s he
bubble displacemen .
Acco ding o Eq. 11, he magni ude o he seconda y adia ion
o ce depends upon he geome ies o he pa icle as well as he
ampli ude and he equency a which a bubble is ac ua ed. The sign
ha de e mines he di ec ion o he o ce i.e. whe he a ac i e o
epulsi e depends on he a io o he pa icle and fluid densi ies.
Insona ed bubbles a e a linea sys em o low ampli udes a which hey
exhibi a s able mo ion: supe imposed s eamlines a e gene a ed
a ound he oscilla ing mic obubble (Figu e 1C).
2.1.3 S eaming o ce gene a ed on a pa icle by an
oscilla ing bubble in a wa e
The adhe ence o pa icles on he bubble’s memb ane is due o he
gene a ed acous ic s eaming a ound he bubble. Ma amizonou e al.
FIGURE 1
(A) pa abolic flow mo ion in a channel o c oss sec ion wi h squa e geome y; (B) nume ical simula ion o h ee pa icles app oaching om h ee ini ial
posi ions owa d he p essu e node; (C) Schema ic o heo e ical s eamlines gene a ed a ound an oscilla ing mic obubble.
F on ie s in Physics on ie sin.o g03
González e al. 10.3389/ phy.2023.1062433
p esen ed a s udy in 2021 [45] o desc ibe acous ic s eaming e ec s on
mic opa icles/d ople s in mic ofluidics. Fo a lamina flow, he
go e ning equa ions o he mo ion in h ee dimensions (i.e., he
con inui y and Na ie -S okes equa ions) can be desc ibed as:
zUax
z +∇ρ U 0 (13)
zρ U
z +U ∇

ρ U −∇P+μ ∇2U +G+FAS (14)
whe e ρ
is he fluid densi y, U
is he fluid eloci y ec o , is he ime,
pis he fluid p essu e, μ
is he fluid iscosi y, G = ρ
g is he g a i y
o ce and F
AS
is he o ce ha he fluid expe iences due o he acous ic
field (Ba chelo , 2000) [46].
Fo a s eady incomp essible fluid flow Eqs 13,14 can be
exp essed as:
∇U 0 (15)
ρ U ∇

U −∇P+μ ∇2U +G+FAS (16)
The acous ic s eaming o ces a e calcula ed in a fluid assuming a s eady
s a e o bo h he acous ic and flow fields using a pe u ba ion me hod
(Shiokawa, Ma sui and Ueda, 1990) [47]. Thus, he p essu e, densi y and
flow field eloci y can be desc ibed as PP0+Pa+Pb,ρ ρ0+ρa+ρb
wi h ρ
a
=P
a
/c
[2]andU
U0+Ua+Ub, whe e 0, a and b indices deno e
undis u bed s a e, fi s o de and second o de app oxima ions o he h ee
a iables p essu e p,densi yρand U
he fluid eloci y ec o .
The acous ic s eaming o ce, F
AS
, ac s as a body o ce on he fluid
FAs 〈ρaz Ua〉+ρ 〈Ua·∇
()
Ua〉(17)
The acous ic s eaming o ce componen s om Eq. 17 we e
calcula ed as:
FAsx ρ
2UaxzUax
zx+zUay
zy+ρ
2Uax
zUax
zx+Uay
zUax
zy
(18)
FAsy ρ
2UayzUax
zx+zUay
zy+ρ
2Uax
zUay
zx+Uay
zUay
zy
(19)
whe e U
ax
and U
ay
a e he wa e eloci ies in x- and y-di ec ions,
espec i ely.
The acous ic s eaming o ce ac s as a body o ce on he fluid
(Ding e al., 2013) [48] and hus Eqs 18,19 can be subs i u ed as he x
and y-componen s o F
AS
in Eq. 16.
