Stochastic Modelling Of Flow Through Fibrous Media

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.