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Xu J, Wang Z, Chu HCW. Unidirectional drying of a suspension of diffusiophoretic colloids under gravity. RSC Adv 2023; 13:9247-9259. [PMID: 36950706 PMCID: PMC10026375 DOI: 10.1039/d3ra00115f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2023] [Accepted: 03/13/2023] [Indexed: 03/24/2023] Open
Abstract
Recent experiments (K. Inoue and S. Inasawa, RSC Adv., 2020, 10, 15763-15768) and simulations (J.-B. Salmon and F. Doumenc, Phys. Rev. Fluids, 2020, 5, 024201) demonstrated the significant impact of gravity on unidirectional drying of a colloidal suspension. However, under gravity, the role of colloid transport induced by an electrolyte concentration gradient, a mechanism known as diffusiophoresis, is unexplored to date. In this work, we employ direct numerical simulations and develop a macrotransport theory to analyze the advective-diffusive transport of an electrolyte-colloid suspension in a unidirectional drying cell under the influence of gravity and diffusiophoresis. We report three key findings. First, drying a suspension of solute-attracted diffusiophoretic colloids causes the strongest phase separation and generates the thinnest colloidal layer compared to non-diffusiophoretic or solute-repelled colloids. Second, when colloids are strongly solute-repelled, diffusiophoresis prevents the formation of colloid concentration gradient and hence gravity has a negligible effect on colloidal layer formation. Third, our macrotransport theory predicts new scalings for the growth of the colloidal layer. The scalings match with direct numerical simulations and indicate that the colloidal layer produced by solute-repelled diffusiophoretic colloids could be an order of magnitude thicker compared to non-diffusiophoretic or solute-attracted colloids. Our results enable tailoring the separation of colloid-electrolyte suspensions by tuning the interactions between the solvent, electrolyte, and colloids under Earth's or microgravity, which is central to ground-based and in-space applications.
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Affiliation(s)
- Jinjie Xu
- Department of Chemical Engineering, University of Florida Gainesville FL 32611 USA
| | - Zhikui Wang
- Department of Chemical Engineering, University of Florida Gainesville FL 32611 USA
| | - Henry C W Chu
- Department of Chemical Engineering, University of Florida Gainesville FL 32611 USA
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Abstract
Recent experiments by Doan et al. (Nano Lett., 2021, 21, 7625-7630) demonstrated and measured colloid diffusiophoresis in porous media but existing theories cannot predict the observed colloid motion. Here, using regular perturbation method, we develop a mathematical model that can predict the diffusiophoretic motion of a charged colloidal particle driven by a binary monovalent electrolyte concentration gradient in a porous medium. The porous medium is modeled as a Brinkman medium with a constant Darcy permeability. The linearized Poisson-Boltzmann equation is employed to model the equilibrium electric potential distribution that is driven out-of-equilibrium under diffusiophoresis. We report three key findings. First, we demonstrate that colloid diffusiophoresis could be drastically hindered in a porous medium due to the additional hydrodynamic drag compared to diffusiophoresis in a free electrolyte solution. Second, we show that the variation of the diffusiophoretic motion with respect to a change in the electrolyte concentration in a porous medium could be qualitatively different from that in a free electrolyte solution. Third, our results match quantitatively with experimental measurements, highlighting the predictive power of the present model. The mathematical model developed here could be employed to design diffusiophoretic colloid transport in porous media, which are central to applications such as nanoparticle drug delivery and enhanced oil recovery.
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Affiliation(s)
| | - Henry C W Chu
- Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA.
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Chu HCW, Garoff S, Tilton RD, Khair AS. Tuning chemotactic and diffusiophoretic spreading via hydrodynamic flows. Soft Matter 2022; 18:1896-1910. [PMID: 35188176 DOI: 10.1039/d2sm00139j] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The transport of microorganisms by chemotaxis is described by the same "log-sensing" response as colloids undergoing diffusiophoresis, despite their different mechanistic origins. We employ a recently-developed macrotransport theory to analyze the advective-diffusive transport of a chemotactic or diffusiophoretic colloidal species (both referred to as "colloids") in a circular tube under a steady pressure-driven flow (referred to as hydrodynamic flow) and transient solute gradient. First, we derive an exact solution to the log-sensing chemotactic/diffusiophoretic macrotransport equation. We demonstrate that a strong hydrodynamic flow can reduce spreading of solute-repelled colloids, by eliminating super-diffusion which occurs in an otherwise quiescent system. In contrast, hydrodynamic flows always enhance spreading of solute-attracted colloids. Second, we generalize the exact solution to show that the above tunable spreading phenomena by hydrodynamic flows persist quantitatively for decaying colloids, as may occur with cell death, for example. Third, we examine the spreading of chemotactic colloids by employing a more general model that captures a hallmark of chemotaxis, that log-sensing occurs only over a finite range of solute concentration. Apart from demonstrating for the first time the generality of the macrotransport theory to incorporate an arbitrary chemotactic flow model, we reveal via numerical solutions new regimes of anomalous spreading, which match qualitatively with experiments and are tunable by hydrodynamic flows. The results presented here could be employed to tailor chemotactic/diffusiophoretic colloid transport using hydrodynamic flows, which are central to applications such as oil recovery and bioremediation of aquifers.
