具熱應力滑移之氣膠粒子於熱泳與光泳之濃度效應

Abstract

本論文旨在探討由相同球形氣膠粒子所構成之均勻分散系統於穩定狀態之熱泳與光泳運動行為，其中粒子具有典型物理性質與表面特性。本研究假設克努森數（Knudsen number）為適當微小的值，使氣體運動處於滑移流動區域，該區域涵蓋了粒子表面的溫度跳躍、熱蠕動、摩擦滑移以及熱應力滑移。當佩克萊特數（Peclet number）與雷諾數（Reynolds number）很小的情況下，採取在實際應用中整合粒子間相互作用的單元小室方法，對耦合之動量與能量方程式進行解析求解。針對均勻溫度梯度驅動的熱泳與入射輻射場引發的光泳，分別推導出表達平均粒子移動速度的解析方程式。研究結果顯示，以單一粒子移動速度為基準之正規化分散系統粒子移動速度一般會隨粒子體積分率增加而下降，但在熱泳時會有例外情形。熱蠕動與熱應力滑移對正規化粒子熱泳速度並無影響，然而對正規化粒子光泳速度則具有顯著作用，其中正規化光泳速度會隨熱應力滑移係數與熱蠕動係數之比值增加而上升。此差異顯示，儘管熱泳與光泳密切相關，兩者卻在相同的界面氣體動力學效應中表現出不對稱性。此外，對於這兩種現象，正規化粒子移動速度皆會隨粒子與氣體間之熱傳導係數比值提升而單調遞增。

An analysis is presented for the steady thermophoresis and photophoresis of a homogeneous dispersion of identical aerosol spheres of typical physical properties and surface characteristics. The analysis assumes a moderately small Knudsen number, such that the gas motion lies within the slip-flow regime, including temperature jump, thermal creep, frictional slip, and thermal stress slip at the particle surfaces. Under conditions of small Reynolds and Peclet numbers, the coupled momentum and energy equations are solved analytically using a unit-cell approach that explicitly incorporates interparticle interactions in practical applications. Closed-form expressions are derived for the mean particle migration velocities in both thermophoresis driven by a uniform temperature gradient and photophoresis induced by an incident radiation field. The results reveal that the normalized particle velocities, referenced to those of an isolated particle, generally decrease with increasing particle volume fraction, though exceptions occur for thermophoresis. While thermal creep and thermal stress slip exert no influence on the normalized thermophoretic velocity, they markedly affect the normalized photophoretic velocity, which rises with the ratio of the thermal stress slip to thermal creep coefficients. This difference points to an asymmetry in how these two closely related phenomena respond to the same interfacial gas-kinetic effect. For both phenomena, the normalized migration velocities increase monotonically with the particle-to-gas thermal conductivity ratio.