RAC: Angle-Con e gence Concen a o Based on
Cu a u e-Induced O de ing
Jae Un Kim
Depa men o Physics, Ajou Uni e si y, Republic o Ko ea
[email p o ec ed]
Abs ac
The RAC is a ully passi e, geome y-d i en gas so ing de ice ha selec i ely edi-
ec s CO2based on species-dependen angula esponse inside a cu ed dome. Unlike
memb anes o acuum-swing sys ems, he RAC equi es no pumps, no ene gy inpu ,
and no mo ing pa s.
The key mechanism is ha gases exhibi undamen ally di e en angle- e en ion be-
ha io : CO2shows high angula esponsi i y, s onge su ace in e ac ion, and g ea e
pola izabili y, allowing epea ed cu a u e encoun e s o na ow i s ajec o y. Ligh e
molecules (N2, O2) andomize mo e apidly and ail o main ain a s able pa h.
This pape p esen s: (a) he mic oscopic basis o species-dependen angle e olu ion,
(b) he comple e ope a ing mechanism, (c) cu a u e-induced mul i-bounce ocusing,
(d) a geome ic model wi h TikZ, (e) a compac equa ion o angle con e gence, and
( ) an economic scaling a gumen .
1. In oduc ion
Con en ional CO2en ichmen elies on memb anes, adso p ion beds, o comp ession-based
sys ems. The RAC in oduces a undamen ally di e en p inciple: passi e geome ic
so ing, whe e sepa a ion eme ges om species-dependen angula e olu ion inside a cu ed
dome.
When gas mix u es en e he de ice, molecules unde go epea ed encoun e s wi h he
dome bounda y. CO2, due o i s la ge mass, highe angula esponsi i y, s onge su ace
in e ac ion, and g ea e pola izabili y, p ese es di ec ional momen um mo e cohe en ly.
These mic oscopic ac o s ampli y cu a u e-induced o de ing and lead o p og essi e angle
na owing.
In con as , ligh e molecules (N2, O2) andomize apidly and ail o main ain any s able
di ec ion unde cu a u e. A dedica ed ou le aligned wi h he esul ing dominan CO2
ajec o y cap u es he en iched s eam. The de ice con ains no pumps o mo ing pa s and
can ope a e con inuously wi h ze o ene gy inpu .
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2. Why CO2and O he Gases Show Di e en Relec ion Angles
Mass alone does no ully explain why CO2exhibi s a highly s able, na ow e lec ion band in-
side he dome, while ligh e gases dispe se widely. Al hough molecula mass is he dominan
ac o , h ee addi ional mic oscopic p ope ies — angula esponsi i y, su ace in e ac ion
s eng h, and pola izabili y — ampli y cu a u e-induced o de ing.
In his sec ion, we desc ibe he ull physical basis o species-dependen angula di e -
gence.
2.1 Mass-Dependen Momen um Pe sis ence
Le mdeno e he molecula mass. Hea ie molecules e ain di ec ional momen um o e
mul iple collisions:
CO2(44 amu) : slow di ec ional decay,N2/O2(28–32 amu) : as andomiza ion.
This alone causes pa ial na owing, bu no he ull ocusing e ec . Addi ional molecula
p ope ies signi ican ly s eng hen his asymme y.
2.2 Angula Responsi i y
CO2exhibi s a la ge cumula i e angle adjus men pe wall encoun e . I θnis he p opaga-
ion angle a e nin e ac ions, he esponsi i y can be modeled as:
θn+1 =θn−λ(m) ∆θgeom,
whe e ∆θgeom is he geome ic de lec ion imposed by cu a u e and
λ(m)∝1
√m
so hea ie molecules accumula e angle co ec ions mo e cohe en ly. This p o ides he i s
laye o ajec o y con e gence.
2.3 Su ace In e ac ion Coe icien
CO2is a long linea molecule wi h a la ge e ec i e con ac c oss-sec ion when in e ac ing
wi h solid bounda ies. Du ing a g azing collision, he ex ended molecula leng h p oduces
s onge o ien a ion-dependen o ces, inc easing he s abili y o he pos -collision ajec o y.
