Mechanisms o De-icing by Su ace Rayleigh and Pla e
Lamb Acous ic Wa es
Shilpi Pandey,* Jaime del Mo al,* S e an Jacob, Lau a Mon es, Jo ge Gil-Ros a,
Alejand o F echilla, A e eh Ka imzadeh, Vic o J. Rico, Raul Kan e , Niklas Kandelin,
Ca men López-San os, Heli Koi uluo o, Luis Angu el, And eas Winkle ,* Ana Bo ás,
and Agus in R. González-Elipe
1. In oduc ion
Ice acc e ion on ma e ials ope a ing ou doo s
o in sub-ze o en i onmen s is a c i ical issue
ha significan ly impac s e ficiency, main e-
nance, and secu i y in a ious indus ies,
including a ia ion, ene gy gene a ion,
and he unc ionali y o senso and came a
windows and sc eens. To add ess his p ob-
lem, wo p ima y app oaches ha e been
p oposed: 1) Passi e an i-icing based on
applying su ace enginee ing p ocesses o
educe o delay ice acc e ion;
[1–5]
e y o en,
hese app oaches ely on supe hyd ophobic
o liquid-in used su aces.
[6–9]
2) Ac i e
de-icing/an i-icing sys ems applying di e -
en s a egies o ice emo al o p e en ing
i s o ma ion; ecen ad ances in he field
include nano echnology-based mel ing by
Joule hea ing,
[10]
using ma e ials such as
g aphene,
[11–13]
o pho o he mal de-icing
using plasmonic o magne ic nanopa -
icles.
[14–18]
An eme gen de-icing app oach
in ol es he ac i a ion o su aces by
high- equency acous ic wa es (AW) wi h
Acous ic wa es (AW) ha e ecen ly eme ged as an ene gy-e ficien ice- emo al
p ocedu e compa ible wi h unc ional and indus ial- ele an subs a es. Howe e ,
c i ical aspec s a undamen al and expe imen al le els ha e ye o be disclosed o
op imize hei ope a ional condi ions. Iden i ying he p ocesses and mechanisms
by which di e en ypes o AWs induce de-icing a e some o hese issues. He ein,
using model LiNbO
3
sys ems and wo ypes o in e digi a ed ansduce s, he
e-icing and an i-icing e ficiencies and mechanisms d i en by Rayleigh su ace
acous ic wa es (R-SAW) and Lamb wa es wi h 120 and 510 μm wa eleng hs,
espec i ely, a e analyzed. Th ough he expe imen al analysis o de-icing and
ac i e an i-icing p ocesses and he fini e elemen simula ion o he AW gene -
a ion, p opaga ion, and in e ac ion wi h small ice agg ega es, i is disclosed ha
Lamb wa es a e mo e a o able han R-SAWs o induce de-icing and/o p e en
he eezing o small ice d ople s. P ospec s o applica ions o his s udy a e
suppo ed by p oo o concep expe imen s, including de-icing in an icing wind
unnel, demons a ing ha Lamb wa es can e ficien ly emo e ice laye s co e ing
la ge LN subs a es. Resul s indica e ha he de-icing mechanism may di e
o Lamb wa es o R-SAWs and ha he wa eleng h mus be conside ed as an
impo an pa ame e o con olling he e ficiency.
S. Pandey,
[+]
S. Jacob, A. Ka imzadeh, A. Winkle
Leibniz IFW D esden, SAWLab Saxony
Ins i u e o Eme ging Elec onic Technologies (IET), G oup “Acous ic
Mic osys ems”
Helmhol zs . 20, 01069 D esden, Ge many
E-mail: shilpi.pandey@ um.de; [email p o ec ed]
The ORCID iden ifica ion numbe (s) o he au ho (s) o his a icle
can be ound unde h ps://doi.o g/10.1002/adem.202401820.
[+]
P esen add ess: Ma e ials Science and En i onmen al Enginee ing,
Facul y o Enginee ing and Na u al Sciences, Tampe e Uni e si y, 589,
33104 Tampe e, Finland
© 2024 The Au ho (s). Ad anced Enginee ing Ma e ials published by
Wiley-VCH GmbH. This is an open access a icle unde he e ms o
he C ea i e Commons A ibu ion-NonComme cial-NoDe i s License,
which pe mi s use and dis ibu ion in any medium, p o ided he
o iginal wo k is p ope ly ci ed, he use is non-comme cial and no
modifica ions o adap a ions a e made.
[Co ec ion added on 17 Decembe 2024, a e fi s online publica ion: The
9 h au ho name has been co ec ed in his e sion.]
DOI: 10.1002/adem.202401820
S. Pandey,
Heinz-Nixdo -Chai o Biomedical Elec onics
School o Compu a ion, In o ma ion and Technology
Technical Uni e si y o Munich
T anslaTUM, 80333 Munich, Ge many
J. del Mo al, L. Mon es, J. Gil-Ros a, V. J. Rico, C. López-San os, A. Bo ás,
A. R. González-Elipe
Nano echnology on Su aces and Plasma Lab
Ma e ials Science Ins i u e o Se ille
Consejo Supe io de In es igaciones Cien íficas (CSIC)
Ame ico Vespucio 49, 41092 Se illa, Spain
E-mail: [email p o ec ed]ic.es
S. Jacob
Ge man Na ional Me ology Ins i u e (PTB)
Bundesallee 100, 38106 B aunschweig, Ge many
A. F echilla, L. Angu el
Ins i u o de Nanociencia y Ma e iales de A agón (INMA)
CSIC-Uni e sidad de Za agoza
50018 Za agoza, Spain
RESEARCH ARTICLE
www.aem-jou nal.com
Ad . Eng. Ma e . 2024, 2401820 2401820 (1 o 16) © 2024 The Au ho (s). Ad anced Enginee ing Ma e ials published by Wiley-VCH GmbH
nano-scale ampli udes, a p ocedu e compa ible wi h indus ial- el-
e an su aces. In his con ex , a key dis inc ion should be made
be ween he localized applica ion o su aces o comme cially
a ailable ul asound gene a o s
[19,20]
and he inno a i e con-
cep s based on he inco po a ion o piezoelec ic ac i e suppo s
o laye s, as well as elec odes (la e al field exci a ion (LFE) o
in e digi a ed ansduce s (IDTs)), as in eg al pa s o he su -
ace o be ac i a ed.
[21–26]
The p esen wo k fi s wi hin his sec-
ond app oach, dealing wi h he in eg a ion o su ace o bulk
acous ic wa es (SAWs and BAWs) o de-icing and ice sensing.