2.2 Expe imen al se up and me hod o
ope a ion
The expe imen s we e pe o med in a glass capilla y ac ua ed by a
piezoelec ic ansduce a 1,153 kHz a ached o i , hos ing 2D
o hogonal hal -wa eleng h esonances ha gene a ed a single-
p essu e-node along i s cen al axis whe e pa icles collec ed
(Figu e 2A). A piezoce amic squa e ce amic PZ26 (Fe ope m
Piezoce amics, K is ga d, Denma k) o 1 dimensions 10 mm ×
5 mm × 1 mm was used as acous ic ansduce , ac ua ed using a
unc ion gene a o (Agilen 33220A, Agilen Technologies Inc., San a
Cla a, CA, Uni ed S a es) equipped wi h a powe amplifie (E&I RF linea
b oad Amplifie 240 L, Resea ch Bl d. Roches e , NY, Uni ed S a es). The
hickness o he piezoelec ic ce amic defined a hickness-mode esonance
a a equency close o 1,150 kHz wi h a hal -wa eleng h s anding wa e
es ablished be ween he wo pa allel elec ode su aces.
The channel o he capilla y (Vi ocom, Fab ine company, Moun ain
Lakes, New Je sey 07,046) had squa e geome y, wi h inne dimensions o
700 μm×700μm × 5 cm. I allowed he es ablishmen o a hal -
wa eleng h esonance wi hin i s c oss sec ion a a equency close o
1 MHz, wi h a eas o maximal p essu e beside he channel walls and nodal
planes in e e ing along he cen al axis o he capilla y. I was go e ned by
he hickness mode esonance o he piezoelec ic ac ua o . A silicone
ubing was coupled o he inle o he capilla y ube o he sample
injec ion. The de ice was moun ed on a mic oscope slide o aid handling
(Figu e 3A), placed unde a mic oscope du ing he acous ic ea men o
he sample obse a ion. A Pho on CCD came a a ached o a Scope
A1 Zeiss ansmission mic oscope connec ed o a compu e unning a
Pho on Fas cam Viewe h ee so wa ewe eused o hecap u e,con ol
and p ocessing o he filmed images. A cap u e speed o he CCD came a
o 60 ames/s was selec ed o he di e en expe imen s o achie e clea
images o he bubble and pa icles in mo ion unde he acous ic wa e
du ing he flowmo iono hesample.Thewallso hecapilla ywe emade
up o Py ex glass, wi h a hickness o 145 μm. In e mi en injec ion o he
liquid sample combined wi h ai was pe o med using a sy inge. Wi h his
echnique, bubbles wi h adii R0 anging be ween 100 μmand200μm
we e ob ained and in used oge he wi h he liquid sample.
The capilla y con aining a wa e -based liquid suspension and
exposed o he ul asounds was modeled and nume ically analyzed
using he FEM (Fini e Elemen Me hod) so wa e COMSOL
Mul iphysics®.Figu e 2B shows he 3D acous ic p essu e
dis ibu ion nume ically ob ained wi h Comsol Mul iphysics inside
he channel a a equency o = 1153 KHz [49].
3 Resul s
In he expe imen s, h ee simul aneous p ocesses we e obse ed once
applied he acous ic field: i) pa icle collec ion and alignmen along he
acous ic p essu e node es ablished inside he capilla y acco ding o Eq. 1;
ii) a e y apid d i mo ion o he bubble owa d he channel wall wi h a
maximal p essu e ampli ude acco ding o Eq. 9; and iii) adhe ence o
pa icles o he bubble su ace acco ding o Eq. 12 espec i ely.
Fi s , he solid pa icles wi h a posi i e acous ic con as ac o
and size much smalle han he acous ic wa eleng h expe ienced
he adia ion o ce o Eq. 1inside he capilla y du ing hei flow
mo ion om igh o le . They we e d i en owa d he p essu e
node, es ablished sligh ly unde he cen al axis along he channel
leng h (see Supplemen a y Video S1) by he sligh ly dis o ed
acous ic p essu e pa e n gene a ed by he p esence o he bubble.
