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At least 433 records · Page 24

Two-Phase Flow Mechanisms Controlling CO2 Intrusion into Shaly Caprock

Abstract Geologic carbon storage in deep saline aquifers has emerged as a promising technique to mitigate climate change. CO 2 is buoyant at the storage conditions and tends to float over the resident brine jeopardizing long-term containment goals. Therefore, the caprock sealing capacity is of great importance and requires detailed assessment. We perform supercritical CO 2 injection experiments on shaly caprock samples (intact caprock and fault zone) under representative subsurface conditions. We numerically simulate the experiments, satisfactorily reproducing the observed evolution trends. Simulation results highlight the dynamics of CO 2 flow through the specimens with implications to CO 2 leakage risk assessment in field practices. The large injection-induced overpressure drives CO 2 in free phase into the caprock specimens. However, the relative permeability increase following the drainage path is insufficient to provoke an effective advancement of the free-phase CO 2 . As a result, the bulk CO 2 front becomes almost immobile. This implies that the caprock sealing capacity is unlikely to be compromised by a rapid capillary breakthrough and the injected CO 2 does not penetrate deep into the caprock. In the long term, the intrinsically slow molecular diffusion appears to dominate the migration of CO 2 dissolved into brine. Nonetheless, the inherently tortuous nature of shaly caprock further holds back the diffusive flow, favoring safe underground storage of CO 2 over geological time scales.

58 GEOSCIENCES↗

Effects of coating rectangular microscopic electrophoresis chamber with methylcellulose

One of the biggest problems in obtaining high accuracy in microscopic electrophoresis is the parabolic flow of liquid in the chamber due to electroosmotic backflow during application of the electric field. In chambers with glass walls the source of polarization leading to electroosmosis is the negative charge of the silicare and other ions that form the wall structure. It was found by Hjerten, who used a rotating 3.0 mm capillary tube for free zone electrophoresis, that precisely neutralizing this charge was extremely difficult, but if a neutral polymer matrix (formaldehyde fixed methylcellulose) was formed over the glass (quartz) wall the double layer was displaced and the viscosity at the shear plane increased so that electroosmotic flow could be eliminated. Experiments were designed to determine the reliability with which methylcellulose coating of the Zeiss Cytopherometer chamber reduced electroosmotic backflow and the effect of coating on the accuracy of cell electrophoretic mobility (EPN) determinations. Fixed rat erythrocytes (RBC) were used as test particles.

Plank, L. D.↗

Stream lamination and rapid mixing in a microfluidic jet for X-ray spectroscopy studies

Microfluidic mixers offer new possibilities for the study of fast reaction kinetics down to the microsecond time scale, and methods such as soft X-ray absorption spectroscopy are powerful analysis techniques. These systems impose challenging constraints on mixing time scales, sample volume, detection region size and component materials. The current work presents a novel micromixer and jet device which aims to address these limitations. The system uses a so-called ‘theta’ mixer consisting of two sintered and fused glass capillaries. Sample and carrier fluids are injected separately into the inlets of the adjacent capillaries. At the downstream end, the two streams exit two micron-scale adjoining nozzles and form a single free-standing jet. The flow-rate difference between the two streams results in the rapid acceleration and lamination of the sample stream. This creates a small transverse dimension and induces diffusive mixing of the sample and carrier stream solutions within a time scale of 0.9 microseconds. The reaction occurs at or very near a free surface so that reactants and products are more directly accessible to interrogation using soft X-ray. We use a simple diffusion model and quantitative measurements of fluorescence quenching (of fluorescein with potassium iodide) to characterize the mixing dynamics across flow-rate ratios.