Among he a icles add essing his opic, he wo k o Yang e al.
(2021), which p oposes a s a egy o weaken ice adhesion using
Rayleigh su ace acous ic wa es (R-SAW),
[21]
is pa icula ly
no ewo hy. Fo his pu pose, IDTs wi h di e en wa eleng hs
(100, 200, 300, and 400 μm) we e manu ac u ed on a 5 μm hick
ZnO piezoelec ic hin film deposi ed on an aluminum sub-
s a e, p oducing SAWs wi h equencies comp ised be ween
7.38 and 27.84 MHz. The au ho s s a e ha SAWs p oduce
ib a ions compa able o “nano-scale ea hquakes”,which
esul in he gene a ion o acous ic-hea ing e ec s, he de elop-
men o mic o-c acks, and he dis u bance o ice nuclea ion
h ough local ib a ions and ene gy s eaming in o he o med
liquid phase. The con ibu ion o Joule hea ing e ec s di ec ly
s emming om ohmic losses in he IDTs canno be disca ded
in hese expe imen s since ice d ople s we e placed di ec ly a op
he IDTs. The same au ho s ha e ecen ly claimed he possibil-
i y o moni o ing ice o ma ion using his ype o SAWs.
[22]
Simila ly, Zeng e al.
[23]
demons a ed a dec ease in
adhesion be ween ice and subs a e due o in e ace hea ing
and a educ ion in elec os a ic o ces and mechanical in e lock-
ing on SAW-ac i a ed subs a es. Del Mo al e al.
[24]
and
Jacob e al.
[25]
ha e ecen ly ex ended he applica ion o
acous ic wa e de-icing o anspa en subs a es and suppo s.
In he fi s wo k, he au ho s demons a ed ha ex ended elec-
odes on piezoelec ic pla es in an LFE configu a ion gene a e
hickness shea mode - bulk acous ic wa es (TSM - BAWs) in
he 3–4 MHz ange. These wa es e ficien ly induced de-icing
and a educ ion o ice acc e ion (i.e., ac i e-an i-icing e ec ),
as well as a dec ease in ice adhesion. A d awback o his
app oach is he necessi y o a as -elec onic uning o he
exci a ion due o he e y na ow bandwid h o BAW modes.
The possibili y o using he same de ice o ice de ec ion unde
ealis ic ope a ion condi ions (i.e., expe imen s in icing wind
unnels (IWT)) and a p ofi able syne gy o educe powe con-
sump ion upon he applica ion o an i-icing coa ings we e also
demons a ed in Del Mo al e al. wo k.
[24]
On he con a y,
Jacob e al.
[25]
demons a ed ha R-SAW echnology can be
applied o la ge a eas and anspa en subs a es beyond he
cen ime e scale, p o ing ha R-SAWs can be used o de-icing
indus ially ele an su aces. In ha wo k, he au ho s also
demons a ed ha R-SAWs gene a ed on piezoelec ic pla es
and piezoelec ic hin films induced he de-icing o glaze ice
h ough a pu e acous ic mechanism, disca ding he mel ing
h ough di ec elec o he mal (Joule) hea ing induced by ohmic
losses in he IDTs on subs a es wi h low he mal conduc i i y.
Recen ly, he same au ho s demons a ed ha a hyb id ope a-
ional mode is possible by combining R-SAW o de-icing and
BAW o sensing by ca e ully con olling he exci a ion mode o
he wo finge combs in eg a ed in o he IDTs.
[26]
O he ele an
s udies on he implemen a ion o AW ice senso s and de-icing
o ime ice ha e also been ecen ly published.
[27–30]
Despi e he significance o hese con ibu ions, de-icing wi h
subs a e-in eg a ed AW sys ems aces subs an ial undamen al
unce ain ies ha s ill hinde he implemen a ion o his echnol-
ogy in eal-wo ld applica ions. C i ical bo lenecks encompass he
assessmen o ac o s a ec ing he ansmission o AW ene gy o
ice o wa e p esen on he de ice su ace, unde s anding he
mechanisms behind ice-c acking and o he p ocesses con ibu -
ing o ice emo al wi hou comple e mel ing, and defining
ac i a ion condi ions o a oid ice o ma ion unde subze o em-
pe a u es, he eby enabling an e ficien an i-icing mode.
Addi ional ea u es p e en ing an unequi ocal compa ison o
e ficiencies and de-icing mechanisms a e he di e ences in he
ype o AWs, ei he SAWs, Lamb wa es, o TSM-BAWs,
[21–26]
he
e ec o he subs a e ma e ials (e.g., anspa en and black LN,
ZnO hin films deposi ed on di e en subs a es such as Al oils,
glass and used silica, he hyd ophobic o hyd ophilic su ace
modifica ion o hese subs a es, e c.), o he ple ho a o condi-
ions used in he expe imen s ( ype o ice, liquid wa e con en
(LWC) when wo king in IWTs, s a ic and windy condi ions,
empe a u es and ela i e humidi y, wa e eezing o ice acc e-
ion, e c.).
To shed some ligh on his wiligh scena io, we he ein sys-
ema ically in es iga e he de-icing and ac i e an i-icing ac i a ion
o he same subs a e wi h ei he R- SAW o Lamb wa es. Fo his
pu pose, we use LiNbO
3
(LN) piezoelec ic chips ac i a ed wi h
IDTs ope a ing a di e en d i ing equencies. The selec ion o
LN o p epa ing specific model sys ems o s udy de-icing wi h
AWs exceeds his opic, as his piezoelec ic ma e ial is widely
u ilized in o he applica ions such as high- empe a u e senso s
o op ical wa eguide ape ed an ennas.
[31–33]
He ein, we ha e
elec o-acous ically cha ac e ized a se ies o IDT configu a ions
o op imize hei pe o mance, ei he o ac i a ing R-SAWs o
Lamb wa es. Then, o hese wo wa e modes and a ious sub-
ze o empe a u es, we pe o med de-icing and ac i e an i-icing
expe imen s o small ice agg ega es and wa e d ople s, moni-
o ing he h eshold powe equi ed in each case. Addi ionally,
an analysis o he ope a ional condi ions o he chips using
fini e elemen model (FEM) simula ions in COMSOL
Mul iphysics is used o model he gene a ion o he R-SAW
and Lamb wa e modes and accoun o hei in e ac ion wi h
ice. Finally, o alida e hese expe imen al and simula ion
esul s o Lamb wa es, we ha e ca ied ou some p oo -o -
concep de-icing expe imen s p o ing he sui abili y o he
Lamb wa e ac i a ion o emo e la ge a eas o acc e ed ice.
