含活性剂液滴的铺展过程研究
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摘要
含有活性剂的液滴或溶液放置在固体表面或预置液膜表面上,液滴或溶液将铺展成薄液膜。该过程在石油化工、磁流体材料制备和微电子硅片清洗以及医疗等领域有着广泛的应用,现已成为流体力学、胶体和表面科学领域的前沿课题,是一个学科交叉的研究热点。
本文采用理论推导和数值计算相结合的方法,深入研究了界面存在热效应时以及分离压作用下含活性剂液滴的铺展问题,主要包括以下内容:
(1)针对含不溶性活性剂液滴的铺展过程,推导了温度和活性剂浓度协同驱动、不存在蒸发和存在蒸发两种情形下液膜厚度和表面活性剂单体浓度的演化方程组。并对这两组模型分别在均匀和非均匀加热条件下的演化历程进行了数值模拟,分析了其演化特征和Marangoni数、气液界面Biot数、液滴表面Peclet数以及存在蒸发时界面热阻、蒸汽反冲数和蒸发数对铺展过程的影响规律。计算结果表明,热毛细力和Marangoni力是铺展过程的主要驱动力,上述物性参数通过影响这两种驱动力进而影响液滴的铺展过程。
(2)针对含低浓度可溶性活性剂液滴的铺展过程,推导了温度和活性剂浓度协同驱动、不存在蒸发和存在蒸发两种情形下液膜厚度和表面、内部活性剂单体浓度的演化方程组。通过对两组演化模型在均匀加热条件下演化历程的数值模拟,分析了其演化特征和难溶性系数、吸附系数、液滴内部Peclet数对铺展过程的影响规律。计算结果表明,活性剂的表面单体和内部单体间的吸附通量减弱了Marangoni力对铺展的稳定作用,是造成可溶性活性剂具有独特铺展特征的内在原因。
(3)针对含超过临界胶束浓度的高浓度可溶性活性剂液滴的铺展过程,推导了温度和活性剂浓度协同驱动、不存在蒸发和存在蒸发两种情形下液膜厚度和表面、内部活性剂单体和胶束浓度的演化方程组。通过对两组演化模型在均匀加热条件下演化历程的数值模拟,分析了其演化特征和活性剂总量、分配系数、胶束表面Peclet数、组成胶束的活性剂单体个数和缔合系数对铺展过程的影响规律。计算结果表明,胶束的缔合或解离导致铺展区域的不同部分被热毛细力和Marangoni力交替控制,使得各区域铺展的主导驱动力出现了差异,令液滴的铺展呈现出新的特点。
(4)针对分离压作用下含不溶性活性剂液膜的铺展问题,基于已有实验结果,通过考虑活性剂特性和浓度对分子间引力和斥力的不同影响,建立了通用的分离压理论模型,给出了自由能表达式,并分析了分离压和自由能与活性剂浓度、液膜厚度比间的变化关系;推导了分离压作用下含不溶性活性剂液膜铺展过程的演化方程并进行了数值模拟。
The liquid drop of surfactant solutions will spread into thin film when deposited on the solid substrate or precursor. Such flows that are driven by so-called interfacial Marangoni stresses are of great importance in a wide range of industrial and biomedical applications including petrochemical engineering, magnetofluid preparation, drying of semiconductor wafers in the microelectronics industry and surfactant replacement therapy for neonates. The spreading of surfactant solutions has attracted considerable interest in the field of fluid mechanics, colloid and interface science both theoretically and experimentally. It is an advancing topic of investigation with subject intersection.
The spreading of surfactant laden-drops on thin liquid film in presence of interfacial heating or disjoining pressure are investigated thoroughly and intensively in the thesis, combining the method of model derivation and numerical simulation. The main parts of the thesis are as following:
(1) For the spreading of drop containing insoluble surfactant driven by thermal and concentration gradients, use of lubrication theory yields two coupled sets of partial differential equations for the film thickness and surfactant surface concentration on conditions of evaporation and no evaporation, respectively. Both coupled equations are numerical simulated for different heating conditions, uniform and non-uniform. The evolution characteristics and the effects of dimensionless parameters on the spreading process are analyzed, including Marangoni parameter, air-liquid Biot number and surface Peclet number, and interfacial thermal resistance, vapor recoil number and evaporation number for evaporation condition. It is shown that thermocapillary and Marangoni stress are main driving force,which are influenced by the above parameters leading to variations of the spreading process.
