RAC: Re lec ion–Angle 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 CO2molecules using momen um-dependen e lec ion dynamics. Unlike mem-
b anes o acuum-swing sys ems, he de ice equi es no pumps, no ene gy inpu , and
no ac i e con ol. The key mechanism is ha gases o di e en molecula masses ex-
hibi dis inc inciden -angle s a is ics inside a cu ed dome, causing hea ie species
(CO2) o main ain na owe e lec ion ajec o ies while ligh e gases sca e b oadly.
This pape p esen s (a) he physical basis o angle di e gence, (b) a comple e op-
e a ing mechanism including con inuous in low, (c) cu a u e-induced mul i-bounce
ocusing, (d) a geome ic model wi h TikZ, (e) one compac o mal equa ion desc ib-
ing angle bias, and ( ) an economic scalabili y a gumen .
1. In oduc ion
Con en ional CO2en ichmen elies on adso p ion beds, memb anes, o acuum/comp ession
de ices. The RAC in oduces a comple ely di e en p inciple: passi e e lec i e gas
so ing, whe e sepa a ion eme ges pu ely om mass-dependen momen um beha io inside
a cu ed geome y.
When gas mix u es en e h ough an in low pipe, he dome shape o ces molecules in o
epea ed specula in e ac ions. Because hea ie molecules lose di ec ionali y mo e slowly,
hey exhibi a s able na owing o e lec ion angles. A dedica ed ou le connec ed o a
CO2-abso bing liquid chambe cap u es hese selec i ely s abilized ajec o ies.
The de ice has no mo ing pa s, consumes no powe , and can be mass-p oduced a
ex emely low cos .
2. Why Re lec ion Angles Di e ge (Co e Physics)
Le mbe molecula mass. When gases en e a con ined dome and collide wi h i s su ace:
- Hea y molecules (CO2, 44 amu) e ain di ec ionali y, - Ligh molecules (N2: 28 amu,
O2: 32 amu) andomize as e .
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Figu e 1: Schema ic o he CO2cap u e geome y.
A e 1–3 e lec ions:
CO2: na ow angula sp ead,o he s : b oad angula sp ead.
Cu a u e ampli ies his di e ence by con e ing ini ial angula bias in o a s able e lec-
ion di ec ion.
Compac Fo mal Exp ession
The dominan angle di e ence is modeled as:
∆θ(m)=θCO2−θligh ≈α1−e−βm
whe e α= geome y cu a u e ac o , β= andomiza ion–momen um ac o .
This cap u es he mono onic inc ease o angle s abili y wi h mass.
3. Ope a ing Mechanism
3.1 Di ec ed In low
A mix u e en e s h ough a sho pipeline wi h mild di ec ionali y.
3.2 Ini ial Re lec ion
CO2bends less on impac due o highe momen um. Ligh molecules sca e widely.
3.3 Mul i-Bounce Focusing
E en a small dome gene a es epea ed collisions because:
- con inuous in low pushes molecules inwa d, - e en 2–3 bounces a e enough o gene a e
s able sepa a ion, - dome cu a u e guides hea ie molecules owa d a p e e ed di ec ion.
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3.4 Angula Funnel Towa d CO2Line
Due o na owe ajec o ies:
CO2−→ dominan exi di ec ion
A CO2-solu ion line (amine/wa e /ca bona e) is ins alled exac ly along his dominan di ec-
ion.
4. Mon e-Ca lo Ve i ica ion o Angle Na owing
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.
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.
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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
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
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.
•No pumps, comp esso s, o ene gy inpu .
•A single indus ial CO2plan can moun 200–600 uni s in pa allel.
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•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 new pa adigm in passi e gas sepa a ion: cu a u e-d i en, momen um-
selec i e e lec ion. A dome-shaped e lec i e su ace, e en a small scale, ocuses CO2
ajec o ies wi hin a ew bounces. A line ins alled along his dominan di ec ion anspo s
he en iched CO2in o a liquid abso p ion chambe .
Re e ences
1. J. C. Maxwell, Illus a ions o he Dynamical Theo y o Gases, Phil. Mag. 19, 19–32
(1860).
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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