纤维集合体内液体流动的统计力学建模
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摘要
液体在纤维集合体内的流动是许多纺织品应用领域的普遍现象，如整理剂对织物的渗透、树脂在纤维预型件内的流动等。在这些领域中，纤维集合体对液体的传递性能将决定产品的应用范围和加工质量。因此，从理论上研究液体在纤维集合体内的流动特性，找出影响液体流动的关键因素，可以指导纤维制品的生产和应用。
本论文的研究目标是建立纤维集合体内液体流动的统计热力学模型和统计动力学模型，具体为：
1．从液体流动系统中的极性／非极性作用出发，建立具有明确物理意义的系统Hamilton函数；通过能量分析，建立模拟系统中空气／液体单元的交换规则。在此基础上建立的统计热力学模型能够准确地描述实际液体流动系统中宏观量的变化规律。
2．探索纤维集合体内流体流动的统计动力学建模方法。从流体微粒间、流体／纤维间的相互作用出发建立统计动力学模型，所建立的模型能够反映流体和纤维的性能对流动的影响；扩展后的模型能够描述流体在纤维束束内／束间两种尺度孔隙中的流动。
为了实现以上目标，论文以统计力学中的系综理论、物理化学中的界面理论和Monte Carlo计算机模拟方法为基础，从热力学和动力学两个方面综合考察纤维集合体内液体的流动特性。同时，把研究尺度定在大于分子尺度的介观尺度，以满足描述纤维集合体复杂边界条件的要求并适应宏观模拟尺寸的要求。
论文的第一部分工作是建立统计热力学模型。为此，论文分析了已有基于Ising模型的热力学模型，发现其中存在系统Hamilton函数的物理意义含糊不清、模拟系统中采用的空气格／液体格交换规则不合理等问题。因此，迄今为止的模型虽能模拟液体流动的现象，却不能定量地描述液体流动的规律。
基于上述分析，论文在建模过程中首先确定系统能量的组成和表征方法。指出液体流动系统的位能由界面位能和重力势能组成。界面位能在数值上等于界面自由能，包括：液体表面自由能γ_l固体表面自由能γ_s，液体／固体界面自由能γ_(al)。在一种物质内部的假想界面上，两侧的分子作用由于对称而相互抵消，界面自由能等于零。界面位能只发生在具有面接触的相邻单元体之间。
当界面上同时存在分子间的极性／非极性作用时，界面自由能由极性和非极性分量组成。当液体流动系统中含有强极性液体(如水)时，必须考虑能量中的极性分量。界面自由能中的极性／非极性分量分别由Lewis酸一碱作用力理论和Good-Girifalco-Fowkes理论确定。
其次，建立了描述系统位能的Hamilton函数。在Hamilton函数的表达形式上，除了采用状态参数s和F表示系统内单元体的物质属性(被空气、液体或纤维中任一物质占据)外，引入作用算子表示位能的强度。定义作用算子f_a、f_c和f_g，分别对应于含有纤维的界面(空气／纤维界面和液体／纤维界面)、空气／液体界面的界面自由能和重力势能的强度。通过计算证明，所建立的Hamilton函数能够正确地区分空气／液体／纤维三相系统中各种位能的属性和强度，因此具有明确的物理意义。此外，在函数中把系统的划分形式和划分尺度对模拟结果的影响归结到模拟系数λ中，使模型能够用于实际液体流动系统中宏观量的定量讨论。
最后，在模拟系统中确定空气／液体单元的交换规则和系统能量的计算方法。指出模拟系统中一个空气／液体单元交换循环包括两个步骤：第一步，空气单元和液体单元发生交换；第二步，空气单元被液体重新填充。
一个交换循环中系统的位能增量是以上两个步骤所产生的系统位能增量之和；而在一个循环的系统总能量变化中，还需计入液体表面张力做功的能量贡献。系统总能量增量可以由液体内聚能、液体／纤维接触角和粘附能计算得到。
为了验证上述热力学模型，论文模拟了圆形截面毛细管内液体垂直芯吸的平衡高度，从模拟结果和试验结果的一致性验证模型的正确性。
试验选用两种非极性液体(庚烷、辛烷)和两种极性液体(水、甲酰胺)，在半径分布于0.15～1.35mm范围内的干燥毛细管内作垂直芯吸试验，测量液体的平衡高度。试验结果表明，不同性能的液体在相同管径毛细管内达到的平衡高度有明显差异；而对于同一种液体而言，液体的芯吸平衡高度与毛细管半径成反比。
