A relation between membrane permeability and flow rate at low Reynolds number in circular pipe

Takeuchi, Shintaro; Tazaki, Asahi; Miyauchi, Satoshi; Kajishima, Takeo

doi:10.1016/j.memsci.2019.03.018

Cited by 15 publications

(19 citation statements)

References 28 publications

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“…Takeuchi et al [21] coupled the above system with the permeate flux and derived a new pressure Poisson equation for a permeable surface system. The validity of the method was established through comparisons with static pressure values for the non-permeable case and an analytical prediction of the permeation across a membrane placed in a 2-D parallel channel in Ref.…”

Section: Discussionmentioning

confidence: 99%

“…The numerical method for permeation employed herein is the same as that used in Takeuchi et al [21], and it is briefly explained in this section.…”

Section: Outline Of the Numerical Methodsmentioning

confidence: 99%

“…The present authors have developed a method that directly discretises the governing equation even at the grid points adjacent to the interface, while at the same time, ensuring consistency between the incompressible velocity and pressure fields [19,21]. By their "consistent direct discretisation" for the discrete-forcing immersed boundary (DF-IB) approach, the non-slip condition on the interface was strictly imposed in a discrete sense while satisfying The above consistent direct discretisation for the DF-IB method is a suitable approach for membrane permeation, as the pressure fields on both sides reflect the local incompressible conservation at a cell level, which results in a sharp representation of the interface.…”

Section: Outline Of the Numerical Methodsmentioning

confidence: 99%

“…By their "consistent direct discretisation" for the discrete-forcing immersed boundary (DF-IB) approach, the non-slip condition on the interface was strictly imposed in a discrete sense while satisfying The above consistent direct discretisation for the DF-IB method is a suitable approach for membrane permeation, as the pressure fields on both sides reflect the local incompressible conservation at a cell level, which results in a sharp representation of the interface. This method has been fully validated for cases with a permeable membrane against a solvent [21] as well as for the non-permeable case (with stationary solid case [19] and moving/deforming membrane case [20]). The details of the numerical method can be found in Appendix A.…”

Section: Outline Of the Numerical Methodsmentioning

confidence: 99%

“…Early efforts on simulating membrane permeation problems [14,15,16,17] employed a diffused interface, where a substantial thickness of the interface may be inevitable [18]. The present authors have focused on the sharpness problem and developed an effective approach (based on the discrete-forcing immersed boundary method [19,20]) that can represent the sharp discontinuity of pressure across a permeable membrane [21] by strictly satisfying mass conservation in the vicinity of the permeable membrane. In addition, the mass transfer problems form a complex numerical system as they constitute a coupled system between the permeate solute/solvent, the membrane motion, and the motion of the ambient fluid [13].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Fluid Permeation Through A Membrane With Infinitesimal Permeability Under Reynolds Lubrication

et al. 2020

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To understand the lubrication-dominated permeation through a membrane, numerical simulations of permeation through a moving corrugated permeable membrane is carried out with a fully validated numerical method. Through comparisons between the numerical results and the results of an asymptotic analysis of permeate flux (under an infinitesimal permeability condition) using Reynolds lubrication equation, the effect of permeation on lubrication and its inverse effect (i.e., the dependence of permeation on lubrication) are discussed. The linear and non-linear dependences of the relaxation of the lubrication pressure due to membrane permeation are identified. The effect of the tangential component of the permeate flux is evaluated by a linear analysis, and the limitation of Reynolds-type lubrication is discussed.

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Section: Discussionmentioning

confidence: 99%

“…The numerical method for permeation employed herein is the same as that used in Takeuchi et al [21], and it is briefly explained in this section.…”

Section: Outline Of the Numerical Methodsmentioning

confidence: 99%

Section: Outline Of the Numerical Methodsmentioning

confidence: 99%

Section: Outline Of the Numerical Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fluid Permeation Through A Membrane With Infinitesimal Permeability Under Reynolds Lubrication

et al. 2020

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Transport of solute and solvent driven by lubrication pressure through non-deformable permeable membranes

Yamada

Takeuchi

Miyauchi

et al. 2021

Microfluid Nanofluid

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A discrete-forcing immersed boundary method with permeable membranes is developed to investigate the effect of lubrication on the permeations of solute and solvent through membrane. The permeation models are incorporated into the discretisation at the fluid cells including the membrane, and discretised equations for the pressure Poisson equation and convection–diffusion equation for the solute are represented with the discontinuities at the membrane. The validity of the proposed method is established by the convergence of the numerical results of the permeate fluxes (solute and solvent) to higher-order analytical models in a lubrication-dominated flow field. As a model of the mass exchange between inside and outside of a biological cell flowing in a capillary, a circular membrane is placed between parallel flat plates, and the effect of lubrication is investigated by varying the distance between the membrane and the walls. The pressure discontinuity near the wall is larger than that at the stagnation point, which is a highlighted effect of lubrication. In the case of a small gap, the solute transport is dominated by convection inside the circular membrane and by diffusion outside. Through the time variation of the concentration in the circular membrane, lubrication is shown to enhance mass transport from/to inside and outside the membrane.

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Flow Rate Prediction for a Semi-permeable Membrane at Low Reynolds Number in a Circular Pipe

et al. 2021

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A concise and accurate prediction method is required for membrane permeability in chemical engineering and biological fields. As a preliminary study on this topic, we propose the concentration polarization model (CPM) of the permeate flux and flow rate under dominant effects of viscosity and solute diffusion. In this model, concentration polarization is incorporated for the solution flow through a semi-permeable membrane (i.e., permeable for solvent but not for solute) in a circular pipe. The effect of the concentration polarization on the flow field in a circular pipe under a viscous-dominant condition (i.e., at a low Reynolds number) is discussed by comparing the CPM with the numerical simulation results and infinitesimal Péclet number model (IPM) for the membrane permeability, strength of the osmotic pressure, and Péclet number. The CPM and IPM are confirmed to be a reasonable extension of the model for a pure fluid, which was proposed previously. The application range of the IPM is narrow because the advection of the solute concentration is not considered, whereas the CPM demonstrates superior applicability in a wide range of parameters, including the permeability coefficient, strength of the osmotic pressure, and Péclet number. This suggests the necessity for considering concentration polarization. Although the mathematical expression of the CPM is more complex than that of the IPM, the CPM exhibits a potential to accurately predict the permeability parameters for a condition in which a large permeate flux and osmotic pressure occur.

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A relation between membrane permeability and flow rate at low Reynolds number in circular pipe

Cited by 15 publications

References 28 publications

Fluid Permeation Through A Membrane With Infinitesimal Permeability Under Reynolds Lubrication

Fluid Permeation Through A Membrane With Infinitesimal Permeability Under Reynolds Lubrication

Transport of solute and solvent driven by lubrication pressure through non-deformable permeable membranes

Flow Rate Prediction for a Semi-permeable Membrane at Low Reynolds Number in a Circular Pipe

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