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Appleby BA, Chacon A, Mishra A, Liserre M, Goggin DM, Samaniuk JR. Subphase Exchange Cell for Studying Fluid-Fluid Interfaces with Optical Microscopy. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2024; 40:2174-2182. [PMID: 38226897 DOI: 10.1021/acs.langmuir.3c03154] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/17/2024]
Abstract
A subphase exchange cell was designed to observe fluid-fluid interfaces with a conventional optical microscope while simultaneously changing the subphase chemistry. Materials including phospholipids, asphaltenes, and nanoparticles at fluid-fluid interfaces exhibit unique morphological changes as a function of the bulk-phase chemistry. These changes can affect their interfacial material properties and, ultimately, the emergent bulk material properties of the films, foams, and emulsions produced from such interfacial systems. In this work, we combine experiments, computational fluid dynamics simulations, and modeling to establish the operating parameters for a subphase exchange cell of this type to reach a desired concentration. We used the experimental setup to investigate changes to a graphene film during a common wet-etching transfer process. Observations reveal that capillary interactions can induce defects and deformations in the graphene film during the wet-etching process, an important finding that must be considered for any wet-etching transfer technique for 2D materials. More generally, conventional optical microscopy was shown to be able to image the dynamics of interfacial systems during a bulk-phase chemistry change. Potential applications for this equipment and technique include observing morphological dynamics of phospholipid film structure with subphase salinity, asphaltene film structure with subphase pH, and particle film synthesis with subphase chemistry.
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Affiliation(s)
- Benjamin A Appleby
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, Colorado 80401, United States
| | - Amy Chacon
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, Colorado 80401, United States
| | - Arpit Mishra
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, Colorado 80401, United States
| | - Matteo Liserre
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, Colorado 80401, United States
| | - David M Goggin
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, Colorado 80401, United States
| | - Joseph R Samaniuk
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, Colorado 80401, United States
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Alicke A, Stricker L, Vermant J. Model aggregated 2D suspensions in shear and compression: From a fluid layer to an auxetic interface? J Colloid Interface Sci 2023; 652:317-328. [PMID: 37597413 DOI: 10.1016/j.jcis.2023.07.159] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Revised: 07/19/2023] [Accepted: 07/25/2023] [Indexed: 08/21/2023]
Abstract
HYPOTHESIS Particle-laden interfaces play a crucial role in engineering stability of multiphase systems. However, a full understanding of the mechanical properties in shear and compression, especially in relation to the underlying microstructural changes, is as yet lacking. In this study, we investigate the interfacial rheological moduli in heterogeneous networks of aggregated 2D suspensions using different deformation modes and relate these moduli to changes in the microstructure. EXPERIMENTS Interfacial rheological experiments were conducted at different surface coverages and clean kinematic conditions, namely in (i) simple shear flow in a modified double wall-ring geometry and (ii) isotropic compression in a custom-built radial trough, while monitoring the evolution of the microstructure. FINDINGS The compressive moduli increase non-monotonically with decreasing void fraction, reflecting the combined effect of aggregate densification and reduction of void structures, with rotation of rigid clusters playing a significant role in closing voids. However, the shear moduli increase monotonically, which correlates with the increase in fractal dimension of the aggregates making up the backbone network. We also observe that these interfaces act as 2D auxetic materials at intermediate coverages, which is surprising given their amorphous structure. This finding has potential implications for the resilience of particle-coated bubbles or droplets subjected to time-varying compression-expansion deformations.
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Affiliation(s)
- Alexandra Alicke
- Department of Materials, ETH Zurich, Vladimir-Prelog-Weg 5, Zurich 8093, Switzerland.
| | - Laura Stricker
- Department of Materials, ETH Zurich, Vladimir-Prelog-Weg 5, Zurich 8093, Switzerland
| | - Jan Vermant
- Department of Materials, ETH Zurich, Vladimir-Prelog-Weg 5, Zurich 8093, Switzerland.