在对实际芯吸系统的模拟过程中，论文针对系统中液体与毛细管壁接触面为圆柱侧面的特征，采用非矩形截面立方体的系统划分方式，同时采用本论文提出的空气／液体单元交换规则和能量计算方法。进行模拟时，输入液体内聚能数值、液体／管壁接触角和粘附能试验值。通过将任一液体在任一管径毛细管内平衡高度的模拟值和试验值进行比较，确定模拟系数λ的大小。然后在同一模拟系数下，模拟庚烷、辛烷、水和甲酰胺在不同管径毛细管内的芯吸平衡高度。模拟结果与试验结果相符，准确地反映了液体在圆形截面毛细管内芯吸平衡高度的变化规律。
对实际芯吸系统的模拟结果表明，论文所建立的统计热力学模型能够正确描述液体流动系统中的各种能量，从而可以定量地描述实际系统中宏观量的变化规律，揭示了宏观流动现象的微观本质，模型具有普适性。
论文的第二部分工作是建立液体流动的统计动力学模型。在所建立的模型中结合了流体微粒间、流体／纤维间和空气／流体界面上的作甩位能。与一般LGA模型建模方法不同的是：
(1)节点的状态除用一个七位的Boolean变量表示其上流体微粒的速度分布状态外，采用状态参数s和F表示节点的物质属性，即是否被液体或纤维占据。
(2)分别定义流体微粒间、流体／纤维间和空气／流体界面作用位能。定义作用算子f_a~′和f_C~′分别表示流体／纤维间和流体微粒间的作用位能。
(3)把原LGA模型的碰撞规则用于流体微粒间的自由碰撞；在流体／纤维界面上定义新的界面碰撞规则；在空气／流体界面上，给出流体微粒的速度调整算法，将其速度调整到界面法向。
(4)在流体微粒的微观动力学方程，即Boltzmann输运方程中引入Metropolis概率判断机制，根据碰撞前后系统能量的变化选择碰撞后流体微粒的出射位形。Metropolis判断机制的引入，建立了各种作用位能与流体微粒微观动力学之间的联系，在动力学中结合了流体内聚能对流动的阻碍作用、纤维表面性能对流动的影响和流体表面张力的作用等。
动力学模型的验证通过对平行平板间Poiseuille流动的模拟实现。模拟结果表明，模拟得到的速度分布曲线是一条抛物线，其函数式与流体力学的理论表达式具有相同的形式，证明论文所建的动力学模型能够正确描述典型流场的速度特征，因而模型和算法是正确的。
把所建模型应用于模拟流体在纤维束内单纤维间横向流动的流场特征。模拟结果显示，该模型能够反映流场中纤维排列结构和纤维表面性能对局部流场的影响。
进一步扩展模型，建立了可渗透纤维介质的统计动力学模型，以模拟流体在不同尺度孔隙中的流动行为。模型扩展时提出渗透概率的概念，以表征纤维集合体的结构特征，并对模拟算法作出相应改进，主要包括：改变纤维介质节点的状态参数设置；判断流体微粒在纤维介质内部的扩散方向和在介质／束间孔隙界面上碰撞后的出射方向时，必须进行渗透概率计算；对纤维介质内部空气／流体界面上的流体微粒进行速度方向调整等。
把扩展模型应用于模拟和分析不同外界压力条件下纤维束束内／束间孔隙中的流体速度分布。结果表明，随着外界压力的增加，纤维束束间孔隙中的流体速度由落后于纤维束内部的流体速度逐渐转变为超前。模拟结果与现有研究中的结论一致。
论文从液体流动系统中各种相互作用出发建立的模型具有普遍适用性，因而可以针对实际系统作进一步模拟，探讨模型的应用和扩展可能性。
Since liquid flow through fibrous media is a common phenomenon in textile processing and composite manufacturing, it is of practical significance to analyze the issue theoretically to find out the key factors that influence flow behavior.
Focusing on micro-nature of liquid flow, this study is to establish two stochastic models, a thermodynamic one and a kinetic one.
