Proceedings of the 4th International Conference of Fluid Flow, Heat and Mass Transfer (FFHMT'17), 2017
Numerical solution of the governing equations for mass, momentum and species can be used to predi... more Numerical solution of the governing equations for mass, momentum and species can be used to predict mass transfer in a rotating spiral device. The case of a dilute solute transferring in counter-current gas-liquid flow is considered. Computations in a twodimensional section of the flow with an existing model for interface shape are used to determine the velocity and solute species fields in each phase. The prediction is assessed along with that of an existing analytical solution for infinite channel width by comparison with some recent mass transfer coefficient data for acetone desorbing from water into air over a range of water flow rates. The computation reproduces the measured results well over the full range of the data. At higher liquid flow rates it is found that secondary motion in each phase generated by Coriolis acceleration acting on the gas phase, causes a doubling of mass transfer coefficient.
R.W. Allen, Small volume lab on a chip measurements incorporating the quartz crystal microbalance... more R.W. Allen, Small volume lab on a chip measurements incorporating the quartz crystal microbalance to measure the viscosity-density product of room temperature ionic liquids, Biomicrofluidics 4 (1) (2010) art. 014107; DOI: 10.1063/1.3353379. The following article appeared in Biomicrofluidics and may be found at
The first substantial experimental measurements of mass transfer in a rotating spiral channel are... more The first substantial experimental measurements of mass transfer in a rotating spiral channel are reported for counter-current physical desorption of a range of organic solutes from water into air. General relations in terms of bulk properties are developed that allow analysis and comparison across different solute properties, operating conditions and contacting equipment. The phase flow rate ratio and cleaned-phase throughput per passage volume emerge as parameters of principal importance, the former measuring sufficiency of solvent phase flow and the later mass transfer effectiveness and, consequently, required device size. The analytical solution for an infinitely wide channel is used to probe the finite-width experimental results and an apparently universal pattern of differences involving a peak in mass transfer coefficient emerges. As liquid flow rate decreases, the thickness of the liquid layer decreases and the mass transfer coefficient rises. But with further decrease in liquid flow rate and liquid layer thickness, an increasing fraction of the liquid flows in the corner regions under the end-wall menisci and the poor contact in these regions leads to a falling mass transfer coefficient. The peak is found to occur at a similar liquid layer thickness regardless of gas flow rate or solute equilibrium characteristics. Comparison is made with packed columns and rotating packed beds using available data in the literature. The rotating spiral performance suggests device sizes will be many times smaller than those for the two packed devices considered. Dependence of rotating spiral device volume on the square of channel size is demonstrated, showing that further reduction in device volume is possible.
This is a repository copy of CO<inf>2</inf> absorption using diethanolamine-water solutions in a ... more This is a repository copy of CO<inf>2</inf> absorption using diethanolamine-water solutions in a rotating spiral contactor.
2008 IEEE International Frequency Control Symposium, 2008
Data for the physical properties of room temperature ionic liquids (RTIL) as a function of chemic... more Data for the physical properties of room temperature ionic liquids (RTIL) as a function of chemical composition is limited, owing to the expense and difficulty of producing large volumes of pure samples for characterization. In this work we demonstrate that the viscosity-density values, obtained using impedance analysis of a quartz crystal microbalance are consistent with those obtained using a viscometer
ABSTRACT Inappropriate initial conditions discovered in a recently reported model calculation of ... more ABSTRACT Inappropriate initial conditions discovered in a recently reported model calculation of the thermal mixing layer are corrected. Good agreement with measurement is restored by a reoptimization of model coefficients.