The o e all assessmen o he de-icing o small ice agg ega es
and la ge ice laye s wi h Lamb wa es has pe mi ed he p oposal
o a specific mechanism o de-icing using Lamb wa es ha
di e s om ha al eady known o R-SAWs.
[25,30]
We a e con-
fiden ha all hese findings will significan ly con ibu e o
es ablishing a a ional pa hway o exploi ing AWs as he basis
o a nex -gene a ion de-icing sys em.
R. Kan e , N. Kandelin, H. Koi uluo o
Ma e ials Science and En i onmen al Enginee ing
Facul y o Enginee ing and Na u al Sciences
Tampe e Uni e si y
589, 33104 Tampe e, Finland
www.ad ancedsciencenews.com www.aem-jou nal.com
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2. Expe imen al Sec ion
2.1. Fab ica ion and Elec oacous ic Cha ac e iza ion o AW
Chip De ices
The selec ed piezoelec ic ma e ial was a 0.5 mm hick black
Li hium Nioba e 128° YX wa e cu pu chased om CSIMC-
F eqcon ol, China. The 4 inch wa e s we e cleaned wi h ace one
and IPA using ul asonic cleaning o 5 min and O
2
plasma ea -
men a 100 W o 10 min. IDTs we e pa e ned using pho o esis
spin-coa ing, a maskless lase w i e (Heidelbe g ins umen s
MLA 100), and he li -o echnique. Ti (5 nm)/Al (295 nm) was
selec ed o IDT me alliza ion. Fu he , 100 nm SiO
2
,
[34]
was
deposi ed by magne on spu e ing on op o he wa e . This laye
ac s as a passi a ion laye and p o ec s he aluminum IDTs om
co osion. This SiO
2
hin film con e s a hyd ophilic cha ac e o
he su ace o p epa ed chips (we ing con ac angle ≈35°). The
con ac pads we e opened o elec ical con ac by a d y e ching
p ocedu e. Figu e S1 in he Suppo ing In o ma ion sec ion (SI)
shows he u ilized mask design and a manu ac u ed wa e aimed
a ab ica ing IDTs wi h wa eleng hs a ying om 120 o 510 μm
and an ape u e o 9.95 mm, including a ious designs wi h a
di e en numbe o finge pai s. Chips ope a ing a di e en
wa eleng hs we e diced in o indi idual chips, as shown in
Figu e S2, Suppo ing In o ma ion. Keeping he same ape u es
and numbe o finge pai s, di e en IDTs layou s and sizes o
diced LN pla es we e used o he chips u ilized o p oo -o -
concep expe imen s, as explained in he co esponding sec ion.
Chip sizes o 15 20, 15 25, and 15 30 mm
2
ha e been p e-
pa ed on he wa e , depending on wa eleng h. The de ices wi h
120 and 510 μm wa eleng h (hence o h called 120 chip and 510
chip, espec i ely), used o he de-icing expe imen s o small ice
agg ega es as done in his wo k, we e p epa ed on 15 20 and
15 30 mm
2
LN pieces, espec i ely. A 420 μm chip was also
p epa ed o a compa a i e de-icing es wi h big ice agg ega es.
This ensu ed a minimum a ea o 15 10 mm
2
wi hou IDTs o
de-icing expe imen s.
Fo he elec oacous ic cha ac e iza ion o he chips as a unc-
ion o finge pai s, on-wa e elec ical measu emen s we e ca -
ied ou using a ec o ne wo k analyze (VNA, Keysigh E5080B)
and a wa e p obe (Figu e S3, Suppo ing In o ma ion). Be o e
RF measu emen , a iscous pho o esis was applied be ween he
IDTs o a enua e he wa es and neglec eflec ions on neighbo -
ing IDTs, hus a oiding undesi ed e ec s by measu ing he
eflec ion coe ficien (S
11
) cu es.
2.2. De-icing and Ac i e An i-icing Tes s wi h Small Ice
Agg ega es
De-icing and an i-icing expe imen s we e ca ied ou in a cus om-
made icing chambe , whe e empe a u es down o a minimum
alue o 20 °C can be con olled (see Figu e S4, Suppo ing
In o ma ion, showcasing a iew o his chambe , he chip
holde , and he wa e dosing sys em). An ad-hoc wa e dosing
sys em consis ing o hea able ubing inse ed ia he wall o he
cooling chambe was employed o enable he dosing o d ople s
o bi-dis illed wa e on he su ace o he chips o p oduce
icepa icles.Inside hechambe , he ubewaskep a a
empe a u e o 2 °C o p e en wa e eezing inside he ube.
The empe a u e o he subs a e was con olled independen ly
om ha o he cooling chambe by a Pel ie pla e on which he
holde and p in ed ci cui boa d (PCB) we e placed. Se e al
he mocouples we e moun ed on he s age and he d ople hose
o p ecisely con ol he empe a u e o he chip and wa e d op-
le dispense . A USB came a wi h an a ached C-moun objec-
i e was placed ou o he cooling chambe o ollow he
e olu ion o ice agg ega es and d ople s.
De-icing and ac i e an i-icing expe imen s we e conduc ed on
chips wi h IDTs o 120 and 510 μm in his cus om-buil cooling
chambe . The icing es s we e pe o med wi h he bes -sui ed
configu a ion o a ailable chips (acco ding o he numbe o finge
pai s) as de e mined by hei elec o-acous ical cha ac e iza ion.
Expe imen s we e ca ied ou a h ee empe a u es (5, 10,
and 15 °C, as con olled on he Pel ie pla e) wi h he s age in a
ho izon al posi ion. A hese empe a u es, he po osi y and
na u e o ice o med upon acc e ion p ocesses om he impac
o supe cooled wa e d ople s change om glaze (a 5 °C) o
mix (a 10 °C) o ime (a 15 °C).
[35]
Howe e , unde he expe -
imen al condi ions o he ein- epo ed expe imen s, he ice did
no o m by acc e ion bu by cooling sessile wa e d ople s.
These condi ions a e p omp o gene a e li le po osi y. The s age
empe a u e was con inuously moni o ed du ing he expe i-
men s using a he mocouple moun ed on an aluminum holde
in di ec con ac wi h he Pel ie pla e. Once he empe a u e was
s abilized, a 22 μL milliQ wa e d ople a þ2 °C was dispensed
on he su ace o he chips a a dis ance o ≈3 mm om he IDTs.