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Huang YH, Frostad JM. A new instrument for interfacial dilational rheology. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2023; 94:115108. [PMID: 37971323 DOI: 10.1063/5.0168137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2023] [Accepted: 09/29/2023] [Indexed: 11/19/2023]
Abstract
We present a new design for an interfacial dilational rheometer that can generate oscillatory dilational strain on a planar air-liquid interface. The strain is generated by a pneumatic mechanism involving a deformable film, which forms a circular barrier that can contract or expand under different pressures. The interfacial stress is measured using a Wilhelmy rod. We carefully examine and demonstrate the effects of potential sources of measurement error, including inertia, drag, buoyancy, flow from the bulk phase, and surface waves. The design avoids mixed deformations present in other instruments and is currently capable of accurate measurements at frequencies up to ∼0.1 Hz and dilational strains below 0.001, with potential for higher frequencies after further theoretical development. We demonstrate the integration of the interfacial dilational rheometer with a Langmuir trough by measuring the compression isotherm of an insoluble surfactant, stearic acid. Furthermore, we verify the capability of the interfacial dilational rheometer to perform frequency and amplitude sweeps and present the storage and loss moduli for a water-soluble surfactant, sodium dodecylbenzenesulfonate, at different concentrations.
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Affiliation(s)
- Yun-Han Huang
- Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, British Columbia V6T 1Z3, Canada
| | - John M Frostad
- Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, British Columbia V6T 1Z3, Canada
- Department of Food Science, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
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Zhang H, Zhang Z, Grauby-Heywang C, Kellay H, Maali A. Air/Water Interface Rheology Probed by Thermal Capillary Waves. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023; 39:3332-3340. [PMID: 36802344 DOI: 10.1021/acs.langmuir.2c03193] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Atomic force microscopy (AFM) was used to study the interfacial rheology of air/water interfaces by investigating the thermal capillary fluctuations of surfactant-loaded interfaces. These interfaces are formed by depositing an air bubble on a solid substrate immersed in a surfactant (Triton X-100) solution. An AFM cantilever, in contact with the north pole of the bubble, probes its thermal fluctuations (amplitude of the vibration versus the frequency). The measured power spectral density of the nanoscale thermal fluctuations presents several resonance peaks corresponding to the different vibration modes of the bubble. The measured damping versus the surfactant concentration of each mode presents a maximum and then decreases to a saturation value. The measurements are in good agreement with the model developed by Levich for the damping of capillary waves in the presence of surfactants. Our results show that the AFM cantilever in contact with a bubble is a powerful tool to probe the rheological properties of air/water interfaces.
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Affiliation(s)
- Hao Zhang
- Laboratoire Ondes et Matière d'Aquitaine, Université de Bordeaux & CNRS, 33405 Talence, France
| | - Zaicheng Zhang
- Laboratoire Ondes et Matière d'Aquitaine, Université de Bordeaux & CNRS, 33405 Talence, France
| | | | - Hamid Kellay
- Laboratoire Ondes et Matière d'Aquitaine, Université de Bordeaux & CNRS, 33405 Talence, France
| | - Abdelhamid Maali
- Laboratoire Ondes et Matière d'Aquitaine, Université de Bordeaux & CNRS, 33405 Talence, France
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5
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Oral bio-interfaces: Properties and functional roles of salivary multilayer in food oral processing. Trends Food Sci Technol 2023. [DOI: 10.1016/j.tifs.2023.01.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
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Ciutara CO, Barman S, Iasella S, Huang B, Zasadzinski JA. Dilatational and shear rheology of soluble and insoluble monolayers with a Langmuir trough. J Colloid Interface Sci 2023; 629:125-135. [PMID: 36063630 PMCID: PMC10038177 DOI: 10.1016/j.jcis.2022.08.051] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2022] [Revised: 07/31/2022] [Accepted: 08/09/2022] [Indexed: 10/15/2022]
Abstract
HYPOTHESIS The surface dilatational and shear moduli of surfactant and protein interfacial layers can be derived from surface pressures measured with a Wilhelmy plate parallel, ΔΠpar and perpendicular ΔΠperp to the barriers in a Langmuir trough. EXPERIMENTAL Applying area oscillations, A0+ ΔAeiωt, in a rectangular Langmuir trough induces changes in surface pressure, ΔΠpar and ΔΠperp for monolayers of soluble palmitoyl-lysophosphatidylcholine (LysoPC), insoluble dipalmitoylphosphatidylcholine (DPPC), and the protein β-lactoglobulin to evaluate Es∗+Gs∗=A0ΔΠparΔA and Es∗-Gs∗=A0ΔΠperpΔA. Gs∗ was independently measured with a double-wall ring apparatus (DWR) and Es∗ by area oscillations of hemispherical bubbles in a capillary pressure microtensiometer (CPM) and the results were compared to the trough measurements. FINDINGS For LysoPC and DPPC, A0ΔΠparΔA≅A0ΔΠperpΔA meaning Es∗≫Gs∗ and Es∗≅A0ΔΠparΔA≅A0ΔΠperpΔA. Trough values for Es∗ were quantitatively similar to CPM when corrected for interfacial curvature. DWR showed G∗ was 4 orders of magnitude smaller than Es∗ for both LysoPC and DPPC. For β-lactoglobulin films, A0ΔΠparΔA>A0ΔΠperpΔA and Es∗ and Gs∗ were in qualitative agreement with independent CPM and DWR measurements. For β-lactoglobulin, both Es∗ and Gs∗ varied with film age and history on the trough, suggesting the evolution of the protein structure.