For the thermodynamic model, a Hamilton function is developed to describe potential energy of the system. Meanwhile, an exchange rule of air/liquid unit in simulation system is proposed, linking unit exchange to actual flow process. The model thus established can be applied in quantitative analysis of flow behavior.
For the kinetic model, interactions between liquid particles, as well as that between liquid particles and fibrous media are taken into account, furthermore, the model is extended to describe two-scale flow in fibrous media.
The investigation is carried out with an overview of current thermodynamic models, which are originated from Ising model. Three main problems are found therein. First, Hamilton functions are not correct enough to distinguish various energies in liquid flow system. Second, polar interactions are not considered even in systems with strong polar liquid, such as water. Third, the exchange rule of air/liquid unit is taken for granted with no verification. As a result, these models can only be used in phenomena simulation but quantitative description.
Then, a new Hamilton function is developed to describe potential energy in flow system. For this purpose, potential energy is explicitly determined as interface potential energy and gravity potential energy. Interface potential energy includes surface free energy of liquidγ_l, surface free energy of fiberγ_f, and liquid/fiber interface free energyγ_fl. On a virtual interface within a certain phase, interface free energy equals to zero.
Under the circumstances of apolar/polar interactions existing simultaneously on an interface, interface free energy is composed of apolar (Lifshitz-van der Waals) and polar (Lewis acid-base) parts, which are calculated by Good-Girifalco-Fowkes theory and Lewis acid-base theory, respectively. When strong polar liquid, such as water, is investigated, the polar part of free energy could not be neglected.
To identify all the potential energies mentioned above, interaction operators ?_a,?_c, ?_g, besides conventional state parameters s and F, are introduced in the new Hamilton function. Operators ?_a, ?_c, ?_g denote intensity of liquid/fiber and air/fiber interface free energy, liquid surface free energy and gravity potential energy, respectively. The correctness of Hamilton function is tested in a simple flow system. In addition, scaling effect due to system division is represented by a simulation coefficientλin the function.
Finally, an exchange rule of air/liquid unit is proposed and a method of energy calculation is offered. It is pointed out that an exchange cycle of air/liquid unit is a two-step process, first, an air unit exchanges with one of the nearest liquid unit, and second, the air unit is subsequently filled with liquid. In one cycle, the change of potential energy is the sum of that caused by each step, while the change of total energy is the sum of the potential energy change and the work done by liquid surface tension. With the data of liquid cohesion energy, liquid/fiber contact angle and adhesion energy, energy change during exchange process can be derived.
To validate the thermodynamic model established, simulation of equilibrium wicking height of liquid in capillary with circle section is implemented. The equilibrium height of two apolar liquids, heptane and octane, also two polar liquids, water and formamide, are recorded. The radii of capillaries are in the range of 0．15～1．35mm.
Test results reveal that equilibrium height of the four liquids differed obviously. In the same capillary, the height of water is maximum and that of octane and heptane are minimum, while the height of formamide is in between. As for one liquid, equilibrium height is inverse proportional to capillary radius.
Simulation procedure of wicking system is provided. Nontraditional column unit is adopted to divide the system. Besides, energy change is calculated from potential energy change caused by air/liquid unit exchange and work done by liquid surface tension.
By inputting the data of liquid cohesion energy, liquid/capillary contact angle and adhesion energy, equilibrium height of four liquids are simulated. Simulation results show good agreement with test data, which verifies the correctness of the thermodynamic model proposed in this study.
In the second part of the research, a kinetic model is established, combining interaction potential energy between liquid particles, between liquid and fiber, also on air/liquid interface. The differences between the new model and a traditional LGA model are as follows.
First, the state of each site is described by two state parameters, namely, s and F, besides a seven-bit Boolean variable.
Second, interaction operator ?_a′and ?_c′is introduced to denote interaction potential energies between liquid and fiber and within liquid phase.
Third, traditional collision rules are applied between liquid particles and new rules are defined on liquid/fiber interface. Procedure of fluid particle velocity adjustment on air/liquid interface is also put forward.
Four, Metropolis function is embedded into Boltzmann transport equation to determine the state of the system after collision.
To testify the validity of the kinetic model, Poiseuille flow is investigated. Simulate results of velocity profile agrees well with analytical solutions, which confirms the correctness of the model and corresponding simulation codes.
The new model is then used to simulate transverse flow in fiber bundles. Simulation result shows that it can reflect the effect of fiber construction and fiber surface properties on local flow field.