A e a while, he dispensed wa e d ople oze in o a small
agg ega e o ice, and hen he chip was elec ically exci ed un il
he ice was comple ely mel ed. The minimum ac i a ion powe
(we deno e his de-icing powe as DP
T
, a magni ude ha depends
on empe a u e T) has been aken as a ele an pa ame e o
compa ing he de-icing e ficiency o he 120 and 510 μm chips.
Fo he ac i e an i-icing expe imen s, he same olume o wa e
was d ipped on an elec o-acous ically ac i a ed chip, and he
minimum powe equi ed o p e en eezing (an i-icing powe ,
AP
T
) was aken as he ele an pa ame e o compa ing e ficien-
cies. In hese expe imen s, he su ace was pe manen ly ac i a ed
o a oid ice nuclea ion and he subsequen eezing o he depos-
i ed wa e d ople .
The RF AW ac i a ion o he chips inside his cooling chambe
was done by con ac ing he diced chips ia a 50 Ωimpedance
PCB p o ided wi h gold-coa ed sp ing-pin connec o s as shown
in Figu e S2, Suppo ing In o ma ion oge he wi h he chip
holde adap ed o conduc he de-icing expe imen . An RF sup-
ply, BSG F20 (Belek oniG GmbH, Ge many), has been used o
elec oacous ic exci a ion, and he powe supplied by he ins u-
men has been aken as a e e ence pa ame e o he ac ual
applied powe .
2.3. P oo o Concep : Expe imen s o De-icing La ge Ice
Laye s wi h Lamb Wa es
Two p oo -o -concep expe imen s using Lamb wa es ha e been
ca ied ou o de e mine he de-icing mechanisms o his ype o
wa e applied o la ge-a ea ice laye s o agg ega es.
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2.3.1. Expe imen 1
In he 510 μm chip used o his expe imen , he IDT and con-
nec ion pads we e s uc u ed on he LN ace ha was no exposed
o ice acc e ion. This means he 510 μm IDTs and PCB boa d
we e on he opposi e side o he ice- o ma ion su ace. The con-
nec ing boa d was adequa ely p o ec ed o p e en sho age o
mal unc ion wi h he IDT layou in he cen e o he LN pla e
and he connec ing pads a each side o he chip (Figu e S5,
Suppo ing In o ma ion shows he chip, PCB, and p o ec ing
boa d). In his configu a ion, he connec ing pad a he op side
o he chip was he elec ically pola ized one, while ha a
he bo om was g ounded. The icing a ea was equi alen o he
15 30 mm
2
chip size. Ice acc e ion was done in he IWT acili y
a ailable a he TAU labo a o y (de ailed in o ma ion abou hese
Ice Labo a o y acili ies can be ound in Koi uluo o e al.
[36]
).
A maximum wind speed o 25 m s
1
, wi h a liquid wa e con en
o 0.5 g m
3
a a empe a u e o 10 °C was used o acc e e he
ice in his expe imen . The o ma ion o a mixed ice ype is
expec ed om hese expe imen al condi ions. An ice film wi h
a hickness be ween 0.5 and 1 mm, depending on he loca ion
on he chip su ace, was acc e ed and kep in he wind unnel
chambe a 10 °C be o e being subjec ed o AW ac i a ion.
2.3.2. Expe imen 2
The expe imen was pe o med wi h a 510 μm chip o
15 30 mm
2
wi h he IDT s uc u ed on he ice-exposed side o
he LN pla e. In his case, a la ge olume o wa e o ≈180 μL was
deposi ed in ambien ai on he chip su ace ou side he zone o
IDTs. The wa e co e ed an a ea o ≈0.9 cm
2
, sepa a ed by a dis-
ance o ≈2 mm om he IDT. Then, he chip and connec ing
boa d we e placed inside he cooling chambe , and he empe a-
u e dec eased up o 15 °C o induce ime ice o ma ion.
A e wa d, he chip and boa d we e emo ed om he cooling
chambe , and he AW de-icing was induced in ambien condi-
ions immedia ely a e connec ing wi h he elec onics ( o al
ime sho e han 10 s). The p ocess was ollowed by placing a
ideo came a ou side. Du ing his ime, he sample empe a u e
ne e su passed 0 °C wi hou AW ac i a ion. These condi ions
gene a ed some os on op o he su ace o he chip due o
wa e apo condensa ion, as isible du ing he expe imen s.
Fo compa a i e pu poses, a simila expe imen o he one done
in Expe imen 2 was also ca ied ou wi h a 420 μm chip gene -
a ing Rayleigh SAWs.
Fo he expe imen s, he elec onic con ol and ac i a ion
sys ems we e placed ou side ei he he cooling chambe
(expe imen 2) o IWT (expe imen 1, al hough in his case, he
ambien empe a u e was 10 °C). Elec onics consis ed o a
ec o ne wo k analyze (VNA) o de e mine he wo king e-
quency du ing and a e ice acc e ion and a swi ch allowing o
au oma ically connec he chip o a signal gene a o sys em con-
sis ing o a signal gene a o (Keysigh 33210A) and an amplifie
(Mini-Ci cui s LZY-22þ). Fu he de ails o his elec onic con-
ol and ac i a ion sys em can be ound in Del Mo al e al.
[24]
The
epo ed de-icing expe imen s we e ca ied ou applying an RF
signal a a ound 7.3 MHz wi h sligh a ia ions in he o de
en hs o kHz depending on he chip and peak- o-peak ol ages
o 53 V (expe imen 1) and 70 V (expe imen 2), equi alen o
app oxima e powe alues o 1.7 and 4.8 W, espec i ely.
2.4. Fini e Elemen Model (FEM) Calcula ions
Fini e elemen (FE) simula ion o he 120 and 510 μm chips was
conduc ed using COMSOL Mul iphysics e sion 6.0. This simu-
la ion desc ibes he gene a ion and p opaga ion o AWs and hei
in e ac ion wi h ice, e i ying he easiness o mechanical ene gy
ansmission h ough he piezoelec ic LN and he ice in e ace.
Fo his pu pose, we ha e calcula ed he displacemen field (u)in
he subs a e and he ice agg ega e unde he assump ion ha
la ge displacemen s in he ice agg ega e mean a be e ansmis-
sion o he mechanical ene gy o he AW om he ac i a ed LN o
ice. The ice agg ega e was loca ed a he same dis ance om he
edge o he las finge o he IDT as in he expe imen s, ying o
ep oduce hei ac ual condi ions. To keep he compu a ional
cos s wi hin easonable limi s, he olume o he simula ed d op-
le has been se led a 4 μL. Ice agg ega es we e assumed o p es-
en a hemisphe ical shape, as i ypically happens a e eezing
wa e d ople s deposi ed on su aces.