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Affiliation(s)
- Clara O Ciutara
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
| | - Sourav Barman
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
| | - Steven Iasella
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
| | - Boxun Huang
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
| | - Joseph A Zasadzinski
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA.
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Tein YS, Thompson BR, Majkrzak C, Maranville B, Renggli D, Vermant J, Wagner NJ. Instrument for measurement of interfacial structure-property relationships with decoupled interfacial shear and dilatational flow: "Quadrotrough". THE REVIEW OF SCIENTIFIC INSTRUMENTS 2022; 93:093903. [PMID: 36182507 DOI: 10.1063/5.0090350] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2022] [Accepted: 08/13/2022] [Indexed: 06/16/2023]
Abstract
Understanding the interfacial structure-property relationship of complex fluid-fluid interfaces is increasingly important for guiding the formulation of systems with targeted interfacial properties, such as those found in multiphase complex fluids, biological systems, biopharmaceuticals formulations, and many consumer products. Mixed interfacial flow fields, typical of classical Langmuir trough experiments, introduce a complex interfacial flow history that complicates the study of interfacial properties of complex fluid interfaces. In this article, we describe the design, implementation, and validation of a new instrument capable of independent application of controlled interfacial dilation and shear kinematics on fluid interfaces. Combining the Quadrotrough with both in situ Brewster angle microscopy and neutron reflectometry provides detailed structural measurements of the interface at the mesoscale and nanoscale in relationship to interfacial material properties under controlled interfacial deformation histories.
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Affiliation(s)
- Y Summer Tein
- Center for Neutron Science, Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716, USA
| | - Benjamin R Thompson
- Center for Neutron Science, Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716, USA
| | - Chuck Majkrzak
- Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Brian Maranville
- Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Damian Renggli
- Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Jan Vermant
- Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Norman J Wagner
- Center for Neutron Science, Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716, USA
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Feller D, Karg M. Fluid interface-assisted assembly of soft microgels: recent developments for structures beyond hexagonal packing. SOFT MATTER 2022; 18:6301-6312. [PMID: 35993260 DOI: 10.1039/d2sm00872f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Microgels adsorb to air/water and oil/water interfaces - a process driven by a significant reduction in interfacial tension. Depending on the available interface area per microgel, strong lateral deformation can be observed. Typically, hexagonally ordered structures appear spontaneously upon contact of the microgel shells. Transfer from the interface to solid substrates gives access to macroscopically sized microgel monolayers that are interesting for photonic and plasmonic studies as well as colloid-based lithography, for example. Significant efforts have been made to understand the phase behavior of microgels at different interfaces and to explore the available parameter space for achieving complex tessellations. In this review, we will discuss the most recent developments in the realization of microgel monolayers with structures beyond hexagonal packing.
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Affiliation(s)
- Déborah Feller
- Institut für Physikalische Chemie I: Kolloide und Nanooptik, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany.
| | - Matthias Karg
- Institut für Physikalische Chemie I: Kolloide und Nanooptik, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany.