The kinetic mode is further extended to investigate flow in fibrous media on a scale larger than pore size. Transport probability is defined to characterize construction of fibrous media. Simulation procedure is amended in twofold. On the one hand, state parameters of fiber site is reset, for air/fiber site, it takes s=0, F=1 and for liquid/fiber site, s=1, F=1．On the other hand, transport probability is inserted into the microdynamics of liquid particles.
The modified model is applied to simulate meso-scale and micro-scale flow in unidirectional fibrous media. Simulation results agree with that given by other references.
Since the stochastic models developed in this thesis are based on micro-interactions in flow systems, both reflect inherent physics of liquid flow. The models can be further applied to more practical systems.
本论文的研究目标是建立纤维集合体内液体流动的统计热力学模型和统计动力学模型，具体为：
1．从液体流动系统中的极性／非极性作用出发，建立具有明确物理意义的系统Hamilton函数；通过能量分析，建立模拟系统中空气／液体单元的交换规则。在此基础上建立的统计热力学模型能够准确地描述实际液体流动系统中宏观量的变化规律。
2．探索纤维集合体内流体流动的统计动力学建模方法。从流体微粒间、流体／纤维间的相互作用出发建立统计动力学模型，所建立的模型能够反映流体和纤维的性能对流动的影响；扩展后的模型能够描述流体在纤维束束内／束间两种尺度孔隙中的流动。
为了实现以上目标，论文以统计力学中的系综理论、物理化学中的界面理论和Monte Carlo计算机模拟方法为基础，从热力学和动力学两个方面综合考察纤维集合体内液体的流动特性。同时，把研究尺度定在大于分子尺度的介观尺度，以满足描述纤维集合体复杂边界条件的要求并适应宏观模拟尺寸的要求。
论文的第一部分工作是建立统计热力学模型。为此，论文分析了已有基于Ising模型的热力学模型，发现其中存在系统Hamilton函数的物理意义含糊不清、模拟系统中采用的空气格／液体格交换规则不合理等问题。因此，迄今为止的模型虽能模拟液体流动的现象，却不能定量地描述液体流动的规律。
基于上述分析，论文在建模过程中首先确定系统能量的组成和表征方法。指出液体流动系统的位能由界面位能和重力势能组成。界面位能在数值上等于界面自由能，包括：液体表面自由能γ_l固体表面自由能γ_s，液体／固体界面自由能γ_(al)。在一种物质内部的假想界面上，两侧的分子作用由于对称而相互抵消，界面自由能等于零。界面位能只发生在具有面接触的相邻单元体之间。
当界面上同时存在分子间的极性／非极性作用时，界面自由能由极性和非极性分量组成。当液体流动系统中含有强极性液体(如水)时，必须考虑能量中的极性分量。界面自由能中的极性／非极性分量分别由Lewis酸一碱作用力理论和Good-Girifalco-Fowkes理论确定。
其次，建立了描述系统位能的Hamilton函数。在Hamilton函数的表达形式上，除了采用状态参数s和F表示系统内单元体的物质属性(被空气、液体或纤维中任一物质占据)外，引入作用算子表示位能的强度。定义作用算子f_a、f_c和f_g，分别对应于含有纤维的界面(空气／纤维界面和液体／纤维界面)、空气／液体界面的界面自由能和重力势能的强度。通过计算证明，所建立的Hamilton函数能够正确地区分空气／液体／纤维三相系统中各种位能的属性和强度，因此具有明确的物理意义。此外，在函数中把系统的划分形式和划分尺度对模拟结果的影响归结到模拟系数λ中，使模型能够用于实际液体流动系统中宏观量的定量讨论。
