Simulation: the deposition behavior of Brownian particles in porous media by using the triangular network model

Chan, Hsun-Chih; Chen, Shan-Chih; Chang, Yu‐Wei

doi:10.1016/j.seppur.2004.12.012

Cited by 6 publications

(12 citation statements)

References 37 publications

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“…( Other symbol average value in their models, the particle's Brownian motion behavior was not considered. In our previous papers [8,9], we adopted the Brownian dynamic simulation method of solving Langevin type equations [10], and assumed that the porous media of the filter bed is unconsolidated, we had successfully tracked the motion of individual particles with Brownian motion behavior as they move through the filter bed, by using the 2-D models of the modified square network and the triangular network, respectively. From which, the temporal variations of the permeability reduction and the pressure drop, either caused by the straining or by the direct deposition of particles on the pore walls, were determined.…”

Section: Hamaker Constant A(t)mentioning

confidence: 99%

“…Similar to the previous papers by Ramarao et al [21] and by authors [8,9,22], with the consideration of the Brownian diffusion force in determining particle trajectories, the method of Brownian dynamics simulation is adopted in the present study. In this simulation method, the new position of the ith particle in the network model can be obtained by the integration of a Langevin type equation with a sufficient short time interval as follows [22],…”

Section: Brownian Dynamics Simulationmentioning

confidence: 99%

“…In this figure, N E1 = 105.0 and N DL = 10.75 for curve A, N E1 = 0.0 and N DL = 0.0 for curve B, and N E2 = 1.0 and N L0 = 7.0 for all two curves. Our previous papers [8,9] calculated the collection efficiencies of particles in SCT, and found that the collection efficiency of curve B is always greater than that of curve A when Reynolds number of fluid is small because there is no energy barrier exists, and the deposition mechanism of particles is controlled by the Brownian diffusion effect. For curves A, it was found that, even with the presence of the deep secondary minimum which increases the accumulation probability of particles, the steepest slope between the secondary minimum and the primary maximum energy barriers of curve A is still the main reason for its low collection efficiency.…”

Section: The Interaction Energy Curve Of Dlvo Theorymentioning

confidence: 99%

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Effects of three different network models on the filter coefficient of brownian particles

Chang

Chan

2006

Separation and Purification Technology

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Section: Hamaker Constant A(t)mentioning

confidence: 99%

Section: Brownian Dynamics Simulationmentioning

confidence: 99%

Section: The Interaction Energy Curve Of Dlvo Theorymentioning

confidence: 99%

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Effects of three different network models on the filter coefficient of brownian particles

Chang

Chan

2006

Separation and Purification Technology

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“…Donaldson, Baker, and Carrol in 1977 [8] were the first to use networks to study particle transport within porous media. The clogging of particles has been studied in networks with different geometries including bundles of parallel tubes [8], square networks [14,16,21], triangular networks [3,25], cubic networks [2,17,29], bubble models [6,20], and the so-called three-dimensional physically representative networks [1,30].…”

Section: Introductionmentioning

confidence: 99%

Filters. The Number of Channels That Can Clog in a Network

Kampel¹,

Goldsztein²

2008

SIAM J. Appl. Math.

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Abstract.We model filters as two-dimensional networks of channels. As a suspension (fluid with particles) flows through the filter, particles clog channels. We assume that there is no flow through clogged channels. In this paper, we compute a sharp upper bound on the number of channels that can clog before fluid can no longer flow through the filter. Fluid suspensions (or suspensions, for short) are fluids with small solid particles in them. According to their size and properties, these particles are called fines or colloids. As a suspension flows through a permeable porous material, some fines are trapped within the material. In fact, the function of the filters we consider in this paper is to clean suspensions by capturing most particles bigger than a certain size.The removal of particles from fluid suspensions is of importance in a wide range of industrial and technological applications such as waste water treatment [18] and other filtration processes [4,31]. Our studies are motivated by the filters used in the process known as deep bed filtration. As a suspension flows through a filter composed of granular or fibrous materials, fines or colloidal particles penetrate the filter and deposit at various depths [32]. As a result, the fluid suspension is cleaner when it exits the filter (i.e., it exits the filter with many fewer solid particles than it originally had when it entered the filter).Theoretical models to study transport in porous media can be classified as either macro-scale [5,15,22,23,24,26,32] or pore-scale [9,19,28] models. Within the latter group, the class of network models, in which the pore space is modeled as a network of channels, is very popular. Network models provide flexibility in modeling different geometries of pore space while keeping the computational cost low. Our work belongs to this class of models.Network models to study transport in porous media were introduced by Fatt in 1956 [10,11,12]. Donaldson, Baker, and Carrol in 1977 [8] were the first to use networks to study particle transport within porous media. The clogging of particles has been studied in networks with different geometries including bundles of parallel tubes [8], square networks [14,16,21], triangular networks [3,25], cubic networks

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“…in networks with different geometries including bundle of parallel tubes [8], square networks [14,16,23], triangular networks [3,27], cubic networks [2,17,33], bubble models [6,22], and the so-called three-dimensional physically representative networks [1,34].…”

mentioning

confidence: 99%

Clogging of Multigraphs as Toy Models of Filters

Goldsztein¹

2009

SIAM J. Appl. Math.

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Abstract. In this paper we model filters as networks of channels. As suspension (fluid with particles) flows through the filter, particles are trapped and clog channels. We assume there is no flow through clogged channels. The filter becomes impermeable after not all, but only a portion, of the channels clog. In this paper we compute an upper bound on the number of channels that clog. This bound is a function of properties of the network. Our results provide an understanding of the relationship between the filter pore space geometry and the filter efficiency. Fluid suspensions, or suspensions for short, are fluids with small solid particles in them. As suspension flows through a permeable porous material, some particles are trapped within the material. In fact, the function of the filters we consider in this paper is to clean suspensions by capturing particles.The removal of particles from fluid suspensions is of importance in a wide range of industrial and technological applications such as wastewater treatment [20], drinking water treatment, and other filtration processes [4,35]. Our studies are motivated by the filters used in the process known as deep bed filtration. In this process, as suspension flows through a filter, particles penetrate the filter and deposit at various depths [36]. As a result, the fluid suspension is cleaner when it exits the filter (i.e., the suspension exits the filter with fewer solid particles than it originally had when it entered the filter).Mathematical models for studying transport in porous media can be classified as either macroscale models [5,15,24,25,26,28,36] or pore-scale models (also known as microscale models) [9,21,31]. Macroscale models are those that model phenomena occurring at length scales much larger than the pore dimensions. On the other hand, pore-scale models, as the name suggests, model phenomena occurring at the length scale of the size of the pores. Within the pore-scale models, the class of network models is very popular. Network models are a class of models that represent the pore space in an idealized fashion, which can be channels, or pore bodies connected by pore throats. Our work belongs to the class of network models.Network models for studying transport in porous media were introduced by Fatt [10,11,12]. Donaldson [8] was the first one to use networks to study particle transport within porous media. The clogging of particles has been studied

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Simulation: the deposition behavior of Brownian particles in porous media by using the triangular network model

Cited by 6 publications

References 37 publications

Effects of three different network models on the filter coefficient of brownian particles

Effects of three different network models on the filter coefficient of brownian particles

Filters. The Number of Channels That Can Clog in a Network

Clogging of Multigraphs as Toy Models of Filters

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