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9
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Fesenmeier DJ, Park S, Kim S, Won YY. Surface mechanical behavior of water-spread poly(styrene)-poly(ethylene glycol) (PS-PEG) micelles at the air-water interface: Effect of micelle size and polymer end/linking group chemistry. J Colloid Interface Sci 2022; 617:764-777. [PMID: 35325653 DOI: 10.1016/j.jcis.2022.03.008] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2021] [Revised: 03/02/2022] [Accepted: 03/03/2022] [Indexed: 12/16/2022]
Abstract
HYPOTHESIS The surface mechanical properties of poly(styrene)-poly(ethylene glycol) (PS-PEG) micelles are influenced by the PEG corona structure. Changes in micelle aggregation number as well as changes in the PEG end group and linking group chemistry of the PS-PEG block copolymer are expected to alter PEG corona characteristics and therefore affect surface mechanical properties of the resulting micelle film. EXPERIMENTS Different sized micelles comprised of PS-PEG block copolymer chains were formulated by equilibrating micelles in different ratios of acetone/water mixtures and subsequently removing acetone using dialysis. Additionally, micelles of a similar size and PS-PEG molecular weight but slightly different chemistry were formulated. The micelles were characterized using dynamic light scattering (DLS), transmission electron microscopy (TEM), 1H NMR, surface pressure-area isotherms and Brewster angle microscopy (BAM). FINDINGS The reduction in micelle aggregation number results in the subsequent monolayer having higher compressibility moduli and bending stiffnesses and collapsing at lower surface pressures. Micelle hydrophobicity was shown to improve readsorption of micelles to interface after collapse. Analysis of Brewster angle microscopy images of out-of-plane wrinkle structures which formed upon monolayer collapse indicates the presence of continuous 1 nm thick PEG layer which allows micelle monolayers to bend under high compression.
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Affiliation(s)
- Daniel J Fesenmeier
- Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN 47907, USA
| | - Sungwan Park
- Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN 47907, USA
| | - Seyoung Kim
- Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN 47907, USA
| | - You-Yeon Won
- Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN 47907, USA; Purdue University Center for Cancer Research, West Lafayette, IN 47906, USA.
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Goggin DM, Samaniuk JR. 2D Colloids: Size- and Shape-Controlled 2D Materials at Fluid-Fluid Interfaces. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2021; 37:14157-14166. [PMID: 34797659 DOI: 10.1021/acs.langmuir.1c02418] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Advances in synthesis of model 3D colloidal particles with exotic shapes and physical properties have enabled discovery of new 3D colloidal phases not observed in atomic systems, and simulations and quasi-2D studies suggest 2D colloidal systems have an even richer phase behavior. However, a model 2D (one-atom-thick) colloidal system has yet to be experimentally realized because of limitations in solution-phase exfoliation of 2D materials and other 2D particle fabrication technologies. Herein, we use a photolithography-based methodology to fabricate size- and shape-controlled monolayer graphene particles, and then transfer the particles to an air-water interface to study their dynamics and self-assembly in real-time using interference reflection microscopy. Results suggest the graphene particles behave as "hard" 2D colloidal particles, with entropy influencing the self-assembled structures. Additional evidence suggests the stability of the self-assembled structures manifests from the edge-to-edge van der Waals force between 2D particles. We also show graphene discs with diameters up to 50 μm exhibit significant Brownian motion under optical microscopy due to their low mass. This work establishes a facile methodology for creating model experimental systems of colloidal 2D materials, which will have a significant impact on our understanding of fundamental 2D physics. Finally, our results advance our understanding of how physical particle properties affect the interparticle interactions between monolayer 2D materials at fluid-fluid interfaces. This information can be used to guide the development of scalable synthesis techniques (e.g., solution-phase processing) to produce bulk suspensions of 2D materials with desired physical particle properties that can be used as building blocks for creating thin films with desired structures and properties via interfacial film assembly.
