Capillary-Driven Ejection of a Droplet from a Micropore into a Channel: A Theoretical Model and a Computational Fluid Dynamics Verification

Salama, Amgad; Kou, Jisheng; Alyan, Adel; Husein, Maen M.

doi:10.1021/acs.langmuir.2c00426

Cited by 10 publications

(6 citation statements)

References 40 publications

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“…In a previous work, Salama et al 39 considered the case of the ejection of a permeating droplet in which two interfaces exist: one in the tube and another one in the reservoir. They showed that when the terminal pressures equalize, the interface inside the tube is able to bring the droplet back to the feed channel, provided the curvature of the interface in the tube is larger than that in the channel.…”

Section: ■ Materials and Methodsmentioning

confidence: 99%

Investigation of the Different Regimes Associated with the Growth of an Interface at the Exit of a Capillary Tube into a Reservoir: Analytical Solutions and CFD Validation

et al. 2022

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The emergence of a droplet from a capillary tube opening into a reservoir is an important phenomenon in several applications. In this work, we are particularly interested in this phenomenon in an attempt to highlight the physics behind droplet appearance. The emergence of a droplet from a tube opening into a reservoir under quasi-static conditions passes through three stages. The first stage starts when the meniscus in the tube reaches the exit. At this moment, the meniscus intersects the wall of the tube at the equilibrium contact angle. The interface then develops until its radius of curvature becomes equal to the tube radius. During this stage, the capillary pressure increases. In the second stage, the interface continues to evolve with its radius of curvature increasing until the static contact angle with respect to the surface of the reservoir is achieved. This marks the end of the second stage and the start of the third in which the contact line (CL) starts to depart the tube opening along the reservoir surface and the contact angle remains constant. Analytical models for the three stages have been derived based on the law of conservation of linear momentum. The models account for pressure, gravitational, capillary, and viscous forces, while inertia force is ignored. The model can predict the profiles of the mean velocity in the tube, the capillary pressure, and the evolution of the contact angle. In addition, a computational fluid dynamics (CFD) simulation has been conducted to provide a framework for validation and verification of the developed model. The CFD simulation shows qualitative behavior in terms of snapshots of the emerging droplet with time similar to that speculated by the analytical model. In addition, quantitative comparisons with respect to velocity, pressure, and volume profiles of the droplet show very good agreement, which builds confidence in the modeling approach.

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Section: ■ Materials and Methodsmentioning

confidence: 99%

Investigation of the Different Regimes Associated with the Growth of an Interface at the Exit of a Capillary Tube into a Reservoir: Analytical Solutions and CFD Validation

et al. 2022

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“…Furthermore, previous computational fluid dynamics (CFD) investigation shows a slight variation of the axial pressure profiles along the centreline in the reservoir (Salama et al. 2022). More discussion on local entrance losses in such set-ups can be found in several previous works, a good list of which may be found in the work of Waghmare & Mittra (2010).…”

Section: Quasi-one-dimensional Modelling Approachmentioning

confidence: 96%

“…Compared with the pressure loss along the capillary tube length, the local pressure drop at the entrance is expected to comprise only a small fraction (Budaraju et al 2016). Furthermore, previous computational fluid dynamics (CFD) investigation shows a slight variation of the axial pressure profiles along the centreline in the reservoir (Salama et al 2022). More discussion on local entrance losses in such set-ups can be found in several previous works, a good list of which may be found in the work of Waghmare & Mittra (2010).…”

Section: Quasi-one-dimensional Modelling Approachmentioning

confidence: 99%

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Investigation of the imbibition/drainage of two immiscible fluids in capillaries with arbitrary axisymmetric cross-sections: a generalized model