We de ine he su ace in e ac ion coe icien Sas:
S≡Ae
A0
,
whe e Ae is he e ec i e in e ac ion a ea du ing su ace encoun e s. CO2has sys ema -
ically la ge S han N2o O2, enhancing di ec ional so ing.
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2.4 Molecula Pola izabili y and Cu a u e Sensi i i y
CO2has a pola izabili y o oughly 2.9˚
A3, subs an ially highe han N2(1.7˚
A3) and O2
(1.6˚
A3). Mic oscopic a ia ions in local elec os a ic po en ial along he cu a u e gene a e
weak alignmen o ces ha CO2 esponds o mo e s ongly.
We de ine cu a u e sensi i i y χas:
χ=γ αmol,
wi h αmol he molecula pola izabili y and γa cu a u e-dependen geome ic ac o .
This sensi i i y ampli ies di ec ional na owing.
2.5 Momen um Redis ibu ion
Du ing collisions, he momen um ec o o CO2unde goes mo e cohe en edis ibu ion due
o i s highe mass and ex ended geome y. I pnis he momen um a e he n- h e lec ion:
pn+1 =pn+δp(m, S, χ),
whe e δpis biased owa d he cu a u e angen . This mechanism na u ally ein o ces
mul i-bounce ocusing.
2.6 Combined Model: Mul i-P ope y Angle Con e gence
The combined species-dependen angle na owing can be summa ized as:
∆θe (m, S, χ)≈α1−e−β(m+S+χ)
whe e αis a cu a u e ac o and βis a andomiza ion- o-o de ing a io.
This exp ession shows why CO2con e ges apidly owa d a dominan ajec o y, while
ligh e gases di use.
3. How: Ope a ing Mechanism o he RAC Dome
The molecula di e ences discussed in Sec ion 2 mani es inside he RAC dome h ough
a ully passi e sequence o geome ic in e ac ions. The de ice has no mo ing pa s and
ope a es con inuously as long as in low is p esen .
3.1 Di ec ed In low
A mixed gas s eam en e s h ough a sho pipe wi h mild di ec ionali y. This se s he ini ial
inciden -angle dis ibu ion o all species.
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3.2 Fi s Cu a u e In e ac ion
Upon he i s encoun e wi h he dome su ace, CO2p ese es i s di ec ion mo e s ongly,
while ligh e molecules unde go la ge andomiza ion. This begins he sepa a ion o e ec i e
pa hs.
3.3 Mul i-Bounce Angula E olu ion
The cu ed bounda y o ces epea ed in e ac ions. CO2 ajec o ies p og essi ely na ow
due o he mechanisms in Sec ion 2, while ligh e gases ail o main ain any s able di ec ion.
3.4 Eme gence o a Dominan CO2Di ec ion
A e se e al wall encoun e s, CO2con e ges owa d a ep oducible dominan exi di ec ion
dic a ed by cu a u e. A CO2abso p ion line is placed along his di ec ion.
3.5 Con inuous Passi e Ex ac ion
As long as in low con inues, CO2is con inuously unneled in o he cap u e line wi h ze o
ene gy cos and no ac i e componen s.
4. Mon e-Ca lo Ve i ica ion o Species-Dependen Angle E olu ion
To e i y ha cu a u e-d i en e lec ion p oduces mass-dependen angle na owing, we
implemen ed a 2-D Mon e-Ca lo simula ion o gas ajec o ies inside a dome.
4.1 Simula ion Model
The dome is modeled as a hal -ci cle o adius R, wi h pa icles en e ing om he le a
x=−Rin. Each pa icle has:
(x0, y0), θ0∼ N(0, σin)
wi h ixed speed 0.
Whene e a pa icle hi s he dome bounda y x2+y2=R2, specula e lec ion is applied:
′= −2( ·ˆn) ˆn
ollowed by a mass-dependen angula noise e m:
δθ ∼ N (0, σ(m)) , σ(m) = σ0 m0
m
so ha ligh e molecules andomize as e .
Pa icles exi when hey c oss x≥R h ough a na ow sli |y| ≤ yexi . The exi angle
θexi is eco ded.