The AW ib a ions o he LN pla e wi h IDTs ha e been mod-
eled using a se ies o elec odynamic and mechanic equa ions, as
p e iously desc ibed by Fakh ou i e al.
[37]
Since R-SAW and
Lamb wa es on 128° X–Y LiNbO
3
a e mainly pola ized in he
median plane,
[38]
a wo-dimensional (2D) model was simula ed
using a gene alized plane s ain assump ion. This assump ion
has been adop ed o simula e bo h he 120 and 510 μm chips.
The 0.5 mm hick subs a e has been desc ibed wi h he elas ic-
i y, piezoelec ic, and elec ic pe mi i i y enso s o LN,
[39]
which
we e adequa ely o a ed o accoun o he ac ual 128° X–Y c ys al
cu o he subs a es used in he expe imen s. The ice was mod-
eled as an iso opic linea -elas ic ma e ial in he o m o a semi-
ci cle geome y, using he ice p ope ies p o ided by Vic o and
Whi wo h,
[40]
co esponding o a compac ype o ice simila o
glaze ice. All his in o ma ion, including he desc ip ion o he
cha ac e is ics o he IDTs, dimensions, applied ol age, ime
s ep used o he simula ions and dimension, and o he compu-
a ional pa ame e s, can be ound in he SI sec ion, SI6. No ably,
he ice–subs a e in e ace be ween he ice and he LN subs a e
has been simula ed as fla , an assump ion ha fi s well wi h he
condi ions o he eal sys em o med by a single c ys alline sub-
s a e wi h e y li le su ace oughness. An ideal sys em consis -
ing o an R-SAW wi h a long wa eleng h (510 μm) in e ac ing
wi h he ice agg ega e was also simula ed o compa a i e and
discussion pu poses. The pa ame e s used o compu ing he
510 μm Lamb wa e sys em we e kep o his ideal sys em, excep
o he assump ion o a fini e hickness o he LN subs a e. This
semi-infini e hickness bounda y condi ion educes eflec ion o
he AW a he bo om ace o he pla e o a minimum, ha is,
imposing a si ua ion ypical o he gene a ion o R-SAWs. This
simula ed model will be designa ed in he ex as 510 μm R-SAW
o di e en ia e i om he simula ed model o he 510 μm Lamb
wa es.
Figu e 1 p esen s a scheme wi h he defini ion o sys em coo -
dina es (x,y,z) used o calcula ions. Since he COMSOL
Mul iphysics calcula ions ha e been ca ied ou in wo dimen-
sions (2D), he ele an coo dina es a e xand z(c. . Figu e 1b).
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The o me co esponds o he p opaga ion di ec ion o he wa e,
while he la e co esponds o he pe pendicula o he LN pla e.
Fo calcula ions, figu es, and da a p esen a ion, we ha e
adop ed he ollowing defini ions: 1) Volume ic displacemen s:
he local, wa e-induced displacemen field unde gone by he la -
ice o he LN pla es. They a e cha ac e ized by a la ice displace-
men ec o u. The ele an magni udes o da a calcula ion and
p esen a ion a e i s modulus in 2D |u| and he wo componen s
u
x
and u
z
. 2) Su ace displacemen s: he displacemen field
unde gone by he ou e su ace o he pla e, which in he icing
expe imen is in con ac wi h he ice and is di ec ly in ol ed in
he ansmission o he mechanical ene gy o he ice. This defi-
ni ion simplifies he no a ion and ema ks on he impo ance o
powe confinemen on he su ace o he chip. Su ace displace-
men s a e cha ac e ized by a su ace displacemen ec o , s. The
ele an magni udes o p esen da a and o calcula ions a e i s
modulus in 2D |s| and he wo componen s s
x
and s
z
.
The geome y o he whole sys em has been disc e ized wi h
an uns uc u ed iangula mesh, and he acous ic modes
ha e been desc ibed wi h a leas 10 elemen s pe wa eleng h
conside ing he ollowing sound eloci ies: in LN subs a e
3981 m s
1
,
[39]
in ice 1850 m s
1
.
[40]
The esul ing g id had
app oxima ely h ee million elemen s (equi alen o ≈18.3 mil-
lion deg ees o eedom). Elec ical exci a ion was modeled using
an elec ic po en ial ha ollows he pe iodici y o he IDT fin-
ge s, which we e loca ed on he le hal o he model geome y,
neglec ing he mechanical damping o he me al elec odes. To
a oid undesi ed eflec ions o he AWs a he edges o he chips,
he AWs we e abso bed by inco po a ing pe ec ly ma ched laye s
(PML) as defined in he COMSOL so wa e documen a ion.
[41]
The model was sol ed in bo h he equency domain and he
ime domain using a equency sol e o a ime-dependen
sol e , espec i ely. In he equency domain, he IDTs we e
defined as an RF po whe e powe is explici ly defined as an
inpu pa ame e (1 W was a bi a ily selec ed o he calcula ions
since simula ions a e linea and p o ide S
11
spec a and ha -
monic solu ions o he displacemen and elec ic fields, no
dependence o esul s is expec ed on he used inpu powe ).
Simula ions we e also done in he ime domain o ob ain eal-
ime es ima ion o he ib oacous ic esponse o he LN pla e
and he LN/ice sys ems upon elec oacous ic exci a ion. In his
case, he elec ical exci a ion is applied o he IDTs as a sinusoidal
ol age signal wi h defined ampli ude and wo king equency as
inpu pa ame e s. Wo king equencies we e selec ed based on
he equency domain esul s ollowing maximum powe ans-
mission c i e ia. To gene a e equi alen mechanical powe s o
he AWs in he simula ion o he 120 and 510 μm chips, he
selec ed ol age ampli udes in each case we e di e en o com-
pensa e o he di e ences in elec oacous ic coupling. The e o e,
he esul ing elec ic powe o each wa eleng h was sligh ly di -
e en o ensu e ha he gene a ed mechanical powe was equi a-
len in all simula ed models.
