Linear Stability of Thin Liquid Film on Solid Surface Under Effect of Apolar and Polar Forces

Abstract

Tenaga lebihan bebas Gibb per unit luas (ΔG) bagi suatu saput nipis yang tulen, tanpa cas pada satu sokongan hanya diterbitkan daripada interaksi antara molekul apolar (Lifshitz - van der Waals) dan polar (acid-bes). Interaksi polar dapat dinyatakan secara berasingan sebagai tekanan penghidratan, interaksi hidrofobik dan intekrasi asid-bes. Jumlah tenaga lebihan bebas Gibb per unit luas (ΔG) bagi satu saput nipis pada satu lapisan bergantung kepada ketebalan saput, dan angkali penyebaran apolar dan polar untuk sistem tersebut. Saput dimodelkan sebagai cecair Newtonian 2-dimensi dengan ketumpatan tetap, Ï, dan kelikatan, μ, mengalir di atas satu permukaan mengufuk. Ketebalan purata saput cecair, h₀, dianggapkan cukup nipis supaya kesan graviti boleh diabaikan dan melambung atas oleh gas pasif dan menyambung secara lateral hingga infiniti (Model dua-dimensi). Daya badan yang disebut dalam persamaan Navier-Stokes adalah diubahsuaikan oleh kandungan interaksi antara molekul lebihan (daya apolar dan polar) antara saput bendalir dan permukaan pepejal bergantung kepada daya-daya apolar dan polar. Persamaan Navier-Stokes telah diubahsuai dengan keadaan sempadan berkaitan diselesaikan bawah kaedah pendekatan gelombong panjang untuk memperolehi persamaan perkembangan tak-linear bagi saput antara permukaan. Daya apolar dan polar telah didapati memainkan peranan pencirian atas saput nipis dan kesan utama pada sifat tenaga lebihan bebas, kadar penubuhan, kadar penubuhan maksimum, gelombong neutral, nombor gelombang yang dominan, jarak gelombong dominan dan masa memecah. Oleh demikian, teori linear adalah kurang sesuai untuk menyatakan kestabilan pencirian selaput. Kata kunci: Daya apolar, daya polar, kestabilan linear, kadar pertumbuhan, masa memecah The total excess free energy per unit area (ΔG) of a pure, uncharged thin film on a support is solely derived from the apolar (Lifshitz - van der Waals) and polar (acid-base) intermolecular interactions. Polar interactions are variously described as the hydration pressure, hydrophobic interaction and acid base interaction. The total free excess energy (per unit area) of a thin film on a substrate depends on the film thickness, and the apolar and polar spreading coefficients for the system. The film is modelled as a two-dimensional Newtonian liquid of constant density, Ï and viscosity, μ, flowing on a horizontal plane. The liquid film of mean thickness, h₀, is assumed to be thin enough to neglect the gravity effect and bounded above by a passive gas and laterally extends to infinity (two-dimensional model). The body force term in the Navier-Stokes equation is modified by the inclusion of excess intermolecular interactions (apolar and polar forces) between fluid film and the solid surface owing to apolar and polar forces. The modified Navier-Stokes equation with associated boundary conditions is solved under long wave approximation method to obtain a nonlinear equation of evolution of the film interface. The apolar and polar forces were found to play the dominant role in characteristic of thin films and the main effect on the behavior of the excess free energy, growth rate, maximum growth rate, neutral wave, dominant wavenumber, dominant wavelength and rupture time. Hence, the linear theory is inadequate to describe the stability characteristics of films. Key words: Apolar force, polar force, linear stability, growth rate, rupture time