We present an experimental investigation of the dynamics and flow coupling of convective turbulen... more We present an experimental investigation of the dynamics and flow coupling of convective turbulent flows in a cylindrical Rayleigh-Bénard convection (RBC) cell with two immiscible fluids, water and Fluorinert FC-77 electronic liquid (FC77). With the lighter water above FC77, the latter is under the condition of constant heat flux at its top and bottom boundaries. It is found that one large-scale circulation (LSC) roll exists in each of the fluid layers, and that their circulation planes have two preferred azimuthal orientations separated by ∼π. A surprising finding of the study is that cessations/reversals of the LSC in FC77 of the two-layer system occur much more frequently than they do in single-layer turbulent RBC, and that a cessation is most likely to result in a flow reversal of the LSC, which is in sharp contrast with the uniform distribution of the orientational angular change of the LSC before and after cessations in single-layer turbulent RBC. This implies that the dynamics governing cessations and reversals in the two systems are very different. Two coupling modes, thermal coupling (the flow directions of the two LSCs are opposite to each other at the fluid-fluid interface) and viscous coupling (the flow directions of the two LSCs are the same at the fluid-fluid interface), are identified, with the former as the predominant mode. That most cessations (in the FC77 layer) end up as reversals can be understood as a symmetry breaking imposed by the orientation of the LSC in the water layer, which remains unchanged most of the time. Furthermore, the frequently occurring cessations and reversals are caused by the system switching between its two metastable states, i.e. thermal and viscous coupling modes. It is also observed that the strength of the LSC in water becomes weaker when the LSC in FC77 rotates faster azimuthally and that the flow strength in FC77 becomes stronger when the LSC in water rotates faster azimuthally, i.e. the influence of the LSC in one fluid layer on the other is not symmetric.
Temperature Oscillations and Flow Dynamics in Turbulent Thermal Convection
ABSTRACT We report an experimental study of three-dimensional structure of the low-frequency temp... more ABSTRACT We report an experimental study of three-dimensional structure of the low-frequency temperature oscillations in a cylindrical Rayleigh-Bénard (RB) convection cell of aspect ratio one. It is found that the hot and cold thermal plumes are not emitted periodically nor alternatively, but continuously and randomly, from the top and bottom plates. We further found that the oscillation of the temperature field does not originate from boundary layers, but rather is a result of the horizontal motion of the hot ascending and cold descending fluids being modulated by the twisting oscillation near the top and bottom plates and the off-center oscillation in the bulk flow field. Evidence will also be presented to show that the off-center oscillation in the bulk flow field is a manifestation of the twisting motion of fluid near the top and bottom plates. In collaboration with Heng-Dong Xi, Quan Zhou, and Sheng-Qi Zhou, The Chinese University of Hong Kong.
We report an experimental study of confinement effects in quasi-2-D turbulent Rayleigh–Bénard con... more We report an experimental study of confinement effects in quasi-2-D turbulent Rayleigh–Bénard convection. The experiments were conducted in five rectangular cells with their height H and length L being the same and fixed, while the width W was different for each cell to produce lateral aspect ratios (Γ = W/H) of 0.6, 0.3, 0.2, 0.15 and 0.1. Direct flow field measurements reveal that the large-scale flow slows down as Γ decreases and there are more plumes travelling through the bulk region. Moreover, the reversal frequency of the large-scale flow is found to increase drastically in smaller Γ cells, by more than 1000-fold for the highest value of Rayleigh number reached in the experiment. The reversal frequency can be well described by a stochastic model developed by Ni et al. (J. Fluid Mech., vol. 778, 2015, R5) and the probability density functions (PDF) of the time interval between successive reversals are found to follow Poisson statistics as in the 3-D system. It is further observed that the bulk temperature fluctuation increases significantly and its PDF changes from exponential to Gaussian as Γ decreases. The influences of geometric confinement on the global heat transport are also investigated. The measured Nu–Ra relationship suggests that, as the lateral aspect ratio decreases, the relative weight of the boundary layer contribution in the global heat transport increases compared to that from the bulk. These results demonstrate that in the quasi-2-D geometry, geometric confinement has strong effects on both the global and local properties in turbulent convective flows, which are very different from the previous findings in 3-D and true 2-D systems.