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Affiliation(s)
- Henry C W Chu
- Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA.
| | - Stephen Garoff
- Department of Physics and Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Robert D Tilton
- Department of Chemical Engineering, Department of Biomedical Engineering and Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Aditya S Khair
- Department of Chemical Engineering and Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
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Sauleda ML, Chu HCW, Tilton RD, Garoff S. Surfactant Driven Marangoni Spreading in the Presence of Predeposited Insoluble Surfactant Monolayers. Langmuir 2021; 37:3309-3320. [PMID: 33689367 DOI: 10.1021/acs.langmuir.0c03348] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
When an insoluble surfactant is deposited on the surface of a thin fluid film, stresses induced by surface tension gradients drive Marangoni spreading across the subphase surface. The presence of a predeposited layer of an insoluble surfactant alters that spreading. In this study, the fluid film was aqueous, the predeposited insoluble surfactant was dipalmitoylphosphatidylcholine (DPPC), and the deposited insoluble surfactant was oleic acid. An optical density-based method was used to measure subphase surface distortion, called the Marangoni ridge, associated with propagation of the spreading front. The movement of the Marangoni ridge was correlated with movement of surface tracer particles that indicated both the boundary between the two surfactant layers and the surface fluid velocities. As the deposited oleic acid monolayer spread, it compressed the predeposited DPPC monolayer. During spreading, the surface tension gradient extended into the predeposited monolayer, which was compressed nonuniformly, from the deposited monolayer. The spreading was so rapid that the compressed predeposited surfactant could not have been in quasi-equilibrium states during the spreading. As the initial concentrations of the predeposited surfactant were increased, the shape of the Marangoni ridge deformed. When the initial concentration of the predeposited surfactant reached about 70 A2/molecule, there was no longer a Marangoni ridge but rather a broadly distributed excess of fluid above the initial fluid height. The nonuniform compression of the annulus of the predeposited monolayer also caused tangential motion ahead of both the Marangoni ridge and the boundary between the two monolayers. Spreading ceased when the two monolayers reached the same final surface tension. The final area per molecule of the DPPC monolayer matched that expected from the equilibrium DPPC isotherm at the same final surface tension. Thus, at the end of spreading, there was a simple surface tension balance between the two distinct monolayers.
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Affiliation(s)
- Madeline L Sauleda
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
- Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
| | - Henry C W Chu
- Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
- Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
- Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611, United States
| | - Robert D Tilton
- Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
- Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
- Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
| | - Stephen Garoff
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
- Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
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Chu HCW, Garoff S, Tilton RD, Khair AS. Advective-diffusive spreading of diffusiophoretic colloids under transient solute gradients. Soft Matter 2020; 16:238-246. [PMID: 31777903 DOI: 10.1039/c9sm01938c] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We analytically calculate the one-dimensional advective-diffusive spreading of a point source of diffusiophoretic (DP) colloids, driven by the simultaneous diffusion of a Gaussian solute patch. The spreading of the DP colloids depends critically on the ratio of the DP mobility, M (which can be positive or negative), to the solute diffusivity, Ds. For instance, we demonstrate, for the first time, that solute-repelling colloids (M < 0) undergo long-time super-diffusive transport for M/Ds < -1. In contrast, the spreading of strongly solute-attracting colloids (M/Ds≫ 1) can be spatially arrested over long periods on the solute diffusion timescale, due to a balance between colloid diffusion and DP under the evolving solute gradient. Further, a patch of the translating solute acts as a "shuttle" that rapidly transports the colloids relative to their diffusive timescale. Finally, we use numerical computations to show that the above behaviors persist for three-dimensional, radially symmetric DP spreading. The results presented here could guide the use of DP colloids for microscale particle sorting, deposition, and delivery.
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Affiliation(s)
- Henry C W Chu
- Department of Chemical Engineering and Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA.
| | - Stephen Garoff
- Department of Physics and Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Robert D Tilton
- Department of Chemical Engineering, Department of Biomedical Engineering and Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Aditya S Khair
- Department of Chemical Engineering and Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA.
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Affiliation(s)
- Henry C. W. Chu
- Center for Complex Fluids Engineering and Department of Chemical Engineering Carnegie Mellon University Pittsburgh Pennsylvania
| | - Stephen Garoff
- Center for Complex Fluids Engineering and Department of Physics Carnegie Mellon University Pittsburgh Pennsylvania
| | - Robert D. Tilton
- Center for Complex Fluids Engineering, Department of Chemical Engineering and Department of Biomedical Engineering Carnegie Mellon University Pittsburgh Pennsylvania
| | - Aditya S. Khair
- Center for Complex Fluids Engineering and Department of Chemical Engineering Carnegie Mellon University Pittsburgh Pennsylvania
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