Huyke, Diego A. (ORCID:0000000283356613)↗

Low-gravity fluid physics: A program overview

An overview is presented of the microgravity fluid physics program at Lewis Research Center. One of the main reasons for conducting low gravity research in fluid physics is to study phenomena such as surface tension, interfacial contact angles, and diffusion independent of such gravitationally induced effects as buoyant convection. Fluid physics is at the heart of many space-based technologies including power systems, thermal control systems, and life support systems. Fundamental understanding of fluid physics is a key ingredient to successful space systems design. In addition to describing ground-based and space-based low-gravity facilities, selected experiments are presented which highlight Lewis work in fluid physics. These experiments can be categorized into five theme areas which summarize the work being conducted at Lewis for OSSA: (1) isothermal/iso-solutal capillary phenomena; (2) capillary phenomena with thermal/solutal gradients; (3) thermal-solutal convection; (4) first- and second-order phase transitions in a static fluid; and (5) multiphase flow.

Source record↗

The effect of original and initial saturation on residual nonwetting phase capillary trapping efficiency

Injection of supercritical carbon dioxide (CO 2 ) into geological formations is a strategy for both atmospheric greenhouse gas reduction (climate change mitigation) and enhanced oil recovery. To understand CO 2 trapping efficiency, the capillary trapping behaviors that immobilize subsurface fluids were analyzed at the pore-scale using pairs of proxy fluids representing the range of in situ nonwetting and wetting fluid properties encountered in geologic storage reservoirs. The pairs of fluids were cycled through imbibition and drainage processes using a flow cell apparatus containing a sintered glass bead column. Computed x-ray microtomography (microCT) was used to identify immobilized nonwetting fluid after imbibition and drainage events. From microCT images, the trapped residual (post-secondary imbibition) nonwetting phase was spatially correlated to both the original (post-primary imbibition) and the initial (post-primary drainage) nonwetting phase; this relationship is referred to here as the original saturation dependence (SO-dependence) and initial saturation dependence (SI-dependence), respectively. Significant trends of decreasing SO- and SI-dependence with increasing wetting and nonwetting fluid phase viscosities were observed. This finding implies that the amount of CO 2 injected and ultimately trapped is dependent on the nonwetting phase (e.g. oil or gas) already present in the formation, as well as on the manner in which supercritical CO 2 is initially injected, which are factors not considered in current trapping models. To explore the potential effect that varying viscosity and interfacial tension (IFT) might have on this process, we report on a variety of fluid pairs with different viscosities and IFT.

42 ENGINEERING↗

Description of concept and first feasibility test results of a life support subsystem of the Botany Facility based on water reclamation

The Botany Facility allows the growth of higher plants and fungi over a period of 6 months maximum. It is a payload planned for the second flight of the Eureca platform around 1990. Major tasks of the Life Support Subsystem (LSS) of the Botany Facility include the control of the pressure and composition of the atmosphere within the plant/fungi growth chambers, control of the temperature and humidity of the air and the regulation of the soil water content within specified limits. Previous studies have shown that various LSS concepts are feasible ranging from heavy, simple and cheap to light, complex and expensive solutions. A summary of those concepts is given. A new approach to accomplish control of the temperature and humidity of the air within the growth chambers based on water reclamation is discussed. This reclamation is achieved by condensation with a heat pump and capillary transport of the condensate back into the soil of the individual growth chamber. Some analytical estimates are given in order to obtain guidelines for circulation flow rates and to determine the specific power consumption.

Loeser, H. R.↗

Preliminary Feasibility Testing of the BRIC Brine Water Recovery Concept

The Brine Residual In-Containment (BRIC) concept was developed as a new technology to recover water from spacecraft wastewater brines. Such capability is considered critical to closing the water loop and achieving a sustained human presence in space. The intention of the BRIC concept is to increase the robustness and efficiency of the dewatering process by performing drying inside the container used for the final disposal of the residual brine solid. Recent efforts in the development of BRIC have focused on preliminary feasibility testing using a laboratory- assembled pre-prototype unit. Observations of the drying behavior of actual brine solutions processed under BRIC-like conditions has been of particular interest. To date, experiments conducted with three types of analogue spacecraft wastewater brines have confirmed the basic premise behind the proposed application of in-place drying for these solutions. Specifically, the dried residual mass from these solutions have tended to exhibit characteristics of adhesion and flow that are expected to continue to challenge process stream management in spacecraft brine dewatering system designs. Yet, these same characteristics may favor the development of capillary- and surface-tension-based approaches envisioned as part of an ultimate microgravity-compatible BRIC design. In addition, preliminary feasibility testing of the BRIC pre-prototype confirmed that high rates of water recovery, up to 98% of the available brine water, may be possible while still removing the majority of the brine contaminants from the influent brine stream. These and other observations from testing are reported.