Meanwhile, some pa icles we e apped by he oscilla ing
bubble (one o de o magni ude bigge ) du ing and a e i s
d i mo ion owa d he channel wall, whe e a maximum o
p essu e ampli ude was eached acco ding o Eq. 9;Figu e 3A
shows a pho og aph o 100 µm-diame e mic obubble aken in he
expe imen s a e picking up a single 20 µm polys y ene sphe e,
which emained adhe ed o i du ing he expe imen s; Figu e 3B
shows nine pa icles adhe ed o he ou e su ace o a 200 µm-sized
sphe ical bubble by he ac ion o ul asounds du ing a flow mo ion
unde lamina flow mo ion egime exposed o a quasi-s anding
wa e. The pa icles we e en ained and d agged by he s eamlines
c ea ed a ound he oscilla ing bubble o adhe e o i s su ace
F on ie s in Physics on ie sin.o g04
González e al. 10.3389/ phy.2023.1062433
(Figu e 3C), acco ding o he mic os eaming pa e n gene a ed by
oscilla ing bubbles in bulk fluid [32]. When pa icles each he
memb ane o he bubble hey a e apped in i .
On he o he hand, he bubble, wi h a diame e app oxima ely 10 imes
la ge han hose o he pa icles (20 µm), is apidly d i en and apped in a
posi ion beside he wall whe e he acous ic p essu e acqui es maximal
ampli ude. Bubbles in a s anding wa e a e exposed o Bje kness o ces and
a e apidly d i en owa d hese loca ions o acous ic equilib ium.
I is known ha he di ec ion o he adia ion o ce depends on he a io
be ween he equency o he ex e nal o ce and he esonan equency o he
bubble. Acco ding o heo y [22,25], small bubbles compa ed o he esonan
equency (which is in e sely p opo ional o he bubble adius: [kHz] ~ 3/R
[mm]) a e d awn in o he s ong field egion, while la ge ones a e pushed ou
in o he weak field egion. Howe e , in he cu en expe imen , a a he la ge
bubble (~100 μm) a a field equency o abou 1 MHz is pushed owa ds he
wall, whe e he field an inode seems o be.
ASupplemen a y Video S1 (Video1.mp4) shows his beha iou .
Once he ai -filled sphe e was a ached o he solid-wall emained
fixed du ing he whole expe imen . Bubble oscilla ions could no be
dis inguished om he filmed images because he empo al esolu ion
FIGURE 2
(A) Expe imen al se up including he mic ofluidic capilla y and a piezoelec ic ansduce a ached unde nea h; (B) 3D acous ic p essu e dis ibu ion
nume ically ob ained wi h Comsol Mul iphysics inside he channel a a equency o = 1153 KHz con aining wa e -based liquid samples [49].
FIGURE 3
(A) pho og aphs o a mic obubble (ϕ= 100 µm) wi h a single 20 µm glass sphe e adhe ed o i and; (B) en pa icles adhe ed o he ou e su ace o a
200 µm-sized sphe ical bubble by he ac ion o ul asounds; (C) scheme o he pa icle adhe ence p ocess on o he oscilla ing bubble due o he acous ic
s eaming gene a ed a ound i .
F on ie s in Physics on ie sin.o g05
González e al. 10.3389/ phy.2023.1062433

associa ed o he CCD cap u e speed is a ious o de s o magni ude lowe
han he acous ic pe iods es ed.
The d i mo ion o he polys y ene small pa icles owa d he
p essu e node was slowe , as shown in subsequen pho os o
Figu e 4A: i ook a ime close o 1 s agains he 34 ms
app oxima ely equi ed by he bubble o each he channel wall.
The pa icles apped by he bubble emained a ached o i s memb ane
and o med a clus e ha desc ibed ce ain displacemen s and o a ions on
he bubble su ace when i was exposed o di e en acous ic condi ions.
Du ing he expe imen s, he equency o he acous ic wa e was
a ied wi hin a ange a ying om 800 kHz up o 1,200 kHz o analyze
he s abili y o he oscilla ing bubble once adhe ed o he channel wall.