(2) For the spreading of drop containing soluble surfactant driven by thermal and concentration gradients, use of lubrication theory yields two coupled sets of partial differential equations for the film thickness, surfactant concentrations on the surface and in the bulk on conditions of evaporation and no evaporation, respectively. Both coupled equations are numerical simulated only for uniform heating conditions. The evolution characteristics and the effects of dimensionless parameters on the spreading process are analyzed, including solubility parameter, dimensionless desorption rate constant and bulk Peclet number. It is shown that sorptive flux between surface monomer and bulk monomer of surfactant weakened the stabilizing effect of Marangoni stress,which leads to unstable aspects in the spreading of soluble surfactant.
(3) For the spreading of a drop containing high concentration of soluble surfactant, which is beyond the CMC, in the presence of thermal effect, use of lubrication theory yields two coupled sets of partial differential equations for the film thickness, surfactant monomer concentrations on the surface and in the bulk and micelle concentration on conditions of evaporation and no evaporation, respectively. Both coupled equations are numerical simulated only for uniform heating conditions. The evolution characteristics and the effects of dimensionless parameters on the spreading process are analyzed, including dimensionless surfactant mass, aggregation constant, micelle size, bulk kinetics parameter and micelle Peclet number. It is shown that the creation of micelles or the breakup of micelles result in the different spreading region dominated by different driving force, either thermocapillary or Marangoni stress,which leads to distinct features in the spreading, such as appearance of secondary leading front.
(4) For the spreading of thin film containing insoluble surfactant under the disjoining pressure, a universal model is constructed on the base of experiment data by considering the influence of surfactant features and concentration on the intermolecular attraction force and repulsion force. The equation of free energy is also presented. The dependences of attraction/repulsion ratio, disjoining pressure and free energy are analyzed due to the variation of surfactant concentration and film thickness. A coupled set of partial differential equations for the film thickness and surfactant surface concentration under disjoining pressure is derived. The results of numerical simulations are presented.
本文采用理论推导和数值计算相结合的方法,深入研究了界面存在热效应时以及分离压作用下含活性剂液滴的铺展问题,主要包括以下内容:
(1)针对含不溶性活性剂液滴的铺展过程,推导了温度和活性剂浓度协同驱动、不存在蒸发和存在蒸发两种情形下液膜厚度和表面活性剂单体浓度的演化方程组。并对这两组模型分别在均匀和非均匀加热条件下的演化历程进行了数值模拟,分析了其演化特征和Marangoni数、气液界面Biot数、液滴表面Peclet数以及存在蒸发时界面热阻、蒸汽反冲数和蒸发数对铺展过程的影响规律。计算结果表明,热毛细力和Marangoni力是铺展过程的主要驱动力,上述物性参数通过影响这两种驱动力进而影响液滴的铺展过程。
(2)针对含低浓度可溶性活性剂液滴的铺展过程,推导了温度和活性剂浓度协同驱动、不存在蒸发和存在蒸发两种情形下液膜厚度和表面、内部活性剂单体浓度的演化方程组。通过对两组演化模型在均匀加热条件下演化历程的数值模拟,分析了其演化特征和难溶性系数、吸附系数、液滴内部Peclet数对铺展过程的影响规律。计算结果表明,活性剂的表面单体和内部单体间的吸附通量减弱了Marangoni力对铺展的稳定作用,是造成可溶性活性剂具有独特铺展特征的内在原因。
(3)针对含超过临界胶束浓度的高浓度可溶性活性剂液滴的铺展过程,推导了温度和活性剂浓度协同驱动、不存在蒸发和存在蒸发两种情形下液膜厚度和表面、内部活性剂单体和胶束浓度的演化方程组。通过对两组演化模型在均匀加热条件下演化历程的数值模拟,分析了其演化特征和活性剂总量、分配系数、胶束表面Peclet数、组成胶束的活性剂单体个数和缔合系数对铺展过程的影响规律。计算结果表明,胶束的缔合或解离导致铺展区域的不同部分被热毛细力和Marangoni力交替控制,使得各区域铺展的主导驱动力出现了差异,令液滴的铺展呈现出新的特点。
(4)针对分离压作用下含不溶性活性剂液膜的铺展问题,基于已有实验结果,通过考虑活性剂特性和浓度对分子间引力和斥力的不同影响,建立了通用的分离压理论模型,给出了自由能表达式,并分析了分离压和自由能与活性剂浓度、液膜厚度比间的变化关系;推导了分离压作用下含不溶性活性剂液膜铺展过程的演化方程并进行了数值模拟。
The liquid drop of surfactant solutions will spread into thin film when deposited on the solid substrate or precursor. Such flows that are driven by so-called interfacial Marangoni stresses are of great importance in a wide range of industrial and biomedical applications including petrochemical engineering, magnetofluid preparation, drying of semiconductor wafers in the microelectronics industry and surfactant replacement therapy for neonates. The spreading of surfactant solutions has attracted considerable interest in the field of fluid mechanics, colloid and interface science both theoretically and experimentally. It is an advancing topic of investigation with subject intersection.