Callahan, Michael R.↗

Preliminary Feasibility Testing of the BRIC Brine Water Recovery Concept

The Brine Residual In-Containment (BRIC) concept is being developed as a new technology to recover water from spacecraft wastewater brines. Such capability is considered critical to closing the water loop and achieving a sustained human presence in space. The intention of the BRIC concept is to increase the robustness and efficiency of the dewatering process by performing drying inside the container used for the final disposal of the residual brine solid. Recent efforts in the development of BRIC have focused on preliminary feasibility testing using a laboratory- assembled pre-prototype unit. Observations of the drying behavior of actual brine solutions processed under BRIC-like conditions has been of particular interest. To date, experiments conducted with three types of analogue spacecraft wastewater brines have confirmed the basic premise behind the proposed application of in-place drying. Specifically, the dried residual mass from these solutions have tended to exhibit characteristics of adhesion and flow that are expected to continue to challenge process stream management designs typically used in spacecraft systems. Yet, these same characteristics may favor the development of capillary- and surface-tension-based approaches currently envisioned as part of an ultimate microgravity-compatible BRIC design. In addition, preliminary feasibility testing of the BRIC pre-prototype confirmed that high rates of water recovery, up to 98% of the available brine water, may be possible while still removing the majority of the brine contaminants from the influent brine stream. These and other early observations from testing are reported.

Callahan, Michael R.↗

Modified Lucas-Washburn theory for fluid filling in nanotubes

Ultrafast water transport in carbon nanotubes (CNTs) has drawn a great deal of attention in a number of applications, such as water desalination, power generation, and biomolecule detection. With the recent experimental advances in water filling of isolated CNTs, the Lucas-Washburn theory for capillary rise in tubes needs to be revisited for a better understanding of the physics and dynamics of water filling in CNTs. Here, the Lucas-Washburn theory is corrected for the hydrodynamic entrance effects as well as the variation of capillary pressure and hydrodynamic properties with the radius and length of CNTs. Due to the large slippage in CNTs, inclusion of the entrance effects is important particularly for the initial stages of filling where a L ∝ t scaling, as opposed to L 2 ∝ t , is observed in our molecular dynamics (MD) simulations. The corrected Lucas-Washburn theory is shown to predict the water filling dynamics in CNTs as observed in MD simulations. With the corrected theory, we achieve a better understanding of capillary rise and water filling dynamics in CNTs.

74 ATOMIC AND MOLECULAR PHYSICS↗

Thermal management of high power space based systems

Conventional techniques of using a portion of the spacecraft skin for radiation of waste heat will be inadequate for high powered payloads (50 to 100 kWe) due to the lack of sufficient area. A Shuttle type system using a pumped single phase fluid loop could be scaled up to higher power but this type of system would require excessive pump power and weight. A pumped two-phase heat transfer loop has a much lower pumping requirement due to the higher latent heat of vaporization of the fluid in comparison to the sensible heat it can absorb through a temperature change. Concepts for an evaporator and a condenser for a pumped two-phase system are described. The condenser uses capillary grooves and a separate pumped condensate return line to achieve high heat transfer coefficients and stable operation due to the separation of the vapor and liquid flows. The cold plate evaporator uses wicks to contain the liquid and transport it to the heated surface. It can also function as a condenser for warming components. Control concepts for the cold plate are discussed. Concepts for deployment or erection of large space radiators are also considered.