Measurements of the capillary length in phase-separated solutions of polymethylmethacrylate in 3-... more Measurements of the capillary length in phase-separated solutions of polymethylmethacrylate in 3-octanone (PMMA/3-0CT) for each of five different molecular weights of PMMA, and in phase-separated solutions of polystyrene in methylcyclohexane (PS/MCH) for a single molecular weight of polymer, are reported. Measurements on PMMA/3-0CT were by the sessile-drop method; those on PS/MCH were by both the sessile-drop and capillary-rise methods. Interfacial tensions are estimated from estimated density differences and the measured capillary lengths. A theoretically predicted scaling law for the dependence of capillary length on polymer molecular weight and temperature is tested and at least semiquantitatively verified. As by-products of the sample preparation, the molecular-weight dependences of the critical composition and critical solution temperature of PMMA/3-OCT were also determined. The volume fraction of polymer at the critical point, ¢'" is found to be proportional to the-0.37 ±0.01 power of the molecular weight, in agreement with values of this exponent found by others for polystyrene solutions.
Measurements of the coexistence curves for phase-separated polymer solutions of polymethylmethacr... more Measurements of the coexistence curves for phase-separated polymer solutions of polymethylmethacrylate in 3-octanone PMMA/3-OCT for six different molecular weights of PMMA have been carried out. We have tested the scaling behavior of the order parameter the difference between polymer volume fractions in the two coexisting phases for its dependence on the degree of polymerization N of the polymer chains and the reduced temperature (T c T)/T c. The experiments reveal that, in the asymptotic regime, the measured order parameter has power-law dependence on both N and , i.e., 3.8N 0.21 0.34. Furthermore, when the symmerization procedure of Sanchez J. Appl. Phys. 58, 2871 1985 is used to analyze the data, it suggests that N 0.46 may be used as a scaling variable for phase separated polymer solutions.
Direct measurements of the velocity boundary layer in turbulent convection have been carried out ... more Direct measurements of the velocity boundary layer in turbulent convection have been carried out using a novel light scattering technique. The experiment reveals that the velocity profile y h ͑z͒ as a function of the distance z from the lower surface of a convection cell has an invariant form y h ͑z͒ y m f͑z͞d y ͒ over varying Rayleigh numbers (Ra). It is found that the scaling velocity y m , the viscous boundary layer thickness d y , and the shear rate g all obey power laws of Ra, i.e., y m ϳ Ra 0.5 , d y ϳ Ra 20.16 , and g ϳ Ra 0.66 . [S0031-9007(96)00765-X]
VISCOUS BOUNDARY LAYER MEASUREMENTS IN RAYLEIGH-BENARD CONVECTION (Session II: Chaos, The 1st Tohwa University International Meeting on Statistical Physics Theories, Experiments and Computer Simulations)
A light scattering experiment of turbulent convection in water is carried out in a convection cel... more A light scattering experiment of turbulent convection in water is carried out in a convection cell with rough upper and lower surfaces. The vertical heat flux is found to be increased by ϳ20% when the Rayleigh number becomes larger than a transition value. The experiment reveals that the main effect of the surface roughness is to increase the emission of large thermal plumes, which travel vertically through the central region. These extra thermal plumes enhance the heat transport, and they are also responsible for the anisotropic behavior of velocity fluctuations at the cell center.