Salama

2022

J. Fluid Mech.

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In this work, we investigate the problem of imbibition/drainage of a fluid in capillaries of arbitrary axisymmetric cross-sections filled initially with another immiscible one. The model predicts the location of the meniscus and its speed along the tube length with time. The two immiscible fluids may assume any density and viscosity contrasts. In addition, the axisymmetric profile of the tube maintains a relatively small angle of tangency to warrant that the axial velocity distribution assumes, approximately, a parabolic profile. The driving forces that may be encountered in this system include the capillary force, pressure force, gravitational force and an opposing viscous force. The orientation of the capillary force can be in the direction of the flow (e.g. during imbibition) or opposite to the flow (e.g. during drainage). Likewise, the gravitational force can be in the direction of the flow or opposite to it. In this work we account for all these possibilities. A differential equation is developed that defines the location of the meniscus with time. A fourth-order-accurate Runge–Kutta scheme has been developed to provide solutions for the different scenarios associated with this system. It is shown that the developed model reduces to those appropriate for straight tubes, which builds confidence in the modelling approach. The effects of changing the tangent along the profile of the tube, which influences the calculation of the radius of curvature of the meniscus, is also considered. Unlike the cases of straight capillary tubes, in tubes with arbitrary symmetric profiles, the friction force depends on the variations of the tube profile. Examples of converging/diverging capillary tubes that follow straight and power law profiles are investigated. In addition, the case of sinusoidal profiles has also been considered.

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“…The idea behind the PFPT is to mitigate fouling by preventing the accumulation of oil droplets at the membrane surface during filtration. The fate of an oil droplet during filtration has been comprehensively studied using computational fluid dynamics (CFD) [29][30][31][32][33][34][35] and direct observation over the membrane surface [36] to understand the physics behind the oil settling and clogging of membrane pores. The results showed that an oil droplet, during the filtration process, undergoes either of the following four fates, namely 1) rejection, 2) permeation, 3) pinning, or 4) breakup.…”

Section: Periodic Feed Pressure Techniquementioning

confidence: 99%

Experimental Investigation of the Novel Periodic Feed Pressure Technique in Minimizing Fouling during the Filtration of Oily Water Systems using Ceramic Membranes

Echakouri¹,

Salama²,

Henni³

2022

Preprint

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Fouling represents a bottleneck problem for promoting the use of membranes in filtration and separation applications. It becomes even more persistent when it comes to the filtration of fluid emulsions. In this case, a gel-like layer that combines droplets, impurities, salts, and other materials form at the membrane's surface, blocking its pores. It is, therefore, a privilege to combat fouling by minimizing the accumulation of these droplets that work as seeds for other incoming droplets to cluster and coalesce with. In this work, we explore the use of the newly developed and novel periodic feed pressure technique (PFPT) in combating the fouling of ceramic membranes upon the filtration of oily water systems. The PFPT is based on alternating the applied transmembrane pressure (TMP) between the operating one and zero. A PFPT cycle is composed of a filtration half-cycle and a cleaning half-cycle. Permeation occurs when the TMP is set at its working value, while the cleaning occurs when it is zero. Three PFPT patterns were examined over two feeds of oily water systems with oil contents of 100 and 200ppm, respectively. The results show that the PFPT is very effective in minimizing the problem of fouling compared to a non-PFPT normal filtration. Furthermore, the overall drops in permeate flux during the cleaning half cycles are compensated by appreciable enhancement due to the significant elimination of fouling development such that the overall production of filtered water is even increased. Inspection of the internal surface of the membrane post rinsing at the end of the experiment proves that all PFPT cycles maintained the ceramic membranes as clean after a 2-hours operation. This can ensure a prolonged lifespan of the ceramic membrane use and a continuous greater permeate volume production. The advantage of the PFPT is that it can be implemented on existing units with minimal modification, ease of operation, and saving energy.

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Capillary-Driven Ejection of a Droplet from a Micropore into a Channel: A Theoretical Model and a Computational Fluid Dynamics Verification

Cited by 10 publications

References 40 publications

Investigation of the Different Regimes Associated with the Growth of an Interface at the Exit of a Capillary Tube into a Reservoir: Analytical Solutions and CFD Validation

Investigation of the Different Regimes Associated with the Growth of an Interface at the Exit of a Capillary Tube into a Reservoir: Analytical Solutions and CFD Validation

Investigation of the imbibition/drainage of two immiscible fluids in capillaries with arbitrary axisymmetric cross-sections: a generalized model

Experimental Investigation of the Novel Periodic Feed Pressure Technique in Minimizing Fouling during the Filtration of Oily Water Systems using Ceramic Membranes

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