Hwangbo, H.↗

Development and Testing of a Variable Conductance Thermal Acquisition, Transport, and Switching System

This paper describes the development and testing of a scalable thermal control architecture for instruments, subsystems, or systems that must operate in severe space environments with wide variations in sink temperature. The architecture is comprised by linking one or more hot-side variable conductance heat pipes (VCHPs) in series with one or more cold-side loop heat pipes (LHPs). The VCHPs provide wide area heat acquisition, limited distance thermal transport, modest against gravity pumping, concentrated LHP startup heating, and high switching ratio variable conductance operation. The LHPs provide localized heat acquisition, long distance thermal transport, significant against gravity pumping, and high switching ratio variable conductance operation. Combining two variable conductance devices in series ensures very high switching ratio isolation from severe environments like the Earth's moon, where each lunar day spans 15 Earth days (270 K sink, with a surface-shielded/space viewing radiator) and each lunar night spans 15 Earth days (80-100 K radiative sink, depending on location). The single VCHP-single LHP system described herein was developed to maintain thermal control of International Lunar Network (ILN) anchor node lander electronics, but it is also applicable to other variable heat rejection space missions in severe environments. The LHPVCHP system utilizes a stainless steel wire mesh wick ammonia VCHP, a Teflon wick propylene LHP, a pair of one-third square meter high  radiators (one capillary-pumped horizontal radiator and a second gravity-fed vertical radiator), a half-meter of transport distance, and a wick-bearing co-located flow regulator (CLFR) to allow operation with a hot (deactivated) radiator. The VCHP was designed with a small reservoir formed by extending the length of its stainless steel heat pipe tubing. The system was able to provide end-to-end switching ratios of 300-500 during thermal vacuum testing at ATK, including 3-5 W/K ON conductance and 0.01 W/K OFF conductance. The test results described herein also include an in-depth analysis of VCHP condenser performance to explain VCHP switching operation in detail. Future multi-VCHP/multi-LHP thermal management system concepts that provide scalability to higher powers/longer transport lengths are also discussed in the paper.

Bugby, D. C.↗

Hydrodynamics of bubble flow through a porous medium with applications to packed bed reactors

Gas-liquid flows through packed bed reactors (PBRs) are challenging to predict due to the tortuous flow paths that fluid interfaces must traverse. Experiments at the International Space Station showed that bubble and pulse flows are predominately observed under microgravity conditions, while the trickle and spray flows observed under terrestrial conditions are not present in microgravity. To understand the physics behind the former experiments, we simulate bubble flow through a PBR for different packing-particle-diameter-based Weber numbers and under different gravity conditions. We demonstrate different pore-scale mechanisms, such as capillary entrapment, buoyancy entrapment, and inertia-induced bubble displacement. Then, we perform a quantitative analysis by introducing new dynamic scales, dependent upon the evolving gas-liquid interfacial area, to understand the dynamic trade-offs between the inertia, capillary, and buoyancy forces on a bubble passing through a PBR. This analysis leads us to define new dimensionless Weber-like numbers that delineate bubble entrapment from bubble displacement.

Pranay P Nagrani↗

Modeling and simulation of vascular tumors embedded in evolving capillary networks

Here in this work, we present a coupled 3D–1D model of solid tumor growth within a dynamically changing vascular network to facilitate realistic simulations of angiogenesis. Additionally, the model includes erosion of the extracellular matrix, interstitial flow, and coupled flow in blood vessels and tissue. We employ continuum mixture theory with stochastic Cahn–Hilliard type phase-field models of tumor growth. The interstitial flow is governed by a mesoscale version of Darcy’s law. The flow in the blood vessels is controlled by Poiseuille flow, and Starling’s law is applied to model the mass transfer in and out of blood vessels. The evolution of the network of blood vessels is orchestrated by the concentration of the tumor angiogenesis factors (TAFs); blood vessels grow towards the increasing TAFs concentrations. This process is not deterministic, allowing random growth of blood vessels and, therefore, due to the coupling of nutrients in tissue and vessels, makes the growth of tumors stochastic. We demonstrate the performance of the model by applying it to a variety of scenarios. Numerical experiments illustrate the flexibility of the model and its ability to generate satellite tumors. Simulations of the effects of angiogenesis on tumor growth are presented as well as sample-independent features of cancer.