An incoherent dynamic light-scattering technique is developed to measure the local velocity and i... more An incoherent dynamic light-scattering technique is developed to measure the local velocity and its statistics. By employing two parallel laser beams of different colors, the technique measures the cross-correlation function of the scattered intensities from two separate illuminating volumes. Because there is no phase coherence between the two laser beams, the measured cross-correlation function is sensitive only to the intensity fluctuations caused by a seed particle that crosses the two beams in succession. The flow velocity is obtained from the measured particle transit time. We frame the scattering theory so as to account for the two-beam scattering geometry. Our experiment verifies the calculation and demonstrates applications of the technique. The method has the unique feature of being able to measure simultaneously the local velocity in two opposite directions perpendicular to the incident laser beams. Its advantages are high spatial resolution and accuracy, fast temporal response, and ease of use. The technique is useful in studies of turbulent flows, sedimentation of heavy particles, and flow phenomena in complex fluids.
Dual-beam intensity cross-correlation spectroscopy is used to measure the viscous boundary layer ... more Dual-beam intensity cross-correlation spectroscopy is used to measure the viscous boundary layer over a rough conducting surface in turbulent convection in water. It is found that the velocity boundary layer near the rough surface can be characterized by three quantities: the maximum velocity v m , the shear rate γ v and the total boundary layer thickness d + δ v ; all of them obey power laws of Rayleigh number Ra. The maximum velocity v m is located outside the rough surface and its numerical value remains the same as that in the smooth cell. The Ra-dependence of d + δ v is found to be the same as that in the smooth cell, but the power-law amplitude is increased by a factor close to 2. Because of the formation of small eddies inside the roughening grooves, the measured γ v is reduced considerably in the groove region. It is also found that the Nusselt number Nu ∼ Ra 0.35 , which is larger in both magnitude and scaling exponent as compared to the smooth case.
A new light scattering method is developed to measure scattering amplitude fluctuations resulting... more A new light scattering method is developed to measure scattering amplitude fluctuations resulting from either internal motions of flexible macromolecules or rotations of rigid particles. With a single-beam two-color cross-correlation scheme, the technique becomes insensitive to rapid phase fluctuations of the scattered light produced by translational motions of the scattering particles. We frame the scattering theory so as to encompass rotations and number fluctuations of small particles in a steady laminar flow. Experiment verifies the theory and demonstrates its applications. The technique can be used to measure the magnitudes of the local velocity and the flow vorticity. It can also be used to measure internal motions and shape fluctuations of flexible macromolecules. The advantages of the technique are its high spatial resolution, fast temporal response, and ease of use. 9256
We have measured the turbidity for a series of solutions of polymethylmethacrylate in 3-octanone ... more We have measured the turbidity for a series of solutions of polymethylmethacrylate in 3-octanone ͑PMMA/3-OCT͒ with various polymer molecular weights. The obtained correlation length ͑͒ and the osmotic compressibility ͑͒ show power law dependence on both the reduced temperature ⑀ ϭ(TϪT c )/T c and the degree of polymerization N of the polymer chains, i.e., ϳN 0.15 ⑀ Ϫ0.63 and ϳN Ϫ0.06 ⑀ Ϫ1.23 , with the associated scaling exponents in good agreement with theoretical predictions. When the results of the present experiment are combined with those from an earlier coexistence curve measurement ͓K.-Q. Xia, X.-Q. An, and W.-G. Shen, J. Chem. Phys. 105, 6018 ͑1996͔͒, it is found that the concept of two-scale-factor universality applies to systems consist of the same polymer/solvent pair but with different molecular weights.
Measurements of the coexistence curves for phase-separated polymer solutions of polymethylmethacr... more Measurements of the coexistence curves for phase-separated polymer solutions of polymethylmethacrylate in 3-octanone ͑PMMA/3-OCT͒ for six different molecular weights of PMMA have been carried out. We have tested the scaling behavior of the order parameter ⌬ ͑the difference between polymer volume fractions in the two coexisting phases͒ for its dependence on the degree of polymerization N of the polymer chains and the reduced temperature ⑀ϭ(T c ϪT)/T c . The experiments reveal that, in the asymptotic regime, the measured order parameter has power-law dependence on both N and ⑀, i.e., ⌬ϭ3.8N Ϫ0.21 ⑀ 0.34 . Furthermore, when the symmerization procedure of Sanchez ͓J. Appl. Phys. 58, 2871 ͑1985͔͒ is used to analyze the data, it suggests that ⑀N 0.46 may be used as a scaling variable for phase separated polymer solutions.