最后，在模拟系统中确定空气／液体单元的交换规则和系统能量的计算方法。指出模拟系统中一个空气／液体单元交换循环包括两个步骤：第一步，空气单元和液体单元发生交换；第二步，空气单元被液体重新填充。
一个交换循环中系统的位能增量是以上两个步骤所产生的系统位能增量之和；而在一个循环的系统总能量变化中，还需计入液体表面张力做功的能量贡献。系统总能量增量可以由液体内聚能、液体／纤维接触角和粘附能计算得到。
为了验证上述热力学模型，论文模拟了圆形截面毛细管内液体垂直芯吸的平衡高度，从模拟结果和试验结果的一致性验证模型的正确性。
试验选用两种非极性液体(庚烷、辛烷)和两种极性液体(水、甲酰胺)，在半径分布于0.15～1.35mm范围内的干燥毛细管内作垂直芯吸试验，测量液体的平衡高度。试验结果表明，不同性能的液体在相同管径毛细管内达到的平衡高度有明显差异；而对于同一种液体而言，液体的芯吸平衡高度与毛细管半径成反比。
在对实际芯吸系统的模拟过程中，论文针对系统中液体与毛细管壁接触面为圆柱侧面的特征，采用非矩形截面立方体的系统划分方式，同时采用本论文提出的空气／液体单元交换规则和能量计算方法。进行模拟时，输入液体内聚能数值、液体／管壁接触角和粘附能试验值。通过将任一液体在任一管径毛细管内平衡高度的模拟值和试验值进行比较，确定模拟系数λ的大小。然后在同一模拟系数下，模拟庚烷、辛烷、水和甲酰胺在不同管径毛细管内的芯吸平衡高度。模拟结果与试验结果相符，准确地反映了液体在圆形截面毛细管内芯吸平衡高度的变化规律。
对实际芯吸系统的模拟结果表明，论文所建立的统计热力学模型能够正确描述液体流动系统中的各种能量，从而可以定量地描述实际系统中宏观量的变化规律，揭示了宏观流动现象的微观本质，模型具有普适性。
论文的第二部分工作是建立液体流动的统计动力学模型。在所建立的模型中结合了流体微粒间、流体／纤维间和空气／流体界面上的作甩位能。与一般LGA模型建模方法不同的是：
(1)节点的状态除用一个七位的Boolean变量表示其上流体微粒的速度分布状态外，采用状态参数s和F表示节点的物质属性，即是否被液体或纤维占据。
(2)分别定义流体微粒间、流体／纤维间和空气／流体界面作用位能。定义作用算子f_a~′和f_C~′分别表示流体／纤维间和流体微粒间的作用位能。
(3)把原LGA模型的碰撞规则用于流体微粒间的自由碰撞；在流体／纤维界面上定义新的界面碰撞规则；在空气／流体界面上，给出流体微粒的速度调整算法，将其速度调整到界面法向。
(4)在流体微粒的微观动力学方程，即Boltzmann输运方程中引入Metropolis概率判断机制，根据碰撞前后系统能量的变化选择碰撞后流体微粒的出射位形。Metropolis判断机制的引入，建立了各种作用位能与流体微粒微观动力学之间的联系，在动力学中结合了流体内聚能对流动的阻碍作用、纤维表面性能对流动的影响和流体表面张力的作用等。
动力学模型的验证通过对平行平板间Poiseuille流动的模拟实现。模拟结果表明，模拟得到的速度分布曲线是一条抛物线，其函数式与流体力学的理论表达式具有相同的形式，证明论文所建的动力学模型能够正确描述典型流场的速度特征，因而模型和算法是正确的。
把所建模型应用于模拟流体在纤维束内单纤维间横向流动的流场特征。模拟结果显示，该模型能够反映流场中纤维排列结构和纤维表面性能对局部流场的影响。
进一步扩展模型，建立了可渗透纤维介质的统计动力学模型，以模拟流体在不同尺度孔隙中的流动行为。模型扩展时提出渗透概率的概念，以表征纤维集合体的结构特征，并对模拟算法作出相应改进，主要包括：改变纤维介质节点的状态参数设置；判断流体微粒在纤维介质内部的扩散方向和在介质／束间孔隙界面上碰撞后的出射方向时，必须进行渗透概率计算；对纤维介质内部空气／流体界面上的流体微粒进行速度方向调整等。
把扩展模型应用于模拟和分析不同外界压力条件下纤维束束内／束间孔隙中的流体速度分布。结果表明，随着外界压力的增加，纤维束束间孔隙中的流体速度由落后于纤维束内部的流体速度逐渐转变为超前。模拟结果与现有研究中的结论一致。
论文从液体流动系统中各种相互作用出发建立的模型具有普遍适用性，因而可以针对实际系统作进一步模拟，探讨模型的应用和扩展可能性。
Since liquid flow through fibrous media is a common phenomenon in textile processing and composite manufacturing, it is of practical significance to analyze the issue theoretically to find out the key factors that influence flow behavior.