The equency a ia ions p oduce ele an a ia ions in he spa ial 3D
acous ic p essu e pa e n inside he capilla y. In consequence,
displacemen s o he bubble should be expec ed.
Figu e 4B shows en cap u ed images o he bubble wi h a clus e
o pa icles adhe ed o i s su ace exposed o he ul asonic wa e a
di e en equencies anging om 800 kHz up o 1,200 kHz.
The clus e shows di e en posi ionson hebubblea each equency.
Compa ing he images o he figu e, iden ical posi ioning o he clus e
was ound a = 980 kHz and 820 kHz espec i ely (Δ = 160 kHz). This
can mean ei he a comple e o a ion o 360°wi h he equency a ia ion
o 180 kHz, o an oscilla o y pa ial o a ion o he bubble owa d fi s one
sense ollowed by a an opposi e di ec ion hal - o a ion. In consequence,
he pa icle agg ega e appea s in he same posi ion a bo h equencies. I
can no be dis inguished om he images o he expe imen s which o
bo h possible mo ions happened om he expe imen s a he cap u e
speed o he came a.
On he o he hand, he pa icle agg ega e p esen s simila
posi ions on he bubble su ace a equencies o 1153 kHz and
951 kHz, which co esponds o a equency a ia ion Δ = 202 kHz.
F equencies o 890 kHz and 800 kHz p o ide also simila posi ions o
he clus e on he bubble (Δ = 90 kHz), as well as simila pa e ns we e
ound a 920 kHz and 851 kHz espec i ely. In his case, he pa icle
agg ega e seem o be behind he bubble, which means an ab up
ho izon al o a ion o almos 270°(o al e na i ely 90°) in a equency
FIGURE 4
Di e en imes filmed on he bubble wi h polys y ene pa icles; (A) he bubble was acous ically apped on he wall in less han 120 ms and emained
immo able all he ime du ing he acous ic ac ua ion; (B) di e en posi ions o he polys y ene bead agg ega e appa en ly ound on he bubble su ace a
di e en acous ic equencies anging om 800 kHz up o 1,200 kHz.
F on ie s in Physics on ie sin.o g06
González e al. 10.3389/ phy.2023.1062433
ise o app oxima ely 70 kHz. Finally, he clus e was ound jus
cen e ed wi h he bubble a he equency o 831 kHz.
In e media e equencies be ween hese desc ibed abo e did no
p o ide clea changes in he pa icle posi ions o e he bubble su ace.
4 Discussion
Fi s , he ampli ude o he acous ic p essu e es ablished inside he
channel was low enough, so ha he a ia ions o equency did no
gene a e de o ma ions in he shape o he bubble, bu ins ead hey
induced ei he o a ions o he bubble a ound i s cen e o g a i y o
cohe en displacemen s o he pa icles apped on i s su ace.
The expe imen s e ealed he s abili y o he bubble once adhe ed
o he channel wall. Nei he displacemen s no landslides we e ound
along such a su ace despi e he s ong a ia ions o he spa ial
p essu e changes associa ed o he equency a ia ions.
On he o he hand, no o a ional mo emen o he bubble has been
di ec ly e idenced wi h he equency a ia ions. Howe e , he
pa icles adhe ed o i s su ace showed ei he displacemen s on he
bubble su ace, o , i i was no he case, hey would be indica o s o he
bubble o a ion. This could no be elucida ed in ou expe imen s.
Anyway, he di e en posi ions ound on he pa icle clus e
posi ion o e he bubble su ace do no show a linea co ela ion
wi h he equency a ia ions, which could be due o he ab up
changes o he p essu e pa e n induced inside he capilla y.
Finally, i should be ema ked he absence o displacemen o he
bubble in he ace o any change in equency es ed. The bubble
emains s able a ached o he uppe wall o he channel wi hou
expe iencing slippage on i a any o he equencies es ed. This
ansla ional mo ion could be only achie ed only by inc easing he
flow a e o he sample ci cula ing along he capilla y. This was he way
o anspo he bubble wi h he pa icle agg ega e adhe ed un il he
end o he channel, whe e collapsed eleasing he pa icles p e iously
apped sepa a ely om hei ini ial hos sample.