We present an experimental investigation of the dynamics and flow coupling of convective turbulen... more We present an experimental investigation of the dynamics and flow coupling of convective turbulent flows in a cylindrical Rayleigh-Bénard convection (RBC) cell with two immiscible fluids, water and Fluorinert FC-77 electronic liquid (FC77). With the lighter water above FC77, the latter is under the condition of constant heat flux at its top and bottom boundaries. It is found that one large-scale circulation (LSC) roll exists in each of the fluid layers, and that their circulation planes have two preferred azimuthal orientations separated by ∼π. A surprising finding of the study is that cessations/reversals of the LSC in FC77 of the two-layer system occur much more frequently than they do in single-layer turbulent RBC, and that a cessation is most likely to result in a flow reversal of the LSC, which is in sharp contrast with the uniform distribution of the orientational angular change of the LSC before and after cessations in single-layer turbulent RBC. This implies that the dynamics governing cessations and reversals in the two systems are very different. Two coupling modes, thermal coupling (the flow directions of the two LSCs are opposite to each other at the fluid-fluid interface) and viscous coupling (the flow directions of the two LSCs are the same at the fluid-fluid interface), are identified, with the former as the predominant mode. That most cessations (in the FC77 layer) end up as reversals can be understood as a symmetry breaking imposed by the orientation of the LSC in the water layer, which remains unchanged most of the time. Furthermore, the frequently occurring cessations and reversals are caused by the system switching between its two metastable states, i.e. thermal and viscous coupling modes. It is also observed that the strength of the LSC in water becomes weaker when the LSC in FC77 rotates faster azimuthally and that the flow strength in FC77 becomes stronger when the LSC in water rotates faster azimuthally, i.e. the influence of the LSC in one fluid layer on the other is not symmetric.
Temperature Oscillations and Flow Dynamics in Turbulent Thermal Convection
ABSTRACT We report an experimental study of three-dimensional structure of the low-frequency temp... more ABSTRACT We report an experimental study of three-dimensional structure of the low-frequency temperature oscillations in a cylindrical Rayleigh-Bénard (RB) convection cell of aspect ratio one. It is found that the hot and cold thermal plumes are not emitted periodically nor alternatively, but continuously and randomly, from the top and bottom plates. We further found that the oscillation of the temperature field does not originate from boundary layers, but rather is a result of the horizontal motion of the hot ascending and cold descending fluids being modulated by the twisting oscillation near the top and bottom plates and the off-center oscillation in the bulk flow field. Evidence will also be presented to show that the off-center oscillation in the bulk flow field is a manifestation of the twisting motion of fluid near the top and bottom plates. In collaboration with Heng-Dong Xi, Quan Zhou, and Sheng-Qi Zhou, The Chinese University of Hong Kong.
We report an experimental study of confinement effects in quasi-2-D turbulent Rayleigh–Bénard con... more We report an experimental study of confinement effects in quasi-2-D turbulent Rayleigh–Bénard convection. The experiments were conducted in five rectangular cells with their height H and length L being the same and fixed, while the width W was different for each cell to produce lateral aspect ratios (Γ = W/H) of 0.6, 0.3, 0.2, 0.15 and 0.1. Direct flow field measurements reveal that the large-scale flow slows down as Γ decreases and there are more plumes travelling through the bulk region. Moreover, the reversal frequency of the large-scale flow is found to increase drastically in smaller Γ cells, by more than 1000-fold for the highest value of Rayleigh number reached in the experiment. The reversal frequency can be well described by a stochastic model developed by Ni et al. (J. Fluid Mech., vol. 778, 2015, R5) and the probability density functions (PDF) of the time interval between successive reversals are found to follow Poisson statistics as in the 3-D system. It is further observed that the bulk temperature fluctuation increases significantly and its PDF changes from exponential to Gaussian as Γ decreases. The influences of geometric confinement on the global heat transport are also investigated. The measured Nu–Ra relationship suggests that, as the lateral aspect ratio decreases, the relative weight of the boundary layer contribution in the global heat transport increases compared to that from the bulk. These results demonstrate that in the quasi-2-D geometry, geometric confinement has strong effects on both the global and local properties in turbulent convective flows, which are very different from the previous findings in 3-D and true 2-D systems.