3. Resul s and Discussion
3.1. RF Cha ac e iza ion o AW Chips
The adio- equency (RF) elec ical cha ac e iza ion o he chips
was pe o med by measu ing he S
11
( e u n loss) and |S
11
|
2
( eflec ion coe ficien o powe ) pa ame e s as a unc ion o e-
quency. The measu ed esonance equencies ( equency o he
S
11
minima) closely ma ch he calcula ed esonance equencies
o he chips, acco ding o he well-known exp ession
¼ s
λ(1)
whe e , s, and λa e, espec i ely, he wo king equency, he
wa e eloci y on 128° YX LN subs a e (3981 m s
1
)
[39]
and
he wa eleng h, his la e defined by he IDT layou (i.e., he dis-
ance be ween finge s). The se ies o e u n loss spec a plo ed
as a unc ion o equency eco ded o he di e en chips p e-
pa ed in his wo k a e epo ed as SI7. These spec a show ha
he S
11
minima deepen o a highe numbe o finge pai s.
To minimize he eflec ed powe , de-icing es s we e ca ied
ou wi h 120 and 510 μm chips wi h he la ges numbe o finge
pai s es ed du ing he elec oacous ic e alua ion, ha is, 15 and
26, espec i ely.
To es ima e he powe e ficiency, he eflec ion coe ficien o
powe |S
11
|
2
is he ele an pa ame e , which can be calcula ed
om Equa ion (2) and (3):
RLðdBÞ¼10 log10
Pi
P
 (2)
jS11j2¼P
Pi
(3)
whe e RL(dB) is he e u n loss o he chips and P
and P
i
a e
eflec ed and inciden powe , espec i ely.
Figu e 2 shows a se ies o plo s o he eflec ion coe ficien o
powe |S
11
|
2
e sus equency as eco ded o he 120 and 510 μm
chips wi h di e en numbe s o finge pai s. A pho og aph o
hese wo chips is also included in he figu e. The ull se o
Figu e 1. Schema ic desc ip ion o he geome y o chips wi h displace-
men field and axis defini ions; a) 3D diag am o he chip; b) 2D diag am
o he chips as used o he calcula ions.
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|S
11
|
2
cu es eco ded o all manu ac u ed chips is shown in
Figu e S7, Suppo ing In o ma ion.
To ensu e he maximum e ficiency o he de ices, hey should
p esen |S
11
|
2
alues close o ze o o minimize he eflec ed
powe upon elec ical ac i a ion. The plo s in Figu e 2 show ha
he eflec ed powe is highly dependen on he numbe o finge
pai s and dec eases when i s numbe inc eases. Fo he longes
wa eleng h chip, ha is, he 510 μm chip, powe losses eached
sa u a ion a |S
11
|
2
alues a ound 0.25 o 26 finge pai s. Fo he
120 μm chip, a |S
11
|
2
alue smalle han 0.1 is eached wi h 15
finge pai s. In gene al, al hough he eflec ion coe ficien o powe
could s ill sligh ly dec ease by inc easing he numbe o finge
pai s, he benefi s would be e y small and likely compensa ed by
he elec ical powe losses ha also inc ease wi h his pa ame e .
The e o e, we ha e selec ed 15 and 26 finge pai s o he 120 and
510 μm chips o de-icing and an i-icing expe imen s. This choice is
a good comp omise be ween low eflec ion and an accep able ee
chip a ea o de-icing expe imen s (see below).
These plo s in Figu e 2 also e eal a lowe ing in baseline o
he 120 μm chip (ideally, |S
11
|
2
should equal one ou side o he
esonance peak), which is pa icula ly no iceable o he 120 μm
chip. This indica es he exis ence o some elec ical powe losses,
which a e no due o he esonance exci a ion o he c ys al and
a e likely caused by ac o s such as pa asi ic capaci ances in he
IDT, ohmic esis ance o he hin film me alliza ion, o con ac
esis ances. These pa asi ic losses a e in he o de o 10–20% o
he cha ac e ized chips, a pe cen age o he inciden powe ha
will no con ibu e o he gene a ion o AW ib a ions h ough
elec omechanical coupling. The plo s in Figu e 2 also show ha ,
as expec ed, hese elec ical powe losses inc ease wi h he num-
be o finge pai s.
Acco ding o Figu e 2, S7/S8, Suppo ing In o ma ion, he
elec oacous ic esponse o he 510 μm chip is di e en . The
beha io o his chip is cha ac e ized by wo esonance minima
ins ead o one in he equency egion o in e es . We a ibu e
hese wo esonances o Lamb pla e wa es ins ead o Rayleigh
Figu e 2. Elec ical cha ac e iza ion o AW chips: a1,b1) |S
11
|
2
e sus equency plo s o ab ica ed AW de ices wi h wa eleng hs (λ) o 120 μm (a1) and
510 μm (b1). No e he di e en span o he xscales used in each case. The a ow and ellipse highligh he p og essi e inc ease o powe losses in he
se ies o 120 μm de ices as he numbe o finge pai s inc eases. Pho og aphs o he 120 μm a2) and 510 μm b2) chip de ices wi h he maximum numbe
o finge pai s.
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wa es. Acco ding o he well-es ablished heo y o SAW gene a-
ion in piezoelec ic pla es,
[42]
an R-SAW can be ega ded as he
high- equency limi o he supe posi ion o symme ic and an i-
symme ic Lamb wa es. These wo coun e pa s s a o sepa a e
o pla e hicknesses o a ound 1.5 λ. F om he |S
11
|
2
plo s in
Figu e 2, i appea s ha when he wa eleng h o he AW
app oaches he hickness o he pla e, he condi ions o pu e
Rayleigh-SAW a e no longe ulfilled. Acco ding o hese consid-
e a ions and Equa ion (1), he esonance a 7.36 MHz co e-
sponds o he A0 Lamb wa e mode, whe eas he ≈8 MHz
esonance mus be a ibu ed o he S0 Lamb wa e mode. In
he nex sec ion, we u he suppo his a ibu ion by he sim-
ula ions ob ained using COMSOL Mul iphysics analysis o he
AWs in he 510 μm chip. RF chips wi h a simila configu a ion
bu a wa eleng h la ge han 510 μm beha e simila ly and gene a e
wo AWs a di e en equencies (see Figu e S8, Suppo ing
In o ma ion o he |S
11
|
2
cu es expe imen ally de e mined o
a600μm chip, which is epo ed o compa ison).
Table 1 includes expe imen al and calcula ed (i.e., Equa ion (1))
esonance equencies o he manu ac u ed chips wi h he maxi-
mum numbe o finge pai s in each case, as well as he ype o
gene a ed AW.
