Fluidisation of yield stress fluids under vibration

Garg, Ashish; Bergemann, Nico; Smith, Beccy; Heil, Matthias; Juel, Anne

doi:10.1016/j.sctalk.2022.100067

“…The mass flow rate in the rigid wall N nanochannels without pulsating pressure field, i.e. α = 0, p n = 0: under these limits, we obtain equation (42) as presented by Neek-Amal et al [30].…”

Section: Resultsmentioning

confidence: 78%

“…The channel is assumed to be sufficiently long and wide in comparison to the height (i.e. H/W ≪ 1, and H/L ≪ 1) to use a two-dimensional planar model [33,52,53]. The external forcing vibrations are applied using a pulsatory pressure gradient in the water reservoirs similar to the pistons placed at infinity from the channel wall [44].…”

Section: D Planar Modelmentioning

confidence: 99%

“…Additionally, we examine the influence of applied pulsating pressure on the water flow rate within these flexible nano capillaries. The application of pulsating pressure fields or vibrations is a well-known technique for enhancing the flow rate of complex fluids through porous mediums, including channels and tube capillaries [23][24][25][40][41][42][43]. However, for a Newtonian fluid (such as water), the pulsating pressure has no effect on the flow rate in a rigid-wall channel/tube [44].…”

Section: Introductionmentioning

confidence: 99%

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Pulsatile pressure enhanced rapid water transport through flexible graphene nano/Angstrom-size channels: a continuum modeling approach using the micro-structure of nanoconfined water

Garg

2023

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Several researchers observed a significant increase in water flow through graphene-based nanocapillaries. As graphene sheets are flexible (Wang and Shi 2015 Energy Environ. Sci. 8 790–823), we represent nanocapillaries with a deformable channel-wall model by using the small displacement structural-mechanics and perturbation theory presented by Gervais et al (2006 Lab Chip 6 500–7), and Christov et al (2018 J. Fluid Mech. 841 267–86), respectively. We assume the lubrication assumption in the shallow nanochannels, and using the microstructure of confined water along with slip at the capillary boundaries and disjoining pressure (Neek-Amal et al 2018 Appl. Phys. Lett. 113 083101), we derive the model for deformable nanochannels. Our derived model also facilitates the flow dynamics of Newtonian fluids under different conditions as its limiting cases, which have been previously reported in literature (Neek-Amal et al 2018 Appl. Phys. Lett. 113 083101; Gervais et al 2006 Lab Chip 6 500–7; Christov et al 2018 J. Fluid Mech. 841 267–86 ; White 1990 Fluid Mechanics; Keith Batchelor 1967 An Introduction to Fluid Dynamics ; Kirby 2010 Micro-and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices). We compare the experimental observations by Radha et al (2016 Nature 538 222–5) and MD simulation results by Neek-Amal et al (2018 Appl. Phys. Lett. 113 083101) with our deformable-wall model. We find that for channel-height H o < 4 Å, the flow-rate prediction by the deformable-wall model is 5%–7% more compared to Neek-Amal et al (2018 Appl. Phys. Lett. 113 083101) well-fitted rigid-wall model. These predictions are within the errorbar of the experimental data as shown by Radha et al (2016 Nature 538 222–5), which indicates that the derived deformable-wall model could be more accurate to model Radha et al (2016 Nature 538 222–5) experiments as compared to the rigid-wall model. Using the model, we study the effect of the flexibility of graphene sheets on the flow rate. As the flexibility α increases (or corresponding thickness T and elastic modulus E of the wall decreases), the flow rate also increases. We find that the flow rate scales as m ˙ flexible ∼ α 0 for ( α Δ p W / E H o ) ≪ 1 ; m ˙ flexible ∼ α for ( α Δ p W / E H o ) ∼ O ( 10 − 1 ) ; and m ˙ flexible ∼ α 3 for ( α Δ p W / E H o ) ∼ O ( 1 ) , respectively. We also find that, for a given thickness T , the percentage change in flow rate in the smaller height of the channel is more than the larger height of the channels. As the channel height decreases for the given reservoir pressure and thickness, the Δ m ˙ / m ˙ increases with H o − 1 followed by H o − 3 after a height-threshold. Further, we investigate how the applied pulsating pressure influences the flow rate. We find that due to the oscillatory pressure field, there is no change in the averaged mass flow rate in the rigid-wall channel, whereas the flow rate increases in the flexible channels with the increasing magnitude of the oscillatory pressure field. Also, in flexible channels, depending on the magnitude of the pressure field, either of the steady or oscillatory or both kinds of pressure field, the averaged mass flow rate dependence varies from Δ p to Δ p 4 as the pressure field increases. The flow rate in the rigid-wall channel scales as m ˙ rigid ∼ Δ p , whereas for the deformable-wall channel it scale as m ˙ flexible ∼ Δ p for ( α Δ p W / E H o ) ≊ 0 , m ˙ flexible ∼ Δ p 2 for ( α Δ p W / E H o ) ∼ O ( 10 − 1 ) , and m ˙ flexible ∼ Δ p 4 for ( α Δ p W / E H o ) ∼ O ( 1 ) . We find that both the flexibility of the graphene sheet and the pulsating pressure fields to these flexible channels intensify the rapid flow rate through nano/Angstrom-size graphene capillaries.