The drive towards cleaner industrial processes has led to the development of room temperature ion... more The drive towards cleaner industrial processes has led to the development of room temperature ionic liquids (RTIL) as environmentally friendly solvents. They comprise solely of ions which are liquid at room temperature and with over one million simple RTIL alone it is important to characterize their physical properties using minimal sample volumes. Here we present a dual quartz crystal microbalance
Rotating spiral channels enable any two immiscible fluid phases to flow counter-currently in para... more Rotating spiral channels enable any two immiscible fluid phases to flow counter-currently in parallel layers allowing independent control of phase flow rates and layer thicknesses. This opens the possibility of application over the full range of fluid contacting operations, including distillation, absorption, extraction and multiphase reaction with separation. A device has been developed that enables wide-ranging experimental studies to support model refinement and design of first-generation applied devices. In this first work with the new device hydrodynamic characteristics are studied for gas-liquid systems as functions of phase flow rates, rotation rate and liquid viscosity. Measurement of the heavy phase layer thickness, using image analysis based on the Young-Laplace theory for interface shape, and measurement of volume flow rate of each phase and pressure and temperature in the spiral channel allows rigorous comparisons with an existing 'wide-channel' model relating flow rates and layer thicknesses to phase properties, geometry and rotation rate. The measured thickness of the heavy-phase layer is predicted well by the wide-channel model at high rotation and phase flow rates, where the deviation from a uniform layer thickness due to menisci at the channel end walls and interface tilt from gravity are small. At low rotation rates, where significant meniscus height and tilt develop, the layer thickness is over-predicted by the wide channel model. The sub 20 µm heavy-phase layer thicknesses measured suggest operation at optimum thickness is possible with the rotating spiral over a wide range of phase and solute systems.
... The value of f at several values of has been determined numerically using the [small-caps FLU... more ... The value of f at several values of has been determined numerically using the [small-caps FLUENT] code. ... Computed T-junction length deviations. ... Chem. 72, 3512 (2000). NA Patankar and HH Hu, Numerical simulation of electroosmotic flow, Anal. Chem. 70, 1870 (1998). ...
The performance of a folding flow micromixer in the Stokes flow regime is investigated computatio... more The performance of a folding flow micromixer in the Stokes flow regime is investigated computationally and experimentally. Consistency with a previously derived general scaling relation is demonstrated and the geometric parameters in the scaling relation are determined for this mixer. Measured data from a second similar mixer are correctly predicted using the scaling relation, thus showing that the approach allows quantitative prediction of mixing. This paper focuses on the errors associated with such predictions. Basic errors, expressed as variations in the standard deviation of the concentration profile, were estimated to be-10% for the computation and-30% for the experiment at the highest values of Péclet number considered. It is shown that this experimental error was mostly due to depth averaging of the spectroscopic technique used for concentration measurement at the high Péclet numbers. However, extra uncertainty is associated with chip fabrication tolerances and this was investigated further. Measurements at the outlet of nine different mixer chips of notionally identical design revealed variations in mixing of ±26%. This variation was attributed to misalignment of the glass layers determining the geometry of the mixer in the chip. Thus, the combination of measurement error and misalignment means predictions of the concentration standard deviation for the mixer may get non-uniformity wrong by up to 50%. Ensuring a required uniformity, however, simply requires adding a few further elements to the mixer to allow for this uncertainty. Application of the scaling relation to mixer design is highlighted by a discussion of the options available for improving the performance of the experimental mixer.
A new microfluidic-based approach to measuring liquid thermal conductivity is developed to addres... more A new microfluidic-based approach to measuring liquid thermal conductivity is developed to address the requirement in many practical applications for measurements using small (microlitre) sample size and integration into a compact device. The approach also gives the possibility of highthroughput testing. A resistance heater and temperature sensor are incorporated into a glass microfluidic chip to allow transmission and detection of a planar thermal wave crossing a thin layer of the sample. The device is designed so that heat transfer is locally one-dimensional during a short initial time period. This allows the detected temperature transient to be separated into two distinct components: a short-time, purely one-dimensional part from which sample thermal conductivity can be determined and a remaining long-time part containing the effects of three-dimensionality and of the finite size of surrounding thermal reservoirs. Identification of the one-dimensional component yields a steady temperature difference from which sample thermal conductivity can be determined. Calibration is required to give correct representation of changing heater resistance, system layer thicknesses and solid material thermal conductivities with temperature. In this preliminary study, methanol/water mixtures are measured at atmospheric pressure over the temperature range 30 to 50 ºC. The results show that the device has produced a measurement accuracy of within 2.5% over the range of thermal conductivity and temperature of the tests. A relation between measurement uncertainty and the geometric and thermal properties of the system is derived and this is used to identify ways that error could be further reduced.