5 Conclusion
An oscilla ing bubble can ac as weeze o mic o-sized objec s
manipula ion, like biological cells. In pa icula , he expe imen s o he
cu en pape ha e shown he abili y o a bubble in mic ofluidics o
ap small pa icles and d i e hem owa d places o acous ic
equilib ium ha no co espond o hose ini ially p edic ed o
hem. The seconda y adia ion o ce gene a ed by he bubble can
be used o cap u e he pa icles, and flow mo ion can be used o mo e
he bubble o a desi ed loca ion o pa icle elease. A compe i ion
be ween he adia ion o ce and he d ag o ce allows his anspo .
The mic obubbles ha e shown o be ema kably esilien o ce ain
a ia ions o he acous ic field condi ions.
This no el mechanism o using a single bubble o mic o
manipula ion could be p omising in acous opho e ic p ocesses. I
elies on a non-con ac based app oach o he bubble weeze o
manipula e mic o-objec s ia ac ion-a -a-dis ance p inciple.
Acous ic oscilla ing mic obubbles ha e shown a huge po en ial
o nume ous applica ions ha could be easily inco po a ed in o
exis ing mic ofluidic pla o ms o achie e a ious asks. Ou
expe imen s confi m ha acous ically ac ua ed mic obubbles a e
a sui able agen o anspo ing ma e . Ou objec i e in his
expe imen al s udy was o know he abili y o oscilla ing
bubbles o manipula e smalle pa icles in a flowing sample
unde he ac ion o ul asounds. S eamlines o he seconda y
flow a e linea and pa allel o he wall on which a bubble is
a ached, a he han e ical.
Da a a ailabili y s a emen
The o iginal con ibu ions p esen ed in he s udy a e included in
he a icle/Supplemen a y Ma e ial, u he inqui ies can be di ec ed
o he co esponding au ho .
Au ho con ibu ions
The co esponding IG p o ided he idea o his esea ch and
pa icipa ed in he expe imen s and w i ing p ocess. JL de eloped
majo i y o he expe imen s and con ibu ed o he w i ing p ocess.
Au ho MC con ibu ed o pe o m he expe imen s.
Funding
This wo k is financed by he Spanish Na ional Plan p ojec
PID2021-128985OB-I00 unded by he Spanish Minis e y o
Science and Inno a ion MICINN and CSIC-In amu al p ojec .
Acknowledgmen s
The au ho s wan o acknowledge he suppo o he Spanish
Minis y o Science and Inno a ion.
Conflic o in e es
The au ho s decla e ha he esea ch was conduc ed in he
absence o any comme cial o financial ela ionships ha could be
cons ued as a po en ial conflic o in e es .
Publishe ’s no e
All claims exp essed in his a icle a e solely hose o he au ho s
and do no necessa ily ep esen hose o hei a filia ed
o ganiza ions, o hose o he publishe , he edi o s and he
e iewe s. Any p oduc ha may be e alua ed in his a icle, o
claim ha may be made by i s manu ac u e , is no gua an eed o
endo sed by he publishe .
