Continuum modeling and simulation of fluids at nanoscale

Popadić, Aleksandar (avtor), Praprotnik, Matej (mentor)

Nanofluidics, a scientific field exploring nanoconfined fluids, has seen increasing interest in recent years. This interest is in large part due to the fascinating phenomena that occur at such small scales, such as ultra-efficient fluid transport through tubes with diameters of the order of nanometers. The development of computer science and technology in recent years has also allowed for efficient studies of matter at nanoscale. In this thesis, we study fluids at nanoscale with the aid of computer simulations. The thesis is roughly divided into two parts. In the first part, we study fluid flow past and through objects with sizes of the order of nanometers, and in the second part, we study conservation equations for polymer chains and the associated coupling of density and directional fluctuations. A widely used approach for studying nanoconfined fluids is molecular dynamics. It is, however, computationally expensive, often mandating the use of supercomputers. Hence, in this thesis we resort to the use of a continuum approach. Various recent studies have suggested that Navier-Stokes equations could be valid down to nanometer scale. However, at such small scales, where the ratio between the surface and bulk volume is not small anymore, the physics at the surface becomes increasingly important. The effective no-slip boundary condition, which is the standard boundary condition at macroscale, is no longer valid. At nanoscale, a slip between the fluid and the surface is observed. We thus use the Navier boundary condition, which takes the slip into account by assuming a linear dependence of shear stress at the surface on the relative velocity between the fluid and the solid at the interface. The boundary condition is parametrized by the slip length, which for straight walls represents the depth to which the fluid velocity profile must be extrapolated to vanish. We perform computational fluid dynamics simulations, subject to the Navier boundary condition, past spherical molecules and through carbon nanotubes. Water flow through carbon nanotubes is subjected to significant slip. This results in energy efficient flow through the carbon nanotubes. Due to this energy efficiency, energy dissipation at the nanotube entrance and exit becomes significant. We thus explore the energy dissipation in the vicinity of carbon nanotube ends. We observe a nonmonotonic dependence of energy dissipation on the slip length. We successfully model and explain the origin of this dependence and accurately predict the optimal slip length at which the energy dissipation is at its minimum. In light of recent reports of phonon modes of carbon nanotubes and subsequent diffusion enhancements, we explore the influence of the oscillating carbon nanotubes on the water flow. To examine the effect of carbon nanotube oscillations, we employ fluctuating hydrodynamics, in which a random fluctuating stress tensor representing thermal fluctuations is introduced to the Navier-Stokes equations. We solve the equations and derive the diffusion coefficient for the center of mass of water in an oscillating carbon nanotube. We show that in the continuum description, the phonon modes of the carbon nanotubes do not contribute to the diffusion. In the second part of this thesis, we study the conservation equations for polymer chain melts. In polymer chain melts, the defects in orientational order are closely related to density. This connection is described by the continuity equation, which is polar in its nature. This presents a problem for nematic polymers as the direction cannot be uniquely defined. In case of long polymer chains with abundant chain folding, the polar order disappears while the nematic order is conserved. By performing Monte Carlo simulations, we show that the continuity equation can be applied if we define a “recovered polar order” by introducing chain cuts at chain fold positions. In the last part, we examine the tensorial conservation equation, which is based on the quadrupolar order. In case of polymer chain folding, the quadrupolar order, in contrast to the polar order, is not lost, thus making the tensorial conservation more appropriate compared to the vectorial conservation equation. We perform Monte Carlo simulations of polymer chains in an istoropic phase and show first evidence of presence of the tensorial constraint.

• Jezik: Angleški jezik
• Ključne besede: fullerenes, carbon nanotubes, polymer melts, computational fluid dynamics, finite volume method, partial slip, molecular dynamics, Monte Carlo
• Vrsta gradiva: Doktorsko delo/naloga
• Tipologija: 2.08 - Doktorska disertacija
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2018
• PID: 20.500.12556/RUL-101420
• COBISS.SI-ID: 3207780
• Datum objave v RUL: 01.06.2018

Sekundarni jezik

• Jezik: Slovenski jezik
• Naslov: Kontinuumsko modeliranje in simulacija tekočin na nanoskali