3D–1D coupled blood flow models↗

Combined Experimental and Modeling Study of the Interactions of Acid Gas with Common Spacecraft Surfaces for Fire Safety Applications

A fire in a spacecraft poses detrimental consequences and risks mission success in addition to crew safety. This is compounded during long-duration missions when the crew has limited options to recover from a fire. A common spacecraft fire concern is the smoldering of wire insulation, typically made from Polyvinyl chloride (PVC) or Polytetrafluoroethylene (PTFE). This creates acid gases such as Hydrogen Chloride (HCl), Hydrogen Fluoride (HF) and Hydrogen Cyanide (HCN). These poisonous gases are hazardous to the crew. They also interact with common surfaces within the spacecraft more than dominant combustion products such as CO2 and H2O. This makes them more difficult to track for potential fire detection techniques, or for postfire clean-up. It is imperative to be able to understand and predict the fate of these poisonous species in a microgravity environment in order to design a safe vehicle. HCl interacts with a number of materials inside a spacecraft. Primary among these materials is aluminum, which is abundantly used due to its strong and light weight nature. Aluminum has a natural oxide layer that protects it from corrosion but is typically treated to enhance this oxide layer. Among these treatments is a chromate conversion coating (CCC), which provides a thin enough protective oxide layer to still conduct electricity, and a traditional anodized material that has a thicker oxide layer that does not conduct electricity. Nomex is another common material found inside a spacecraft. It is a flame-resistant woven polymer that is related to nylon. This commercially available material is used for cargo storage bags and as a fire barrier. Physics-based models were developed to predict the uptake of HCl by these materials. The ultimate objective of these models is to predict the fate of HCl within the spacecraft so that sensors can be placed in meaningful locations in future missions based on the model predictions. To support these modeling efforts, experiments were performed in a cast acrylic test cell that measured the difference between the inlet and outlet concentration of HCl after inserting a sample rod of the test material. Different uptake capacities were realized for each type of sample tested. A computational fluid dynamics model (CFD) model of the reactor was then constructed that used a one-step global reaction rate with calibratable reaction (or kinetic) constants. These constants were calibrated to match the HCl uptake on the CCC aluminum samples, and the same kinetic constants were then tested for the stock and anodized aluminum samples. Model predictions matched the experimental data for the stock aluminum, and to a much lesser extent, the anodized aluminum. The model was additionally validated at different flow rates, sample surface areas, and inlet concentrations, and showed good agreement for all stock and CCC samples. The model did not accurately predict the HCl uptake in the anodized samples compared to the other two types of aluminum. Adjusting the kinetic constants and transport properties did little to improve the prediction. X-Ray Photoelectron Spectroscopy (XPS) was used to determine that the oxide layer thickness of anodized aluminum is approximately 5,000 nm, compared to 250 nm for CCC and 50 nm for stock. XPS also revealed presence of chlorine further down in the aluminum oxide layer in anodized samples than CCC and stock samples after the samples were saturated with HCl, indicating that accounting for diffusion of HCl into the oxide layer is important for accurate prediction of HCl uptake onto anodized aluminum. Consequently, a multi-scale model was developed and tested. First, a single pore inside the anodized aluminum oxide layer was modeled and is referred to as the pore-scale model. In this model, HCl diffused through the pore and reacted with the aluminum oxide pore wall to create aluminum chloride. The sample was then saturated when the mass transfer resistance through the growing aluminum chloride layer became too large for the HCl to reach the aluminum oxide wall and continue the reaction. This pore-scale model was coupled to the reactor-scale model using a concentration-dependent diffusion coefficient, resulting in much more accurate predictions (approximately half the sum square error of the aforementioned reactor-scale model that produced good agreement for stock and CCC) for a variety of operating conditions. The amount of water vapor or relative humidity (RH) in the flow during a reactor experiment was determined to influence HCl uptake. Experiments were performed to understand the interaction of gaseous HCl with aluminum surfaces in the presence of water vapor. The results show that increasing levels of RH increased the capacity of aluminum to adsorb HCl but decreased the capacity of Nomex to uptake HCl. A series of tests were performed on individual aluminum samples after they had been saturated with a fixed concentration of HCl in dry air conditions with the goal of determining how their HCl uptake capacity changes after various treatments with water relative to the original saturation tests. HCl-saturated aluminum samples subjected to a second dry air flow at the same HCl concentration as the original test had an uptake of 23.5% of the original sample with no treatment in between. Saturated aluminum samples subjected to an air flow with a RH of 90% in between tests had an uptake of 35.6% of the original. Saturated aluminum samples submerged in distilled water for 12 hours in between tests had an uptake of 82.2% of the original sample. Previously saturated aluminum tested with HCl and a 50% RH air flow resulted in similar uptake characteristics in multiple repeated tests. The experiments show the profound effect water vapor has on HCl uptake onto aluminum surfaces. In the samples subjected to water vapor or liquid water, capillary condensation and capillary diffusion alters the transport of HCl significantly. A model was proposed that developed a relationship between RH and the coefficient of HCl diffusion in aluminum chloride. This produced an “S-shaped” curve with diffusion coefficient as a function of RH, with 45% RH represented as the point where the diffusion coefficient is halfway between no water saturation and 100% water saturation in the aluminum chloride product layer. No difference in uptake characteristics for the experiment or model were realized between 50% and 62% RH. The results from the large-scale microgravity experiment, Saffire, are discussed as they pertain to the fate of HCl throughout a spacecraft. HCl was released, both as a standalone event, and in concurrence with the burning of a structured cloth. These events only produced a small response in the far field HCl sensor, while a PMMA burn that did not produce HCl had a significantly greater response. A ground-based large-scale facility was constructed to flow acid gas at the scale and configuration realized in the Saffire experiments. A CFD model of this duct was constructed to test kinetic parameters developed in this work at a larger scale and different geometric configuration and to predict the results of the large-scale facility. The models developed in this work were used to interpret the results of the microgravity tests and lead the discussion on what further experiments and models are needed in order to predict the fate of acid gas in a spacecraft environment. To summarize, the major contributions of this work are as follows: the capacity to uptake HCl, with and without the presence of water vapor, was measured for a variety of real spacecraft surfaces. Several different models (single reactor-scale, multiscale, spacecraft-scale) were developed and with the aid of modeling, the rate of uptake for those surfaces was also predicted and validated. The kinetic parameters determined from the small-scale reactor experiments and models were used to predict large-scale and microgravity tests. Conclusions from this research will be used in the design of spacecraft vehicles and large-scale microgravity fire safety experiments. The models built by this work will aid designers in sensor placement and could be used to predict acid gas transport from fires in partial gravity, as would be seen in Lunar and Martian habitats.