Supplemen a y ma e ial
The Supplemen a y Ma e ial o his a icle can be ound online a :
h ps://www. on ie sin.o g/a icles/10.3389/ phy.2023.1062433/
ull#supplemen a y-ma e ial
F on ie s in Physics on ie sin.o g07
González e al. 10.3389/ phy.2023.1062433
Re e ences
1. Gosse DR, Wea e WM, Mach AJ, Hu SC, Kwong Tse HT, Lee W, e al. Label- ee
cell sepa a ion and so ing in mic ofluidic sys ems. Anal Bioanal Chem (2010) 397:
3249–67. doi:10.1007/s00216-010-3721-9
2. Yamada M, Seki M. Hyd odynamic fil a ion o on-chip pa icle concen a ion and
classifica ion u ilizing mic ofluidics. Lab Chip (2005) 5:1233–9. doi:10.1039/b509386d
3. Yi C, Li C, Ji S, Yang M. Mic ofluidics echnology o manipula ion and analysis o
biological cells. Anal Chim Ac a (2006) 560:1–23. doi:10.1016/j.aca.2005.12.037
4. Pamme N. Con inuous flow sepa a ions in mic ofluidic de ices. Lab Chip (2007) 7:
1644–59. doi:10.1039/b712784g
5. Bhaga AA, Bow H, Wei Hou H, Tan SJ, Han J, Lim CT. Mic ofluidics o cell
sepa a ion. Med Biol Eng Compu (2010) 48:999–1014. doi:10.1007/s11517-010-0611-4
6.HouHW,Wa kianiME,KhooBL,LiZR,SooRA,TanDS,e al.Isola ionand e ie alo
ci cula ing umo cells using cen i ugal o ces. Sci Rep (2013) 3:1259. doi:10.1038/s ep01259
7. Wa kiani ME, Guan G, Luan KB, Lee WC, Bhaga AA, Chaudhu i PK, e al. Slan ed
spi al mic ofluidics o he ul a- as , label- ee isola ion o ci cula ing umo cells. Lab
Chip (2014) 14(1):128–37. doi:10.1039/c3lc50617g
8. KhooWa kiani BLME, Tan DS, Bhaga AA, I win D, LauLim DPAS, Lim KH, e al. Clinical
alida ion o an ul a high- h oughpu spi al mic ofluidics o he de ec ion and en ichmen o
iable ci cula ing umo cells. PLoS One (2014) 9(7):e99409. doi:10.1371/jou nal.pone.0099409
9. Nag a h S, Sequis LV, Maheswa an S, Bell DW, I imia D, Ulkus L, e al. Isola ion o
a e ci cula ing umou cells in cance pa ien s by mic ochip echnology. Na u e (2007)
450(7173):1235–9. doi:10.1038/na u e06385
10. Bhaga AAS, Hou HW, Li LD, Lim CT. Pinched flow coupled shea -modula ed
ine ial mic ofluidics o high- h oughpu a e blood cell sepa a ion. J Han, Lab A Chip
(2011) 11:1870–8. doi:10.1039/c0lc00633e
11. Sa ioglu F, Ace o N, Kojic N, Donaldson MC, Zeinali M, Hamza B, e al. A
mic ofluidic de ice o label- ee, physical cap u e o ci cula ing umo cell clus e s. Na
Me hods (2015) 12(7):685–91. doi:10.1038/nme h.3404
12. Kim B, Lee JK, Choi S. Con inuous so ing and washing o cance cells om blood
cells by hyd opho esis. Biochip J (2016) 10(2):81–7. doi:10.1007/s13206-016-0201-0
13. Huang LR, Cox EC, Aus in RTH, S u m C. Con inuous pa icle sepa a ion h ough
de e minis ic la e al displacemen . Science (2004) 304:987–90. doi:10.1126/science.1094567
14.CheYuJV,Dha M,Renie C,Ma sumo oM,Hei ichGa onKEB,GoldmanJ,e al.
Classifica ion o la ge ci cula ing umo cells isola ed wi h ul a-high h oughpu mic ofluidic
Vo ex echnology. Onco a ge (2016) 7(11):12748–60. doi:10.18632/onco a ge .7220
15. Tan SJ, Lakshmi RL, Chen PF, Lim WT, Yobas L, Lim CT. Ve sa ile label ee biochip
o he de ec ion o ci cula ing umo cells om pe iphe al blood in cance pa ien s.