3.2. FEM Simula ion o AW
Simula ion esul s o he AW gene a ion and p opaga ion in he
120 and 510 μm chips we e ca ied ou as desc ibed in he
Expe imen al and Me hods sec ion. Figu e 3a,b p esen selec ed
esul s o his simula ion analysis o each ype o wa e. Videos
(V1_S10) and (V2_S11) p o ided as SI showcase he ime-
dependen a ia ion o olume ic displacemen s ep esen ed
in he o m o colo maps wi h he same colo code as o he
snapsho s in Figu e 3a2,b2.
The plo s in Figu e 3a1,b1 compa e he expe imen al and cal-
cula ed |S
11
|
2
spec a o he 120 and 510 μm chips. The conco -
dance be ween cu es ob ained wi h expe imen s and simula ions
confi ms ha simula ions ep oduce he expe imen ally eco ded
signals, excep o he elec ical IDT powe losses e idenced by he
non-ze o backg ounds o he expe imen al cu es, a ea u e pa -
icula ly no iceable o he 120 μm R-SAW. This p o es ha , excep
o his de ia ion a ibu able o ohmic losses and/o capaci i e
e ec s in he eal chips no included in he analysis, he simula-
ions o he wo chips ag ee wi h hei ac ual beha io .
The analysis in Figu e 3a2 o he olume ic displacemen s
de e mined in he ime domain o he 120 μm chip confi ms
ha ib a ions only a ec he ou e su ace laye s o he LN pla e,
as expec ed o a ypical R-SAW ype (see ideo (V2_S11),
Suppo ing In o ma ion). This is e idenced by he colo maps
in his figu e showcasing snapsho s o he modulus (|u|) and
u
x
and u
z
componen s o olume ic displacemen s o his wa e
ha confi m he confinemen in he ou e su ace egions o he
pla e. The plo s in he same figu e ep esen ing he alue o |u|
along he pla e hickness as a unc ion o he coo dina e z show
ha he displacemen field goes o ze o in he bulk.
Figu e 3a3 p esen s he plo s o su ace displacemen compo-
nen s s
x
,s
z
, and he modulus o he displacemen ec o a he su -
ace |s| along he di ec ion o wa e p opaga ion (x). No ably, hese
pa ame e s co espond o he AW-induced displacemen s in he
pla e ou e plane o he chip pla e, ha is, he su ace ha will
be in con ac wi h he ice. Figu e 3a3 e eals ha maximum dis-
placemen s along xand za e almos equi alen and a e sepa a ed
by a phase shi o 93°. This esul means ha he su ace displace-
men field app oaches a ci cula pola iza ion, as shown by he plo
in Figu e 3c ep esen ing he componen s
x
e sus s
z
(no e ha he
di e en ci cles in he plo e e o calcula ions a di e en imes).
The “in he ime domain”simula ion o he elec oacous ic
ac i a ion o he 510 μm chip in Figu e 3b
1
gi es ise o wo
well-defined and dis inguishable |S
11
|
2
peaks ma ching he shape
o he expe imen al cu es, as well as he equency alues o he
minima (Table 1). Meanwhile, he analysis in Figu e 3b
1
demon-
s a es ha olume ic displacemen s a ec he whole pla e hick-
ness. The colo plo s in his figu e show ha he fi s peak a
7.4 MHz (no e ha he e is a small di e ence wi h espec o
he expe imen al minimum a 7.36 MHz) co esponds o ib a-
ions wi h an i-symme ical cha ac e and should be a ibu ed
o a A0 ib a ional mode. Meanwhile, olume ic displacemen s
co esponding o he second peak a 8.1 MHz ha e a symme ical
cha ac e (i.e., ypical o an S0 mode, da a no p esen ed).
Meanwhile, plo s in his figu e o |u| as a unc ion o he coo di-
na e zwi hin he pla e show ha he displacemen field does no
anish in i s in e io and ex ends om one ace o he opposi e o
he LN pla e. Figu e 3b
3
shows ha he magni ude o s
x
and s
z
componen s is simila , and he e is a phase shi o 91º be ween
hem, ha is, he su ace displacemen s a e ci cula ly pola ized.
This is confi med by he ep esen a ion o s
x
e sus s
z
in Figu e 3c.
When compa ing he wa es gene a ed in he 120 and 510 μm
chips, i is no ewo hy ha hey p esen su ace and pla e cha -
ac e , espec i ely. Ano he significan di e ence is ha he su -
ace displacemen s in he 510 μm chip o he A0 mode a e
sligh ly smalle han o he 120 μm chip, and hey p esen a ce -
ain modula ion due o he supe posi ion o a second con ibu-
ion o much la ge wa eleng h in he o de o 4–5 mm. This
second con ibu ion is likely due o a weak s anding wa e mode
wi h a la ge wa eleng h ha is supe imposed on he main one
(see Figu e S9, Suppo ing In o ma ion).
3.3. De-icing Expe imen s o Small Ice Agg ega es
To e i y he e ec o he AW cha ac e is ics on he de-icing p o-
cess, we ha e sys ema ically compa ed a se ies o de-icing expe i-
men s ca ied ou wi h he 120 and 510 μm chips. Acco ding o
he p e ious simula ions in Sec ion 3.2, hese chips gene a e
Rayleigh SAW and Lamb wa es, espec i ely.
Table 1. Calcula ed and expe imen al equencies o he bes IDT
configu a ion o he chips in e ms o he numbe o finge pai s.