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Affiliation(s)
- David M Goggin
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, Colorado 80401, United States
| | - Joseph R Samaniuk
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, Colorado 80401, United States
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Carrera Sánchez C, Rodríguez Patino JM. Contribution of the engineering of tailored interfaces to the formulation of novel food colloids. Food Hydrocoll 2021. [DOI: 10.1016/j.foodhyd.2021.106838] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
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12
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The Oscillatory Spinning Drop Technique. An Innovative Method to Measure Dilational Interfacial Rheological Properties of Brine-Crude Oil Systems in the Presence of Asphaltenes. COLLOIDS AND INTERFACES 2021. [DOI: 10.3390/colloids5030042] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The oscillatory spinning drop method has been proven recently to be an accurate technique to measure dilational interfacial rheological properties. It is the only available equipment for measuring dilational moduli in low interfacial tension systems, as it is the case in applications dealing with surfactant-oil-water three-phase behavior like enhanced oil recovery, crude oil dehydration, or extreme microemulsion solubilization. Different systems can be studied, bubble-in-liquid, oil-in-water, microemulsion-in-water, oil-in-microemulsion, and systems with the presence of complex natural surfactants like asphaltene aggregates or particles. The technique allows studying the characteristics and properties of water/oil interfaces, particularly when the oil contains asphaltenes and when surfactants are present. In this work, we present a review of the measurements of crude oil-brine interfaces with the oscillating spinning drop technique. The review is divided into four sections. First, an introduction on the oscillating spinning drop technique, fundamental and applied concepts are presented. The three sections that follow are divided according to the complexity of the systems measured with the oscillating spinning drop, starting with simple surfactant-oil-water systems. Then the complexity increases, presenting interfacial rheology properties of crude oil-brine systems, and finally, more complex surfactant-crude oil-brine systems are reviewed. We have found that using the oscillating spinning drop method to measure interfacial rheology properties can help make precise measurements in a reasonable amount of time. This is of significance when systems with long equilibration times, e.g., asphaltene or high molecular weight surfactant-containing systems are measured, or with systems formulated with a demulsifier which is generally associated with low interfacial tension.
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Fajardo-Rojas F, Alvarez Solano OA, Samaniuk JR, Pradilla D. Deviation from Equilibrium Thermodynamics of an Asphaltene Model Compound during Compression-Expansion Experiments at Fluid-Fluid Interfaces. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2021; 37:1799-1810. [PMID: 33497231 DOI: 10.1021/acs.langmuir.0c03151] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Asphaltenes play a crucial role in crude oil behavior, and model compounds are often used to capture, mimic, and predict certain interfacial properties. In previous works, sorption of an asphaltene model compound (C5PeC11) was studied using surface pressure isotherms, where a deviation from the expected thermodynamic behavior of the interface during decane-water and air-water compression experiments was observed but not explained. In this work, the interfacial behavior of C5PeC11 was assessed at the decane-water and the air-water interfaces using a multiscale approach that includes: compression-expansion experiments on rectangular and radial Langmuir troughs, dynamic interfacial stress relaxation, and fluorescence microscopy imaging. Connections between molecular and microscopic phenomena strongly suggest that the nonthermodynamic response can be explained through a dynamic effect whose origin lies in the predominance of intermolecular forces in C5PeC11 molecules over the mechanical compression force applied. When aggregation begins at the air-water interface, stable structures are formed, and the nonthermodynamic phenomenon is not observed in subsequent compressions. However, at the decane-water interface, the initial aggregation is not consolidated due to the effect of the oil phase on the free energy of the interface allowing the high reproducibility of the dynamic effect in subsequent compression cycles. These results highlight the need to probe interfacial systems at various length scales to adequately separate equilibrium thermodynamics from dynamic responses.
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Affiliation(s)
- Fernando Fajardo-Rojas
- Grupo de Diseño de Productos y Procesos (GDPP), Departamento de Ingeniería Química, Universidad de los Andes, Carrera 1 Este No. 18A-12, Edificio Mario Laserna, Piso 7, Bogotá 110111, Colombia
| | - Oscar Alberto Alvarez Solano
- Grupo de Diseño de Productos y Procesos (GDPP), Departamento de Ingeniería Química, Universidad de los Andes, Carrera 1 Este No. 18A-12, Edificio Mario Laserna, Piso 7, Bogotá 110111, Colombia
| | - Joseph R Samaniuk
- Soft Matter and Interfaces Laboratory, Department of Chemical and Biological Engineering, Colorado School of Mines, 1500 Illinois Street, Golden, Colorado 80401, United States
| | - Diego Pradilla
- Grupo de Diseño de Productos y Procesos (GDPP), Departamento de Ingeniería Química, Universidad de los Andes, Carrera 1 Este No. 18A-12, Edificio Mario Laserna, Piso 7, Bogotá 110111, Colombia
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