Two-dimensional, two-component micron resolution particle image velocimetry (micro-PIV) allows me... more Two-dimensional, two-component micron resolution particle image velocimetry (micro-PIV) allows measurement of the in-plane velocity components across a single plane within a micro-scale device. The technique has become well established over recent years for the study of micro-scale flows. Stereoscopic micro-PIV uses two cameras and a stereomicroscope to capture all three components of the velocity field. Recently, preliminary results have been
Recently, a number of techniques have been presented for the determination of the third ''outof-p... more Recently, a number of techniques have been presented for the determination of the third ''outof-plane'' velocity component in micro particle image velocimetry (micro-PIV) data. In particular, the conventional macroscopic stereo-PIV technique has been converted to the micro scale by the use of stereomicroscopy. In this work a different technique is investigated, which uses conventional, two-component micro-PIV to generate velocity data on a number of planes. The in-plane velocity gradients are then calculated, which can be used in the continuity equation to produce the out-of-plane velocity gradients. These, together with the no-penetration boundary condition, can then be used to calculate the out-of-plane velocities. An algorithm is presented that is capable of handling up to one invalid vector per column of data by using a combination of first order and second order projections of the velocity. The advantage of the continuity based technique is that it uses the existing twocomponent micro-PIV technology, which at present is in a more advanced stage of development then stereomicroscopy based micro-PIV. The technique is investigated using a flow similar to one used previously to assess stereoscopic micro-PIV (Meas Sci Technol 17:2175-2185, 2006). This allows a comparison of the performance of the two techniques. The results show that the continuity based data agrees well with an independent computational fluid dynamics solution and has a smaller experimental uncertainty than the stereoscopic technique at a better spatial resolution. There are, however, potential limitations to the continuity based technique. These include the two-dimensionality of the data, which is limited to the planes on which the original images were taken, and the dependence of the technique on the data close to surfaces, where the experimental errors are often greatest. Stereoscopic micro-PIV does not have these limitations so, whilst at present it appears that continuity based techniques may be more accurate, there is sufficient potential for stereoscopic techniques to justify their further development.
The separation of one component from a multicomponent fluid solution is commonly achieved by brin... more The separation of one component from a multicomponent fluid solution is commonly achieved by bringing the solution into contact with a second immiscible phase, as in liquid-liquid or gas-liquid contactors. Counter-current flow of the phases allows high purity separations and existing approaches typically force one of the phases to disperse into the other, producing the close contact necessary for the solute species to be distributed by diffusion throughout the volume of each phase. This phase mixing leaves the contacting strongly dependent on fluid and interface mechanical properties. Thus an approach that suits one phase and solute system will not necessarily suit others. In addition, it is then necessary to separate the dispersed phase which can be a major drawback of the operation sometimes posing substantial difficulties in easily emulsified liquid-liquid systems or in easily foamed gas-liquid systems. A new approach, which has recently been demonstrated experimentally for microchannels, uses a rotating spiral channel to allow controlled contacting giving a very high ratio of interfacial surface area to fluid volume but avoids phase mixing. Its application to larger channels, up to millimetres in size, is considered here. The two phases are forced to flow side by side in parallel layers along the narrow spiral channel. Selection of spiral parameters, rotation rate and pressure gradient along the channel controls the flow rate ratio of the phases and the relative thickness of the phase layers. This allows adjustment to reach the optimum mass transfer (limited strongly neither by one phase nor the other) and adaptation to phase and solute systems having widely differing fluid viscosities, densities, solute diffusivities and interface equilibria. With appropriate control over these parameters, a single device is, in principle, capable of application to a wide range of separation requirements. This rotating spiral contacting is, however, a new technology and remains to be investigated and tested in detail. The present work develops a model yielding both quantitative prediction of flow and mass transfer in the contacting channel and a framework for determining suitable designs, operating conditions and mass transfer performance for liquid-liquid and gas-liquid operations.