The spreading of surfactant laden-drops on thin liquid film in presence of interfacial heating or disjoining pressure are investigated thoroughly and intensively in the thesis, combining the method of model derivation and numerical simulation. The main parts of the thesis are as following:
(1) For the spreading of drop containing insoluble surfactant driven by thermal and concentration gradients, use of lubrication theory yields two coupled sets of partial differential equations for the film thickness and surfactant surface concentration on conditions of evaporation and no evaporation, respectively. Both coupled equations are numerical simulated for different heating conditions, uniform and non-uniform. The evolution characteristics and the effects of dimensionless parameters on the spreading process are analyzed, including Marangoni parameter, air-liquid Biot number and surface Peclet number, and interfacial thermal resistance, vapor recoil number and evaporation number for evaporation condition. It is shown that thermocapillary and Marangoni stress are main driving force,which are influenced by the above parameters leading to variations of the spreading process.
(2) For the spreading of drop containing soluble surfactant driven by thermal and concentration gradients, use of lubrication theory yields two coupled sets of partial differential equations for the film thickness, surfactant concentrations on the surface and in the bulk on conditions of evaporation and no evaporation, respectively. Both coupled equations are numerical simulated only for uniform heating conditions. The evolution characteristics and the effects of dimensionless parameters on the spreading process are analyzed, including solubility parameter, dimensionless desorption rate constant and bulk Peclet number. It is shown that sorptive flux between surface monomer and bulk monomer of surfactant weakened the stabilizing effect of Marangoni stress,which leads to unstable aspects in the spreading of soluble surfactant.
(3) For the spreading of a drop containing high concentration of soluble surfactant, which is beyond the CMC, in the presence of thermal effect, use of lubrication theory yields two coupled sets of partial differential equations for the film thickness, surfactant monomer concentrations on the surface and in the bulk and micelle concentration on conditions of evaporation and no evaporation, respectively. Both coupled equations are numerical simulated only for uniform heating conditions. The evolution characteristics and the effects of dimensionless parameters on the spreading process are analyzed, including dimensionless surfactant mass, aggregation constant, micelle size, bulk kinetics parameter and micelle Peclet number. It is shown that the creation of micelles or the breakup of micelles result in the different spreading region dominated by different driving force, either thermocapillary or Marangoni stress,which leads to distinct features in the spreading, such as appearance of secondary leading front.
(4) For the spreading of thin film containing insoluble surfactant under the disjoining pressure, a universal model is constructed on the base of experiment data by considering the influence of surfactant features and concentration on the intermolecular attraction force and repulsion force. The equation of free energy is also presented. The dependences of attraction/repulsion ratio, disjoining pressure and free energy are analyzed due to the variation of surfactant concentration and film thickness. A coupled set of partial differential equations for the film thickness and surfactant surface concentration under disjoining pressure is derived. The results of numerical simulations are presented.
引文
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