Focusing on micro-nature of liquid flow, this study is to establish two stochastic models, a thermodynamic one and a kinetic one.
For the thermodynamic model, a Hamilton function is developed to describe potential energy of the system. Meanwhile, an exchange rule of air/liquid unit in simulation system is proposed, linking unit exchange to actual flow process. The model thus established can be applied in quantitative analysis of flow behavior.
For the kinetic model, interactions between liquid particles, as well as that between liquid particles and fibrous media are taken into account, furthermore, the model is extended to describe two-scale flow in fibrous media.
The investigation is carried out with an overview of current thermodynamic models, which are originated from Ising model. Three main problems are found therein. First, Hamilton functions are not correct enough to distinguish various energies in liquid flow system. Second, polar interactions are not considered even in systems with strong polar liquid, such as water. Third, the exchange rule of air/liquid unit is taken for granted with no verification. As a result, these models can only be used in phenomena simulation but quantitative description.
Then, a new Hamilton function is developed to describe potential energy in flow system. For this purpose, potential energy is explicitly determined as interface potential energy and gravity potential energy. Interface potential energy includes surface free energy of liquidγ_l, surface free energy of fiberγ_f, and liquid/fiber interface free energyγ_fl. On a virtual interface within a certain phase, interface free energy equals to zero.
Under the circumstances of apolar/polar interactions existing simultaneously on an interface, interface free energy is composed of apolar (Lifshitz-van der Waals) and polar (Lewis acid-base) parts, which are calculated by Good-Girifalco-Fowkes theory and Lewis acid-base theory, respectively. When strong polar liquid, such as water, is investigated, the polar part of free energy could not be neglected.
To identify all the potential energies mentioned above, interaction operators ?_a,?_c, ?_g, besides conventional state parameters s and F, are introduced in the new Hamilton function. Operators ?_a, ?_c, ?_g denote intensity of liquid/fiber and air/fiber interface free energy, liquid surface free energy and gravity potential energy, respectively. The correctness of Hamilton function is tested in a simple flow system. In addition, scaling effect due to system division is represented by a simulation coefficientλin the function.
Finally, an exchange rule of air/liquid unit is proposed and a method of energy calculation is offered. It is pointed out that an exchange cycle of air/liquid unit is a two-step process, first, an air unit exchanges with one of the nearest liquid unit, and second, the air unit is subsequently filled with liquid. In one cycle, the change of potential energy is the sum of that caused by each step, while the change of total energy is the sum of the potential energy change and the work done by liquid surface tension. With the data of liquid cohesion energy, liquid/fiber contact angle and adhesion energy, energy change during exchange process can be derived.
To validate the thermodynamic model established, simulation of equilibrium wicking height of liquid in capillary with circle section is implemented. The equilibrium height of two apolar liquids, heptane and octane, also two polar liquids, water and formamide, are recorded. The radii of capillaries are in the range of 0．15～1．35mm.
Test results reveal that equilibrium height of the four liquids differed obviously. In the same capillary, the height of water is maximum and that of octane and heptane are minimum, while the height of formamide is in between. As for one liquid, equilibrium height is inverse proportional to capillary radius.
Simulation procedure of wicking system is provided. Nontraditional column unit is adopted to divide the system. Besides, energy change is calculated from potential energy change caused by air/liquid unit exchange and work done by liquid surface tension.
By inputting the data of liquid cohesion energy, liquid/capillary contact angle and adhesion energy, equilibrium height of four liquids are simulated. Simulation results show good agreement with test data, which verifies the correctness of the thermodynamic model proposed in this study.
In the second part of the research, a kinetic model is established, combining interaction potential energy between liquid particles, between liquid and fiber, also on air/liquid interface. The differences between the new model and a traditional LGA model are as follows.
First, the state of each site is described by two state parameters, namely, s and F, besides a seven-bit Boolean variable.
Second, interaction operator ?_a′and ?_c′is introduced to denote interaction potential energies between liquid and fiber and within liquid phase.
Third, traditional collision rules are applied between liquid particles and new rules are defined on liquid/fiber interface. Procedure of fluid particle velocity adjustment on air/liquid interface is also put forward.
Four, Metropolis function is embedded into Boltzmann transport equation to determine the state of the system after collision.