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“…We find that as D tends to infinity, the relative viscosity approaches a constant value a, whereas if a = 1, it approaches a regular bulk value of the viscosity. We also find that the proposed function is continuous and has a continuous derivative, making it appropriate to use in numerical simulations [43][44][45][46]. [14] in the literature.…”

Section: Viscosity Of Nanoconfined Fluidmentioning

confidence: 82%

An empirical experimental observations and MD simulation data-based model for the material properties of confined fluids in nano/Angstrom size tubes

Garg,

Bishnoi

2024

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The transport of fluids in nano/Angstrom-sized pores has gotten much attention because of its potential uses in nanotechnology, energy storage, and healthcare sectors. Understanding the distinct material properties of fluids in such close confinement is critical and dictate the fluid's behavior in determining flow dynamics, transport processes, and, ultimately, the performance of nanoscale devices. Remarkably, many researchers observed that the size of the geometry, such as confining nanotube diameter, exerts a profound and intriguing influence on the material properties, including on the critical parameters such as density, viscosity, and slip length. Many researchers tried to model viscosity $\eta$, density $\rho$, and slip $\lambda$ using various models with multiple dependencies on the tube-diameter. It is somewhat confusing and tough to decide which model is appropriate and can be incorporated in simulation. In this paper, we propose a simple single equation for each nanoconfined material property such as for density $\displaystyle \rho(D)/\rho_o = a+ b/(D-c)^n$, viscosity $\displaystyle \eta(D)/\eta_o = a+ b/(D-c)^n$, and the slip length $\lambda(D) = \lambda_1~D~e^{-n~D}+ \lambda_o$ (where $a,~b,~c,~n,~\lambda_1,~\lambda_o$ are the free fitting parameters). We model a wealth of previous experimental and MD simulation data from the literature using our proposed model for each material property of nanoconfined fluids. Our single proposed equation effectively captures and models all the data, even though many different models have been employed in literature to describe the same material property. Our proposed model exhibits exceptional agreement with multiple independent datasets from the experimental observations and MD simulations. Additionally, the model possesses continuity and continuous derivative, so that it is well-suited for simulations. The proposed models also obey the far boundary conditions, i.e., when tube-diameter $D \implies \infty$, the material properties approaches bulk properties of fluid. Because of models' simplicity, smooth, and generic nature, it holds promise to apply in simulations to design/optimize nanoscale-devices.

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“…This model comprehensively accounts for factors such as yield stress, shear thinning, and shear thickening in the material [3]. HerschelBulkley fluids, which exhibit these characteristics, are commonly encountered in various applications, including but not limited to food processing [4][5][6], the oil and gas industry [7], biomedical applications [8,9] such as the flow through tubes, pipes, and hoses, and in polymer processing industries like extrusion and injection molding [10,11]. Additionally, they find use in pharmaceutical formulations and processing [12][13][14][15] as well as in waste management [16,17].…”

Section: Introductionmentioning

confidence: 99%

Yield–stress shear thinning and shear thickening fluid flows in deformable channels

Garg,

Prasad

2024

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Yield stress shear thinning/thickening fluids flow through flexible channels, tubes are widespread in the natural world with many technological applications. In this paper, analytical formulae for the velocity profiles and flow rate are derived using the Herschel--Bulkley rheological model in both rigid and deformable shallow channels, employing the lubrication approximation. To account for deformable walls, the approach outlined by \citet{gervais2006flow} and \citet{christov2018flow} is utilized, applying small displacement structural mechanics and perturbation theory, respectively. The newly derived formulae also enable the analysis of flow dynamics in Newtonian fluids, power-law fluids, and Bingham fluids as their limiting cases, all of which have been previously described in the literature and also serves as the validation cases. It is observed that deformability increases the effective channel height and the flow rate within the channel. Multiple scaling relationships for the flow rate are identified under different applied pressure regimes and deformability parameters. Additionally, it is noted that increasing the yield stress results in decreased velocity in both the plug flow and non-plug flow regions. Higher yield stress also corresponds to an increase in the yield surface height and the solid plug within the central region, leading to a reduction in the flow rate. Furthermore, the shear thinning/thickening index is found to have no impact on plug height, although an increase in this index causes a reduction in the flow rate due to the corresponding increase in shear thickening of the material.

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Fluidisation of yield stress fluids under vibration

Cited by 26 publications

References 4 publications

Pulsatile pressure enhanced rapid water transport through flexible graphene nano/Angstrom-size channels: a continuum modeling approach using the micro-structure of nanoconfined water

Pulsatile pressure enhanced rapid water transport through flexible graphene nano/Angstrom-size channels: a continuum modeling approach using the micro-structure of nanoconfined water

An empirical experimental observations and MD simulation data-based model for the material properties of confined fluids in nano/Angstrom size tubes

Yield–stress shear thinning and shear thickening fluid flows in deformable channels

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