ABSTRACT A number of different approaches to mixing liquids in microscale systems can be found in... more ABSTRACT A number of different approaches to mixing liquids in microscale systems can be found in the literature. In the case of miscible liquids it is desirable to produce mixtures with residual non-uniformity in composition that is below some specified level. Yet very little quantitative information is available concerning the conditions required to produce a given level of mixture uniformity. A theoretical approach to this problem is described. Computational fluid dynamics and simple scaling are used to develop a quantitative understanding of the alternating flow method of mixing using pressure driven flow. In this approach, external flow control is used to produce alternating injection into a single microchannel of two or more solutions to be mixed. The resulting streamwise slugs of solution then mix by the stretching of the slugs into thin striations resulting from shear strain. The most challenging condition for mixing is where the Reynolds number is approaching zero and inertia effects are negligible, a common situation in microchannel flows, particularly where relatively high-viscosity liquids, for example ionic liquids, are involved. The scaling theory demonstrates that an initial time period of rapid mixing of fluid outside the core of the flow, scaling as Pe-2/3, is followed by a far slower process of mixing in the core region, scaling as Pe-1/2. An approximate correlation for the deviation from the perfectly mixed state as a function of time is found. This correlation applies over the range of Peclet number, slug length and solution mixture ratio that are of interest. The mixture uniformity produced is shown to be limited by the initial uniformity of each solution over the channel section resulting from the injection process.
Micromixers have been considered in numerous recent studies with the aim of mixing different liqu... more Micromixers have been considered in numerous recent studies with the aim of mixing different liquid streams for the common circumstance of non-inertial flow, i.e., in the Stokes flow regime. Under such conditions, the diffusion of momentum is dominant but the diffusion of species remains weak because the Schmidt number of liquids is large. Most mixers that have potential for application in the Stokes regime make use of a folding flow pattern that approximates the baker's transformation. In the work presented here, the general scaling of mixers of this type is developed from the exact equation for species transport and computations are made for a specimen mixer geometry to test the effectiveness of the resulting scaling. The scaling relation developed is found to give an excellent representation of the actual mixing characteristics of the specimen mixer over the entire range of Péclet number of practical interest. Finite volume computations are employed to solve the governing equations up to around Pe = 10 3. At higher Péclet numbers, where finite volume numerical solution becomes inaccurate with affordable mesh sizes, the species equation is solved using a Monte Carlo method instead. Finally, the scaling relation is used to develop the design relations needed to determine the number of mixing elements, the pressure drop incurred and the Péclet number of operation to achieve a given mixture uniformity within a specified mixing time.
Proceedings of the 4th International Conference of Fluid Flow, Heat and Mass Transfer (FFHMT'17), 2017
Numerical solution of the governing equations for mass, momentum and species can be used to predi... more Numerical solution of the governing equations for mass, momentum and species can be used to predict mass transfer in a rotating spiral device. The case of a dilute solute transferring in counter-current gas-liquid flow is considered. Computations in a twodimensional section of the flow with an existing model for interface shape are used to determine the velocity and solute species fields in each phase. The prediction is assessed along with that of an existing analytical solution for infinite channel width by comparison with some recent mass transfer coefficient data for acetone desorbing from water into air over a range of water flow rates. The computation reproduces the measured results well over the full range of the data. At higher liquid flow rates it is found that secondary motion in each phase generated by Coriolis acceleration acting on the gas phase, causes a doubling of mass transfer coefficient.
R.W. Allen, Small volume lab on a chip measurements incorporating the quartz crystal microbalance... more R.W. Allen, Small volume lab on a chip measurements incorporating the quartz crystal microbalance to measure the viscosity-density product of room temperature ionic liquids, Biomicrofluidics 4 (1) (2010) art. 014107; DOI: 10.1063/1.3353379. The following article appeared in Biomicrofluidics and may be found at
The first substantial experimental measurements of mass transfer in a rotating spiral channel are... more The first substantial experimental measurements of mass transfer in a rotating spiral channel are reported for counter-current physical desorption of a range of organic solutes from water into air. General relations in terms of bulk properties are developed that allow analysis and comparison across different solute properties, operating conditions and contacting equipment. The phase flow rate ratio and cleaned-phase throughput per passage volume emerge as parameters of principal importance, the former measuring sufficiency of solvent phase flow and the later mass transfer effectiveness and, consequently, required device size. The analytical solution for an infinitely wide channel is used to probe the finite-width experimental results and an apparently universal pattern of differences involving a peak in mass transfer coefficient emerges. As liquid flow rate decreases, the thickness of the liquid layer decreases and the mass transfer coefficient rises. But with further decrease in liquid flow rate and liquid layer thickness, an increasing fraction of the liquid flows in the corner regions under the end-wall menisci and the poor contact in these regions leads to a falling mass transfer coefficient. The peak is found to occur at a similar liquid layer thickness regardless of gas flow rate or solute equilibrium characteristics. Comparison is made with packed columns and rotating packed beds using available data in the literature. The rotating spiral performance suggests device sizes will be many times smaller than those for the two packed devices considered. Dependence of rotating spiral device volume on the square of channel size is demonstrated, showing that further reduction in device volume is possible.