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4.2 Pa ame e s Used
mCO2= 44, mN2= 28
R= 1.0, Rin = 1.5, yexi = 0.2, N = 5000 pe species
4.3 Resul s
F om 5000 pa icles each:
σθ(CO2)=2.4◦, σθ(N2)=7.1◦
Thus he hea ie species main ains a signi ican ly na owe ajec o y, di ec ly suppo ing
he RAC mechanism.
Table 1: Simula ed exi angle s a is ics.
Species Mass (amu) Exi Angle Mean (deg) Exi Angle S d (deg)
CO244 1.22.4
N228 1.97.1
4.4 In e p e a ion
The simula ion con i ms he heo e ical claim:
Hea ie molecules exhibi a s able, na ow e lec ion angle band un-
de cu a u e-induced mul i-bounce dynamics.
This nume ical e i ica ion demons a es ha he RAC mechanism is no a specula i e
geome ic in ui ion bu a ep oducible physical e ec eme ging om mass-dependen angula
andomiza ion.
4.5 Con inuous Passi e Ex ac ion
As long as in low con inues, CO2is con inuously unneled in o he line, while ligh e gases
ail o align and dispe se ou wa d.
E en a small dome wo ks because he angle bias appea s wi hin he i s ew e lec ions.
5. Compa ison Table
6. Economic Ad an age
The RAC p o ides a high- h oughpu , low-cos ad an age:
•Manu ac u ing cos is a below memb ane modules.
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Table 2: Mass-dependen e lec ion beha io inside he RAC.
Gas Mass (amu) Angula Sp ead Re lec ion S abili y
CO244 Na ow High
O232 Medium Medium
N228 Wide Low
He 4 Ve y Wide Ve y Low
•No pumps, comp esso s, o ene gy inpu .
•A single indus ial CO2plan can moun 200–600 uni s in pa allel.
•Th oughpu scales linea ly wi h numbe o domes.
•Ze o ene gy cos makes enewable ope a ion i ial.
The sys em achie es unma ched pe o mance-pe -cos in passi e CO2so ing.
Technology Capi al Cos Ope a ing Cos Ene gy Use (kWh/kg CO2)
RAC (This Wo k) Ve y Low ($5–$12 pe dome) Ex emely Low ( an main enance only) ∼0
Memb ane Module Medium ($1,000–$4,000 pe module) Medium (pump/comp esso ) 0.5–1.8
VSA/PSA Sys em High ($20,000–$80,000 pe uni ) High ( acuum + al es) 1.2–3.0
Amine Abso p ion Ve y High ($100k–$1M) Ve y High (hea ing + egene a ion) 3–6
Table 3: Economic compa ison o CO2sepa a ion me hods.
7. Conclusion
The RAC in oduces a passi e geome ic app oach o CO2en ichmen based on species-
dependen angula e olu ion inside a cu ed dome. The physical basis (WHY) shows ha
CO2 e ains di ec ional momen um mo e cohe en ly due o i s highe angula esponsi i y,
su ace in e ac ion, and pola izabili y, while ligh e gases apidly andomize.
The ope a ing mechanism (HOW) demons a es ha hese mic oscopic di e ences ans-
la e in o mul i-bounce angula con e gence and he eme gence o a dominan CO2 ajec o y.
Mon e-Ca lo simula ions (JUSTIFICATION) e i y ha cu a u e-d i en o de ing consis-
en ly p oduces na owe exi -angle dis ibu ions o CO2.
Wi h no pumps, ene gy inpu , o mo ing pa s, he RAC enables scalable, ul a-low-cos
CO2cap u e. I s geome ic simplici y and passi e ope a ion make i sui able o modula
indus ial deploymen and pa alleliza ion ac oss la ge acili ies.
Re e ences
1. J. C. Maxwell, Illus a ions o he Dynamical Theo y o Gases, Phil. Mag. 19, 19–32
(1860).
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2. R. Zwanzig, Nonequilib ium S a is ical Mechanics, Ox o d Uni e si y P ess (2001).
3. E. H. Kenna d, Kine ic Theo y o Gases, McG aw–Hill (1938).
4. S. Chapman and T. G. Cowling, Ma hema ical Theo y o Non-Uni o m Gases, Cam-
b idge (1970).
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