fire safety↗

Non-local model for surface tension in fluid-fluid simulations

We propose a non-local model for surface tension obtained in the form of an integral of a molecular-force-like function with support 3.5e added to the Navier-Stokes momentum conservation equation. We demonstrate analytically and numerically that with the non-local model interfaces with a radius of curvature larger than the support length behave macroscopically and microscopically, otherwise. For static droplets, the pressure difference Pe,in - Pe,out satisfies the Young-Laplace law for droplet radius greater than 3.5e and other- wise deviates from the Young-Laplace law. The latter indicates that the surface tension in the proposed model decreases with decreasing radius of curvature, which agrees with molecular dynamics and experimental studies of nanodroplets. Using the non-local model we perform numerical simulations of droplets under dynamic conditions, including a rising droplet, a droplet in shear flow, and two colliding droplets in shear flow, and compare results with a standard Navier-Stokes model subject to the Young-Laplace boundary condition at the fluid-fluid interface implemented via the Conservative Level Set (CLS) method. We find good agreement with existing numerical methods and analytical results for a rising macroscopic droplet and a droplet in a shear flow. For colliding droplets in shear flow, the non- local model converges (with respect to the grid size) to the correct behavior, including sliding, coalescence, and merging and breaking of two droplets depending on the capillary number. In contrast, we find that the results of the CLS model are highly grid-size dependent.