This is a repository copy of CO<inf>2</inf> absorption using diethanolamine-water solutions in a ... more This is a repository copy of CO<inf>2</inf> absorption using diethanolamine-water solutions in a rotating spiral contactor.
2008 IEEE International Frequency Control Symposium, 2008
Data for the physical properties of room temperature ionic liquids (RTIL) as a function of chemic... more Data for the physical properties of room temperature ionic liquids (RTIL) as a function of chemical composition is limited, owing to the expense and difficulty of producing large volumes of pure samples for characterization. In this work we demonstrate that the viscosity-density values, obtained using impedance analysis of a quartz crystal microbalance are consistent with those obtained using a viscometer
ABSTRACT Inappropriate initial conditions discovered in a recently reported model calculation of ... more ABSTRACT Inappropriate initial conditions discovered in a recently reported model calculation of the thermal mixing layer are corrected. Good agreement with measurement is restored by a reoptimization of model coefficients.
The drive towards cleaner industrial processes has led to the development of room temperature ion... more The drive towards cleaner industrial processes has led to the development of room temperature ionic liquids (RTIL) as environmentally friendly solvents. They comprise solely of ions which are liquid at room temperature and with over one million simple RTIL alone it is important to characterize their physical properties using minimal sample volumes. Here we present a dual quartz crystal microbalance
Rotating spiral channels enable any two immiscible fluid phases to flow counter-currently in para... more Rotating spiral channels enable any two immiscible fluid phases to flow counter-currently in parallel layers allowing independent control of phase flow rates and layer thicknesses. This opens the possibility of application over the full range of fluid contacting operations, including distillation, absorption, extraction and multiphase reaction with separation. A device has been developed that enables wide-ranging experimental studies to support model refinement and design of first-generation applied devices. In this first work with the new device hydrodynamic characteristics are studied for gas-liquid systems as functions of phase flow rates, rotation rate and liquid viscosity. Measurement of the heavy phase layer thickness, using image analysis based on the Young-Laplace theory for interface shape, and measurement of volume flow rate of each phase and pressure and temperature in the spiral channel allows rigorous comparisons with an existing 'wide-channel' model relating flow rates and layer thicknesses to phase properties, geometry and rotation rate. The measured thickness of the heavy-phase layer is predicted well by the wide-channel model at high rotation and phase flow rates, where the deviation from a uniform layer thickness due to menisci at the channel end walls and interface tilt from gravity are small. At low rotation rates, where significant meniscus height and tilt develop, the layer thickness is over-predicted by the wide channel model. The sub 20 µm heavy-phase layer thicknesses measured suggest operation at optimum thickness is possible with the rotating spiral over a wide range of phase and solute systems.
... The value of f at several values of has been determined numerically using the [small-caps FLU... more ... The value of f at several values of has been determined numerically using the [small-caps FLUENT] code. ... Computed T-junction length deviations. ... Chem. 72, 3512 (2000). NA Patankar and HH Hu, Numerical simulation of electroosmotic flow, Anal. Chem. 70, 1870 (1998). ...
The performance of a folding flow micromixer in the Stokes flow regime is investigated computatio... more The performance of a folding flow micromixer in the Stokes flow regime is investigated computationally and experimentally. Consistency with a previously derived general scaling relation is demonstrated and the geometric parameters in the scaling relation are determined for this mixer. Measured data from a second similar mixer are correctly predicted using the scaling relation, thus showing that the approach allows quantitative prediction of mixing. This paper focuses on the errors associated with such predictions. Basic errors, expressed as variations in the standard deviation of the concentration profile, were estimated to be-10% for the computation and-30% for the experiment at the highest values of Péclet number considered. It is shown that this experimental error was mostly due to depth averaging of the spectroscopic technique used for concentration measurement at the high Péclet numbers. However, extra uncertainty is associated with chip fabrication tolerances and this was investigated further. Measurements at the outlet of nine different mixer chips of notionally identical design revealed variations in mixing of ±26%. This variation was attributed to misalignment of the glass layers determining the geometry of the mixer in the chip. Thus, the combination of measurement error and misalignment means predictions of the concentration standard deviation for the mixer may get non-uniformity wrong by up to 50%. Ensuring a required uniformity, however, simply requires adding a few further elements to the mixer to allow for this uncertainty. Application of the scaling relation to mixer design is highlighted by a discussion of the options available for improving the performance of the experimental mixer.