Wa eleng h
[μm]
Numbe o
finge pai
Measu ed
equency [MHz]
Calcula ed
equency [MHz]
Mode
120 15 32.32 33.25 R-SAW
150 16 25.79 26.60 R-SAW
240 20 16.10 16.62 R-SAW
330 22 11.68 12.09 R-SAW
420 28 ≈9.20 9.50 R-SAW
510 26 ≈7.36 & 8.14 –Lamb wa e
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Expe imen s we e done a empe a u es o 5, 10, and
15 °C. A summa y o he expe imen al condi ions is shown
in Table 2, including in o ma ion abou empe a u e, ac ual e-
quency, and inciden powe alues (i.e., DPT alues), as well as
an es ima ion o he e ec i e powe ac ually a ailable o AW
exci a ion. The la e ha e been es ima ed a e he co ec ion
o he expe imen al DP
T
alues. A fi s co ec ion conside s ha
he elec ical powe ha is no inse ed in o he LN pla e in he
o m o AW elec omechanical ac i a ion would be equi alen o
1- |S
11
|
2
. Fo ins ance, o he 120 μm chip wi h 15 finge pai s, i
0 0.1 0.2 0.3 0.4 0.5
0
0.4
0.8
1.2
1.6
= 1/5T
= 2/5T
= 3/5T
= 3/5T
= T
)
mn
(
||u||
z (mm)
0 0.1 0.2 0.3 0.4 0.5
0
0.4
0.8
1.2
1.6
=1/5T
=2/5T
=3/5T
=4/5T
=T
)mn( ||u||
z (mm)
(b)(a)
28 30 32 34 36
0
0.2
0.4
0.6
0.8
1
F equency (MHz)
Expe imen al
Simula ion
|11S|
2
32.5 MHz
= 120 m
6 6.5 7 7.5 8 8.5
0
0.2
0.4
0.6
0.8
1
F equency (MHz)
Expe imen al
Simula ion
|
11S
|
2
7.4 MHz 8.1 MHz
= 510 m
-2 -1 0 1 2
-2
-1
0
1
2
510um BAW
120um SAW
sz)m
n
(
s
x
(nm)
(a2)
(a3)(b
3)
(a1)(b
1)
(b2)
345
-1.5
-1
-0.5
0
0.5
1
1.5
)mn(
x(mm)
sx
sz
||
s
||
0.75 1 1.25
-1.5
-1
-0.5
0
0.5
1
1.5
sx
sz
||
s
||
)mn(
x(mm)
Su ace displacemen ield (
)
(c)
Volume ic displacemen ield (
)
9.6 x10
x (mm)
)mm( z
6.4
x10
x (mm)
2.6
z (mm)
x10
1.3
x (mm)
z (mm)
9.6 9.6 x10
x10
6.46.4
x (mm)
z (mm)
9.6 9.6
x10
1.31.3
Figu e 3. Simula ion o he AWs: a,b) simula ions o he o he 120 μm (a) and 510 μm (7.4 MHz peak) (b) chips. a
1
,b
1
) simula ion in he equency
domain o |S
11
|
2
.a
2
,b
2
) simula ion in he ime domain o he bulk displacemen s. Simula ions include: i) colo maps snapsho s o he bulk displacemen s
(modulus |u| and u
x
and u
z
componen s); ii) plo s a a ious imes o he modulus o he bulk displacemen ec o |u| along he coo dina e z( hickness o
he pla e). a
3
,b
3
) plo s he modulus |s| and s
x
and s
z
componen s. No e ha he xscale is no he same o he wo wa es o p ope ly compa e he
displacemen fields. c) Plo o he s
x
e sus s
z
componen s o assess he pola iza ion o he displacemen field a he su ace in he wo chips.
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appea ed ha app oxima ely an 8% o he inciden elec ical
powe is no e ficien ly coupled o he de ice. As indica ed in
Sec ion 3.1, pa asi ic elec ical powe losses associa ed wi h
he IDTs should be summed up in his co ec ion. Pa asi ic
losses we e impo an o he 120 μm chip wi h 15 finge pai s,
which amoun ed o ≈20% o inciden powe (c. ., Figu e 2). In
o al, a ough es ima e o he elec ical powe ac ually con e ed
in o mechanical exci a ion wi h his chip migh be in he o de o
72% o he inciden powe ( his pe cen age s ems upon subs a -
ing he 20% o pa asi ic losses plus ≈8% due o he coupling
issues). Fo he 510 μm chip, a simila analysis gi es an es i-
ma ed co ec ing ac o o 69% (no e ha in his case ohmic
o capaci i e losses associa ed o he IDTs we e smalle , c. .
Figu e 2). Since he es ima ed powe losses esul ing om hese
co ec ing ac o s we e a he simila o he 120 and 510 μm
chips, compa a i e assessmen s o powe s and e ficiencies would
be equi alen using ei he inciden o e ec i e powe alues.
No e, howe e , ha hea ing e ec s due o ohmic losses a he
IDTs will likely be highe o he 120 μm chip.
The de-icing expe imen s p oceeded in he ollowing way:
once he chip empe a u e was s abilized in he cooling chambe ,
he sys em was kep unde hese condi ions o a leas 30 min o
empe a u e homogeniza ion. Then, a liquid d ople (þ2 °C,
22 μL) was deli e ed and ozen on he su ace o he chips, o m-
ing a hemisphe ical ice agg ega e defined by a ci cula pe ime e
o ≈4.5 mm. Then, an RF signal wi h he inciden (DP
T
) powe
epo ed in Table 2 was applied o gene a e AWs a he esonance
equencies o each chip. The epo ed alues co espond o he
minimum inciden powe equi ed o induce mel ing. Bo h DP
T
and he e ec i e AW powe alues in Table 2 confi m ha mel -
ing on he 510 μm chip is mo e a o able han on he 120 μm
chip. We en a i ely a ibu e his di e ence o he dis inc cha -
ac e is ics o he wa es gene a ed in each case, a ea u e ha will
be u he discussed in he ollowing sec ions.
The mel ing sequence induced upon applica ion o he
epo ed powe s in Table 2 was ideo- eco ded o bo h chips.
Figu e 4 shows a se ies o snapsho s ep esen ing d ipping
(Figu e 4a1,b1), eezing (Figu e 4a2,b2), pa ial mel ing
Table 2. De-icing da a o he 120 and 510 μm chips: empe a u e,
ope a ing equencies, inciden (DP
T
), and e ec i e AW powe s a e
co ec ion by he es ima ed losses.
Chip [μm] Tempe a u e [°C] F equency [MHz] Inciden powe
a)
(DP
T
) [W] e o
E ec i e
powe [W]
120 15 32.33 3.76 0.26 2.70
10 32.40 2.76 0.68 1.98
5 32.44 1.46 0.20 1.05
510 15 7.36 2.02 0.39 1.39
10 7.40 1.46 0.29 1.00
5 7.36 1.45 0.16 1.00
a)
The unce ain y limi s o he DP
T
alues define he a ia ion in he measu emen s
in each case.
Figu e 4. Compa ison o de-icing p ocess on he a) 120 μm and b) 510 μm chips. A 22 μL d ople is deli e ed on he chips a –15 °C a1,b1); d ople is
ozen; a2,b2): d ople s a s mel ing, a e chip ac i a ion wi h he DP
T
powe s epo ed in Table 2 a3,b3); d ople emains liquid (ac i e an i-icing e ec )
a4,b4). The beha io o he mel ed wa e d ople was di e en o he wo chips: i sp ead o he 120 μm chip bu was pushed owa d he chip edge in he
case o he 510 μm chip. The wa e d ople was dispensed a almos simila dis ance om he las finge o he IDTs (i.e., a abou 3 mm).
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15272648, 0, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1002/adem.202401820 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [19/02/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License