Howard, Amanda A.↗

Remobilizing the Interfaces of Thermocapillary Driven Bubbles Retarded by the Adsorption of a Surfactant Impurity on the Bubble Surface

Thermocapillary migration is a method for moving bubbles in space in the absence of buoyancy. A temperature gradient is applied to the continuous phase in which a bubble is situated, and the applied gradient impressed on the bubble surface causes one pole of the drop to be cooler than the opposite pole. As the surface tension is a decreasing function of temperature, the cooler pole pulls at the warmer pole, creating a flow which propels the bubble in the direction of the warmer fluid. A major impediment to the practical use of thermocapillarity to direct the movement of bubbles in space is the fact that surfactant impurities which are unavoidably present in the continuous phase can significantly reduce the migration velocity. A surfactant impurity adsorbed onto the bubble interface is swept to the trailing end of the bubble. When bulk concentrations are low (which is the case with an impurity), diffusion of surfactant to the front end is slow relative to convection, and surfactant collects at the back end of the bubble. Collection at the back lowers the surface tension relative to the front end setting up a reverse tension gradient. For buoyancy driven bubble motions in the absence of a thermocapillarity, the tension gradient opposes the surface flow, and reduces the surface and terminal velocities (the interface becomes more solid-like). When thermocapillary forces are present, the reverse tension gradient set up by the surfactant accumulation reduces the temperature tension gradient, and decreases to near zero the thermocapillary velocity. The objective of our research is to develop a method for enhancing the thermocapillary migration of bubbles which have been retarded by the adsorption onto the bubble surface of a surfactant impurity, Our remobilization theory proposes to use surfactant molecules which kinetically rapidly exchange between the bulk and the surface and are at high bulk concentrations. Because the remobilizing surfactant is present at much higher concentrations than the impurity, it adsorbs to the bubble much faster than the impurity when the bubble is formed, and thereby prevents the impurity from adsorbing onto the surface. In addition the rapid kinetic exchange and high bulk concentration maintain a saturated surface with a uniform surface concentrations. This prevents retarding surface tension gradients and keeps the velocity high. In our first report last year, we detailed experimental results which verified the theory of remobilization in ground based experiments in which the steady velocity of rising bubbles was measured in a continuous phase consisting of a glycerol/water mixture containing a polyethylene glycol surfactant C12E6 (CH3(CH2)11(OCH2CH2)6OH). In our report this year, we detail our efforts to describe theoretically the remobilization observed. We construct a model in which a bubble rises steadily by buoyancy in a continuous (Newtonian) viscous fluid containing surfactant with a uniform far field bulk concentration. We account for the effects of inertia as well as viscosity in the flow in the continuous phase caused by the bubble motion (order one Reynolds number), and we assume that the bubble shape remains spherical (viscous and inertial forces are smaller than capillary forces, i e. small Weber and capillary numbers). The surfactant distribution is calculated by solving the mass transfer equations including convection and diffusion in the bulk, and finite kinetic exchange the bulk and the surface. Convective effects dominate diffusive mass transfer in the bulk of the liquid (high Peclet numbers) except in a thin boundary layer near the surface. A finite volume method is used to numerically solve the hydrodynamic and mass transfer equations on a staggered grid which accounts specifically for the thin boundary layer. We present the results of the nondimensional drag as a function of the bulk concentration of surfactant for different rates of kinetic exchange, from which we develop criteria for the concentration necessary to develop a prescribed degree of remobilization. The criteria compare favorably with the experimental results.

Palaparthi, Ravi↗