To testify the validity of the kinetic model, Poiseuille flow is investigated. Simulate results of velocity profile agrees well with analytical solutions, which confirms the correctness of the model and corresponding simulation codes.
The new model is then used to simulate transverse flow in fiber bundles. Simulation result shows that it can reflect the effect of fiber construction and fiber surface properties on local flow field.
The kinetic mode is further extended to investigate flow in fibrous media on a scale larger than pore size. Transport probability is defined to characterize construction of fibrous media. Simulation procedure is amended in twofold. On the one hand, state parameters of fiber site is reset, for air/fiber site, it takes s=0, F=1 and for liquid/fiber site, s=1, F=1．On the other hand, transport probability is inserted into the microdynamics of liquid particles.
The modified model is applied to simulate meso-scale and micro-scale flow in unidirectional fibrous media. Simulation results agree with that given by other references.
Since the stochastic models developed in this thesis are based on micro-interactions in flow systems, both reflect inherent physics of liquid flow. The models can be further applied to more practical systems.
引文
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[2] van Oss C J, Acid-base interfacial interactions in aqueous media. Colloids Surface A, 1993, 78: 1-49.
[3] Good R J, Girifalco L A, A theory for estimation of surface and interfacial energies Ⅲ. estimation of surface energies of solids from contact angle data. J. Phys. Chem., 1960, 64: 561-565.
[4] van Oss C J, Good R J, Chaudhury M K, Determination of hydrophobic interaction energy - application to separation processes. Sep. Sci. Technol., 1987, 22: 1-24.
[5] van Oss C J, Ju L, Chaudhury M K, Good R J, Estimation of the polar parameters of the surface tensions of water by contact angle measurements on gels. J. Colloid Interface Sci., 1989, 128: 313-319.
[6] Schrader M E, Loeb G, Approach to wettability: theory and application. 1991, New York: Plenum Press.
[7] Costanzo P M, Giese R F, van Oss C J, Determination of the acid-base characteristics of clay mineral surfaces by contact angle measurements - implications for the adsorption of organic solutes from aqueous media. J. Adhesion Sci. Technol., 1990, 4 (4): 267-275.
[8] Birdi K s，表面和胶体化学手册．1999，北京：世界图书出版公司．
[9] Good R J, Girifalco L A, A theory for the estimation of surface and interfacial energies Ⅰ. derivation and application to interfacial tension. J. Phys. Chem., 1957, 61: 904-909.
[10] Good R J, Contact angle, wetting, and adhesion: a critical review. J. Adhesion Sci. Technol., 1992, 6 (12): 1269-1302.
[11] 胡英，吕瑞东，刘国杰，叶汝强，物理化学(下册)，第四版．1999，北京：高等教育出版社．
[12] Chibowski E, Solid surface free energy components determination by the thin-layer wicking technique. J. Adhesion Sci. Technol. 1992, 6 (9): 1069-1090.
[13] Chibowski E, González-Caballero F, Theory and practice of thin-layer wicking. Langmuir, 1993, 9: 330-340.
[14] Dourado F, Gama F M, Chibowski E, Mota M, Characterization of cellulose surface free energy. J. Adhesion Sci. Technol., 1998, 12 (10): 1081-1091.
[15] Chibowski E, Espinosa-Jimenez M, Ontiveros-Ortega A, Gimenez-Martin E, Surface free energy, adsorption and zeta potential in leacril/tannic acid system. Langmuir, 1998, 14: 5237-5244.
[16] Dimitrovová Z, Advani S G, Free boundary viscous flow at micro and mesolevel during liquid composites moulding process. Int. J. Numer. Meth. Fluids, 2004, 46: 435-455.
[17] Amico S, Lekakou C, Flow through a two-scale porosity, oriented fibre porous medium. Trans. in Porous Media, 2004, 54: 35-53.
[18] Ranganathan S, Phelan Jr F R, Advani S G, A generalized model for the transverse fluid permeability in unidirectional fibrous media. Polym. Compos., 1996, 17 (2): 222-230.
[19] Ngo N D, Tamma K K, Complex three-dimensional microstructural permeability prediction of porous fibrous media with and without compaction. Int. J. Numer. Meth. Engng., 2004, 60: 1741-1757.