A new microfluidic-based approach to measuring liquid thermal conductivity is developed to addres... more A new microfluidic-based approach to measuring liquid thermal conductivity is developed to address the requirement in many practical applications for measurements using small (microlitre) sample size and integration into a compact device. The approach also gives the possibility of highthroughput testing. A resistance heater and temperature sensor are incorporated into a glass microfluidic chip to allow transmission and detection of a planar thermal wave crossing a thin layer of the sample. The device is designed so that heat transfer is locally one-dimensional during a short initial time period. This allows the detected temperature transient to be separated into two distinct components: a short-time, purely one-dimensional part from which sample thermal conductivity can be determined and a remaining long-time part containing the effects of three-dimensionality and of the finite size of surrounding thermal reservoirs. Identification of the one-dimensional component yields a steady temperature difference from which sample thermal conductivity can be determined. Calibration is required to give correct representation of changing heater resistance, system layer thicknesses and solid material thermal conductivities with temperature. In this preliminary study, methanol/water mixtures are measured at atmospheric pressure over the temperature range 30 to 50 ºC. The results show that the device has produced a measurement accuracy of within 2.5% over the range of thermal conductivity and temperature of the tests. A relation between measurement uncertainty and the geometric and thermal properties of the system is derived and this is used to identify ways that error could be further reduced.
Two-dimensional, two-component micron resolution particle image velocimetry (micro-PIV) allows me... more Two-dimensional, two-component micron resolution particle image velocimetry (micro-PIV) allows measurement of the in-plane velocity components across a single plane within a micro-scale device. The technique has become well established over recent years for the study of micro-scale flows. Stereoscopic micro-PIV uses two cameras and a stereomicroscope to capture all three components of the velocity field. Recently, preliminary results have been
Recently, a number of techniques have been presented for the determination of the third ''outof-p... more Recently, a number of techniques have been presented for the determination of the third ''outof-plane'' velocity component in micro particle image velocimetry (micro-PIV) data. In particular, the conventional macroscopic stereo-PIV technique has been converted to the micro scale by the use of stereomicroscopy. In this work a different technique is investigated, which uses conventional, two-component micro-PIV to generate velocity data on a number of planes. The in-plane velocity gradients are then calculated, which can be used in the continuity equation to produce the out-of-plane velocity gradients. These, together with the no-penetration boundary condition, can then be used to calculate the out-of-plane velocities. An algorithm is presented that is capable of handling up to one invalid vector per column of data by using a combination of first order and second order projections of the velocity. The advantage of the continuity based technique is that it uses the existing twocomponent micro-PIV technology, which at present is in a more advanced stage of development then stereomicroscopy based micro-PIV. The technique is investigated using a flow similar to one used previously to assess stereoscopic micro-PIV (Meas Sci Technol 17:2175-2185, 2006). This allows a comparison of the performance of the two techniques. The results show that the continuity based data agrees well with an independent computational fluid dynamics solution and has a smaller experimental uncertainty than the stereoscopic technique at a better spatial resolution. There are, however, potential limitations to the continuity based technique. These include the two-dimensionality of the data, which is limited to the planes on which the original images were taken, and the dependence of the technique on the data close to surfaces, where the experimental errors are often greatest. Stereoscopic micro-PIV does not have these limitations so, whilst at present it appears that continuity based techniques may be more accurate, there is sufficient potential for stereoscopic techniques to justify their further development.