Biosens &Bioelec onics (2010) 26:1701–5. doi:10.1016/j.bios.2010.07.054
16. Kuo JS, Zhao YX, Schi o PG, Ng LY, Lim DSW, Shelby JP, e al. De o mabili y
conside a ions in fil a ion o biological cells. Lab A Chip (2010) 10:837–42. doi:10.1039/
b922301k
17. Dessi e I, Gue ouahena BS, Benali-Fu e N, Weschle J, Janne PA, Kuang Y, e al.
A New de ice o apid isola ion by size and cha ac e iza ion o a e ci cula ing umo
cells. An icance Res (2011) 31:427–42.
18. Haake A, Neild A, Kim D, Ihm J, Sun Y, Dual J, e al. Manipula ion o cells using an
ul asonic p essu e field. Ul asound Med Biol (2005) 31:857–64. doi:10.1016/j.
ul asmedbio.2005.03.004
19. Kapishniko S, Kan sle V, S einbe g V. Con inuous pa icle size sepa a ion and size
so ing using ul asound in a Mic ochannel. J S a Mech Theo Exp. (2006) 2006:P01012.
doi:10.1088/1742-5468/2006/01/p01012
20. Lau ell T, Pe e sson F, Nilsson A. Chip in eg a ed s a egies o acous ic sepa a ion
and manipula ion o cells and pa icles. Chem Soc Re (2007) 36:492–506. doi:10.1039/
b601326k
21. González I, Fe nandez LJ, Gomez T, Be ganzo J, So o JL, Ca a o A. A polyme ic chip
o mic omanipula ion and pa icle so ing by ul asounds based on a mul ilaye
configu a ion. Sens Ac ua o s B Chem (2010) 144:310–7. doi:10.1016/j.snb.2009.10.042
22. Leigh on T. The acous ic bubble. San Diego: Academic P ess (1994).
23. Hawkes J, Coakley WT. Fo ce field pa icle fil e combining ul asound s anding
wa es and lamina flow. Sens Ac ua o s B Chem (2001) 75:213–22. doi:10.1016/s0925-
4005(01)00553-6
24. Doiniko A, Bouakaz A. Acous ic mic os eaming a ound a gas bubble. J Acous Soc
Am (2010) 127(2):703–9. doi:10.1121/1.3279793
25. Elle A. ‘Fo ce on a bubble in a s anding acous ic wa e. J Acous Soc Am (1968) 43:
170–1. doi:10.1121/1.1910755
26. Yosioka K, Kawasima Y, Hi ano H. ‘Acous ic adia ion p essu e on bubbles and hei
loga i hmic dec emen . Acus ica (1955) 5:173.
27. Elle A, C um LA. ‘Ins abili y o he mo ion o a pulsa ing bubble in a sound field.
J Acous Soc Am (1970) 47:762–7. doi:10.1121/1.1911956
28. Wa anabe T, Kuki a Y. ‘T ansla ional and adial mo ions o a bubble in an acous ic
s anding wa e field. Phys Fluidsa (1993) 5:2682–8. doi:10.1063/1.858731
29. Lei J, Hill M, Glynne-Jones P. Nume ical simula ion o 3D bounda y-d i en acous ic
s eaming in mic ofluidic de ices. Lab Chip (2014) 14(3):532–41. doi:10.1039/
C3LC50985K
30. Tho P, Manasseh R, Ooi A. Ca i a ion mic os eaming pa e ns in single and
mul iple bubble sys ems. J Fluid Mech (2007) 576:191–233. doi:10.1017/
S0022112006004393
31. Ma mo an P, Hilgen eld S. Con olled esicle de o ma ion and lysis by single
oscilla ing bubbles. Na u e (2003) 423(6936):153–6. doi:10.1038/na u e01613
32. Longue –Higgins MS, Pa icle d i nea an oscilla ing bubble, P oceedings o he
Royal Socie y o London. Se ies A: Ma hema ical, Physical and Enginee ing
Sciences.(1998). doi:10.1098/ spa.1997.0083
33. Doiniko AA, Bouakaz A. Acous ic mic os eaming a ound an encapsula ed pa icle.
J Acous Soc Am (2010) 127(3):1218–27. doi:10.1121/1.3290997
34. Mekki-Be ada F, Comb ia T, Thibaul P, Ma mo an P. In e ac ions enhance he
acous ic s eaming a ound fla ened mic ofluidic bubbles. J Fluid Mech (2016) 797:851–73.