[20] Phelan Jr F R, Wise G, Analysis of transverse flow in aligned fibrous porous media. Composites: Part A, 1996, 27A: 25-34.
[21] Nordlund M, Lundstrom T S, Numerical study of the local permeability of noncrimp fabrics. J. Composo Mater., 2005, 39 (10): 929-947.
[22] Nedanov P B, Advani S G, A method to determine 3D permeability of fibrous reinforcements. J. Compos. Mater., 2002, 36 (2): 241-254.
[23] Simacek P, Advani S G, Permeability model for a woven fabric. Polym. Compos., 1996, 17 (6):887-899.
[24] Markicevic B, Papathanasiou T D, A model for the transverse permeability of bi-material layered fibrous performs. Polym. Compos., 2003, 24 (1): 68-82.
[25] Chatterjee P K, Absorbency. 1985, New York: Elsevier Science Publishing Company Inc..
[26] Chen S, Diemer K, Doolen G D, Eggert K, Lattice gas automata for flow through porous media. Physica D, 1991, 47: 72-84.
[27] Markicevic B, Papathanasiou T D, The hydraulic permeability of dual porosity fibrous media. J. Reinforced Plast. Compos., 2001, 20 (10): 871-880.
[28] Bechtold G, Ye L, Influence of fiber distribution on the transverse flow permeability in fibre bundles. Compos. Sci. Technol., 2003, 63: 2069-2079.
[29] Clague D S, Phillips R J, A numerical calculation of the hydraulic permeability of three-dimensional disordered fibrous media. Phys. Fluids, 1997, 9 (6): 1562-1572.
[30] Koponen A, Kandhai D, Hellen E, Alava M, Hoekstra A, Kataja M, Niskanen K, Sloot P, Timonen J, Permeability of three-dimensional random fiber webs. Phys. Rev. Lett, 1998, 80 (4): 716-719.
[31] Drapier S, Monatte J, Elbouazzaoui O, Henrat P, Characterization of transient through-thickness permeabilities of non crimp new concept (NC2) multiaxial fabrics. Composites: Part A, 2005, 36: 877-892.
[32] Laudau D P, Binder K, A guide to Monte Carlo simulations in statistical physics. 2000, Cambridge: The Press Syndicate of the University of Cambridge.
[33] Binder K, Landau D P, Wetting versus layering near the roughening transition in the three-dimensional Ising model. Phys. Rev., 1992, 46 (8): 4844-4854.
[34] Gompper G, Kroll D M, Lipowsky R, Nonclassical wetting behavior in the solid-on-solid limit of the three-dimensional Ising model. Phys. Rev., 1990, 42 (1): 961-964.
[35] Manna S S, Herrmann H J, Landau D P, A stochastic method to determine the shape of a drop on a wall. J. Stat. Phys., 1992, 66 (3/4): 1155-1163.
[36] Lukas D, Glazyrina E, Pan N, Computer simulation of liquid wetting dynamics in fiber structures using the Ising model. J. Text. Inst., 1997, 88 Part1 (2): 149-161
[37] Zhong W, Ding X, Tang Z L, Modelling and analyzing liquid wetting in fibrous assemblies. Textile Res. J., 2001, 71 (9): 762-766.
[38] Zhong W, Ding X, Tang Z L, Analysis of fluid flow through fibrous structures. Textile Res. J., 2002, 72 (9), 751-755.
[39] Zhong W, Xing M Q, A statistic model of mold filling through fibrous structures. J. Compos. Mater., 2004, 38 (17): 1545-1557.
[40] Zhong W, Xing M Q, A stochastic model in liquid penetration through fibrous media. J. Colloid Interface Sci., 2004, 275: 264-269.
[41] Weng M, Ding X, The effect of surface free energy of liquid on wicking in a fiber bundle. Proceedings of the 2~(nd) International Textile Clothing & Design Conference, 2004, Dubrovnik, Croatia: 467-470.
[42] Lukas D, Pan N, Wetting of a fiber bundle in fibrous structures. Polym. Compos., 2003, 24 (3): 314-322.
[43] Lukas D, Pan N, Parikh D V, Computer simulation of 3-D liquid transport in fibrous materials. Simulation, 2004, 80 (11): 547-557.
[44] Kawasaki K, Diffusion constants near the critical point for time-dependent Ising models I. Phys. Rev., 1966, 145 (1): 224-230.
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