Izvleček

Nanofluidika je področje znanosti, ki preučuje dinamiko tekočin na nanoskali. Zanimanje zanjo v zadnjih letih raste zaradi zanimivih fizikalnih pojavov na majhnih skalah, kot je na primer hiter pretok tekočin skozi kanale velikostnega reda nanometra. Razvoj računalniške znanosti in tehnologije v preteklih letih omogoča učinkovito študiranje materije na nanoskali. V tej doktorski disertaciji bomo študirali tekočine na nanoskali z uporabo računalniških simulacij. Disertacija je razdeljena v dva dela. V prvem delu študiramo tok tekočin mimo in skozi objekte z velikostjo reda nanometra. V drugem delu pa študiramo ohranitvene enačbe za polimerne verige in sklopitev fluktuacij gostote in orientacijskega reda. Široko uporabljen pristop k študiranju tekočin na nanoskali so simulacije molekulske dinamike. Simulacije molekulske dinamike so računsko zahtevne in pogosto zahtevajo uporabo superračunalnikov. Zato v tej doktorski tezi uporabimo kontinuumski pristop. Več raziskav je pokazalo, da so Navier-Stokesove enačbe lahko veljavne vse do nanoskale. Vendar na tako majhnih skalah, ko razmerje med površino in prostornino ni več majhno, postane dogajanje na površini pomembno. Zato standardni robni pogoj brez zdrsa, ki ga uporabimo na makroskali, ni ustrezen. Na nanoskali opazimo zdrs med tekočino in steno na njunem stiku. Za ustrezen opis zdrsa uporabimo Navierov robni pogoj, ki predpostavi linearno odvisnost strižne napetosti na stiku med tekočino in steno od relativne hitrosti med tekočino in steno. Parameter, ki določa Navierov robni pogoj, je zdrsna dolžina. Ta za ravne stene predstavlja globino, do katere moramo ekstrapolirati hitrostni profil tekočine, da bo ta enak nič. Izvajamo simulacije računske dinamike tekočin mimo sferičnih molekul in skozi ogljikove nanocevke, kjer uporabimo Navierov robni pogoj. Značilnost toka vode skozi ogljikove nanocevke je velik zdrs. Posledica tega velikega zdrsa je energijska učinkovitost toka vode skozi nanocevke. Zaradi energijske učinkovitosti toka vode znotraj ogljikovih nanocevk pridejo do izraza energijske izgube v okolici koncev nanocevk. Študiramo energijske izgube v okolici koncev nanocevk in odvisnost teh energijskih izgub od zdrsne dolžine. Razvijemo model, ki opiše izvor odvisnosti energijskih izgub od zdrsne dolžine n pravilno napove obstoj optimalne zdrsne dolžine, kjer je izguba energije najmanjša. V luči nedavnih odkritij fononskih načinov v ogljikovih nanocevkah pri toku vode skozi njih in posledičnem povečanju difuzije študiramo vpliv oscilirajočih sten nanocevk na tok tekočin skozi njih. Da bi ustrezno proučili vpliv oscilacij na difuzijo, uporabimo fluktuirajočo hidrodinamiko, kjer v Navier-Stokesove enačbe vključimo termične fluktuacije. Diferencialne enačbe rešimo za primer toka vode skozi dolgo oscilirajočo nanocevko in izpeljemo difuzijsko konstanto vode. Dobljena difuzijska konstanta nam pokaže, da oscilacije sten nanocevk ne vplivajo na difuzijo vode v nanocevki. V drugem delu teze študiramo ohranitvene zakone polimernih verig. V talinah polimernih verig so defekti orientacijskega reda in gostote tesno povezani. Ta povezava je izražena v kontinuitetni enačbi, ki je vektorske oblike. To predstavlja problem za apolarne verige, ki jim ni mogoče enolično določiti smeri. V primeru dolgih polimernih verig, ki se prepogibajo, to predstavlja problem, ker prisotnost pregibom zmanjša polarni red, medtem ko se nematski red ohranja. Izvajamo simulacije Monte Carlo talin polimernih verig v nematični fazi. S simulacijami pokažemo, da z uvedbo »popravljenega polarnega reda« kontinuitetna enačba velja tudi v prisotnosti pregibov polimernih verig. Na koncu raziščemo tenzorski ohranitveni zakon, ki je osnovan na kvadrupolnem redu. V primeru pregibanj polimernih verig se kvadrupolni red, za razliko od polarnega, ohranja in je zato tenzorski ohranitveni zakon za apolarne verige primernejši od vektorskega. Izvajamo simulacije Monte Carlo talin polimernih verig v izotropni fazi. V simulacijah odkrijemo prve indikacije fenomenov, ki so posledica tenzorskega ohranitvenega zakona.

• Ključne besede: fulereni, ogljikove nanocevke, taline polimerov, računska dinamika tekočin, metoda končnih volumnov, delni zdrs, molekulska dinamika, Monte Carlo