doi:10.1017/j m.2016.289
35. Wes e el PJ. The heo y o s eady o a ional flow gene a ed by a sound field. The
J Acous Soc Ame ica (1953) 25(60):60–7. doi:10.1121/1.1907009
36. Hol sma k J, Johnsen I, Sikkeland T, Ska lem S. Bounda y laye flow nea a
cylind ical obs acle in an oscilla ing incomp essible fluid. J Acous Soc Ame ica (1954)
26:102. doi:10.1121/1.1907271
37. Go ’ko LP. On he o ces ac ing on a small pa icle in an acous ical field in an ideal
fluid. So Phys Dokl (1962) 6:773–5.
38. Zheng X, Silbe -Li Z. Measu emen o eloci y p ofiles in a ec angula mic ochannel
wi h aspec a io α= 0.35. Expe imen s in Fluids (2008) 44:951–9. doi:10.1007/s00348-
007-0454-4
39. Kashaninejad NA. New o m o eloci y dis ibu ion in ec angula mic ochannels
wi h fini e aspec a ios. P ep in s (2019) 2019:2019050316. doi:10.20944/p ep in s201905.
0316. 1
40. Tokmako PE, Gu ba o SN, Didenkulo IN, P oncha o -Rub so NV. On
influence o an acous ic field on spa ial dis ibu ion o gas bubbles in a esona o .
Ves nik Nizhny No go od S a e Uni Radiophysics (2006) 1(4):31–40.
41. Didenkulo IN, Ko chagina TS, P oncha o -Rub so NV, Sagache a AA.
P opaga ion o sound in suspensions: Ro a ional mo ions o pa icles and con olling
flows. Bull Russ Acad Sci Phys (2020) 84:634–7. No.6. doi:10.3103/s1062873820060076
42. Doiniko A. T ansla ional mo ion o a sphe ical bubble in an acous ic s anding wa e
o high in ensi y. Phys Fluids (2002) 14(4):1420–5. doi:10.1063/1.1458597
43. C owe CT, Schwa zkop JD, Somme eld M, Tsuji Y. Mul iphase flows wi h d ople s
and pa icles. Uni ed S a es: CRC P ess (2012).
44. B ennen CE. Ca i a ion and bubble dynamics. Uni ed Kingdom: Ox o d Uni e si y
P ess (1995).
45. Ma amizonouz S, Rahma i M, Link A, F anke T, Fu Y. Nume ical and expe imen al
s udies o acous ic s eaming e ec s on mic opa icles/d ople s in mic ochannel flow. In
J Eng Sci (2021) 169:103563. doi:10.1016/j.ijengsci.2021.103563
46. Ba chelo GK. An In oduc ion o fluid dynamics. Camb idge: Camb idge
Ma hema ical Lib a y)Camb idge Uni e si y P ess (2000).
47. Shiokawa S, Ma sui Y, Ueda T. S udy on SAW s eaming and i s applica ion o fluid
de ices. Jpn J Appl Phys (1990) 29(S1):137. doi:10.7567/jjaps.29s1.137
48. Ding X, Li P, Lin SCS, S a on ZS, Nama N, Guo F, e al. Su ace acous ic wa e
mic ofluidics. Lab A Chip (2013) 13(18):3626–49. doi:10.1039/c3lc50361e
49. de los Reyes E, Acos a V, Ca e as P, Pin o A, Gonzalez I. Th ee-dimensional
nume ical analysis as a ool o op imiza ion o acous opho e ic sepa a ion in polyme ic
chips. J Acous Soc Ame ica (2021) 150:646–56. doi:10.1121/10.0005629
F on ie s in Physics on ie sin.o g08
González e al. 10.3389/ phy.2023.1062433