The separation of one component from a multicomponent fluid solution is commonly achieved by brin... more The separation of one component from a multicomponent fluid solution is commonly achieved by bringing the solution into contact with a second immiscible phase, as in liquid-liquid or gas-liquid contactors. Counter-current flow of the phases allows high purity separations and existing approaches typically force one of the phases to disperse into the other, producing the close contact necessary for the solute species to be distributed by diffusion throughout the volume of each phase. This phase mixing leaves the contacting strongly dependent on fluid and interface mechanical properties. Thus an approach that suits one phase and solute system will not necessarily suit others. In addition, it is then necessary to separate the dispersed phase which can be a major drawback of the operation sometimes posing substantial difficulties in easily emulsified liquid-liquid systems or in easily foamed gas-liquid systems. A new approach, which has recently been demonstrated experimentally for microchannels, uses a rotating spiral channel to allow controlled contacting giving a very high ratio of interfacial surface area to fluid volume but avoids phase mixing. Its application to larger channels, up to millimetres in size, is considered here. The two phases are forced to flow side by side in parallel layers along the narrow spiral channel. Selection of spiral parameters, rotation rate and pressure gradient along the channel controls the flow rate ratio of the phases and the relative thickness of the phase layers. This allows adjustment to reach the optimum mass transfer (limited strongly neither by one phase nor the other) and adaptation to phase and solute systems having widely differing fluid viscosities, densities, solute diffusivities and interface equilibria. With appropriate control over these parameters, a single device is, in principle, capable of application to a wide range of separation requirements. This rotating spiral contacting is, however, a new technology and remains to be investigated and tested in detail. The present work develops a model yielding both quantitative prediction of flow and mass transfer in the contacting channel and a framework for determining suitable designs, operating conditions and mass transfer performance for liquid-liquid and gas-liquid operations.
ABSTRACT A number of different approaches to mixing liquids in microscale systems can be found in... more ABSTRACT A number of different approaches to mixing liquids in microscale systems can be found in the literature. In the case of miscible liquids it is desirable to produce mixtures with residual non-uniformity in composition that is below some specified level. Yet very little quantitative information is available concerning the conditions required to produce a given level of mixture uniformity. A theoretical approach to this problem is described. Computational fluid dynamics and simple scaling are used to develop a quantitative understanding of the alternating flow method of mixing using pressure driven flow. In this approach, external flow control is used to produce alternating injection into a single microchannel of two or more solutions to be mixed. The resulting streamwise slugs of solution then mix by the stretching of the slugs into thin striations resulting from shear strain. The most challenging condition for mixing is where the Reynolds number is approaching zero and inertia effects are negligible, a common situation in microchannel flows, particularly where relatively high-viscosity liquids, for example ionic liquids, are involved. The scaling theory demonstrates that an initial time period of rapid mixing of fluid outside the core of the flow, scaling as Pe-2/3, is followed by a far slower process of mixing in the core region, scaling as Pe-1/2. An approximate correlation for the deviation from the perfectly mixed state as a function of time is found. This correlation applies over the range of Peclet number, slug length and solution mixture ratio that are of interest. The mixture uniformity produced is shown to be limited by the initial uniformity of each solution over the channel section resulting from the injection process.
Micromixers have been considered in numerous recent studies with the aim of mixing different liqu... more Micromixers have been considered in numerous recent studies with the aim of mixing different liquid streams for the common circumstance of non-inertial flow, i.e., in the Stokes flow regime. Under such conditions, the diffusion of momentum is dominant but the diffusion of species remains weak because the Schmidt number of liquids is large. Most mixers that have potential for application in the Stokes regime make use of a folding flow pattern that approximates the baker's transformation. In the work presented here, the general scaling of mixers of this type is developed from the exact equation for species transport and computations are made for a specimen mixer geometry to test the effectiveness of the resulting scaling. The scaling relation developed is found to give an excellent representation of the actual mixing characteristics of the specimen mixer over the entire range of Péclet number of practical interest. Finite volume computations are employed to solve the governing equations up to around Pe = 10 3. At higher Péclet numbers, where finite volume numerical solution becomes inaccurate with affordable mesh sizes, the species equation is solved using a Monte Carlo method instead. Finally, the scaling relation is used to develop the design relations needed to determine the number of mixing elements, the pressure drop incurred and the Péclet number of operation to achieve a given mixture uniformity within a specified mixing time.
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Papers by J.m Macinnes