Measurements of the capillary length in phase-separated solutions of polymethylmethacrylate in 3-... more Measurements of the capillary length in phase-separated solutions of polymethylmethacrylate in 3-octanone (PMMA/3-0CT) for each of five different molecular weights of PMMA, and in phase-separated solutions of polystyrene in methylcyclohexane (PS/MCH) for a single molecular weight of polymer, are reported. Measurements on PMMA/3-0CT were by the sessile-drop method; those on PS/MCH were by both the sessile-drop and capillary-rise methods. Interfacial tensions are estimated from estimated density differences and the measured capillary lengths. A theoretically predicted scaling law for the dependence of capillary length on polymer molecular weight and temperature is tested and at least semiquantitatively verified. As by-products of the sample preparation, the molecular-weight dependences of the critical composition and critical solution temperature of PMMA/3-OCT were also determined. The volume fraction of polymer at the critical point, ¢'" is found to be proportional to the-0.37 ±0.01 power of the molecular weight, in agreement with values of this exponent found by others for polystyrene solutions.
Measurements of the coexistence curves for phase-separated polymer solutions of polymethylmethacr... more Measurements of the coexistence curves for phase-separated polymer solutions of polymethylmethacrylate in 3-octanone PMMA/3-OCT for six different molecular weights of PMMA have been carried out. We have tested the scaling behavior of the order parameter the difference between polymer volume fractions in the two coexisting phases for its dependence on the degree of polymerization N of the polymer chains and the reduced temperature (T c T)/T c. The experiments reveal that, in the asymptotic regime, the measured order parameter has power-law dependence on both N and , i.e., 3.8N 0.21 0.34. Furthermore, when the symmerization procedure of Sanchez J. Appl. Phys. 58, 2871 1985 is used to analyze the data, it suggests that N 0.46 may be used as a scaling variable for phase separated polymer solutions.
Direct measurements of the velocity boundary layer in turbulent convection have been carried out ... more Direct measurements of the velocity boundary layer in turbulent convection have been carried out using a novel light scattering technique. The experiment reveals that the velocity profile y h ͑z͒ as a function of the distance z from the lower surface of a convection cell has an invariant form y h ͑z͒ y m f͑z͞d y ͒ over varying Rayleigh numbers (Ra). It is found that the scaling velocity y m , the viscous boundary layer thickness d y , and the shear rate g all obey power laws of Ra, i.e., y m ϳ Ra 0.5 , d y ϳ Ra 20.16 , and g ϳ Ra 0.66 . [S0031-9007(96)00765-X]
VISCOUS BOUNDARY LAYER MEASUREMENTS IN RAYLEIGH-BENARD CONVECTION (Session II: Chaos, The 1st Tohwa University International Meeting on Statistical Physics Theories, Experiments and Computer Simulations)
A light scattering experiment of turbulent convection in water is carried out in a convection cel... more A light scattering experiment of turbulent convection in water is carried out in a convection cell with rough upper and lower surfaces. The vertical heat flux is found to be increased by ϳ20% when the Rayleigh number becomes larger than a transition value. The experiment reveals that the main effect of the surface roughness is to increase the emission of large thermal plumes, which travel vertically through the central region. These extra thermal plumes enhance the heat transport, and they are also responsible for the anisotropic behavior of velocity fluctuations at the cell center.
An incoherent dynamic light-scattering technique is developed to measure the local velocity and i... more An incoherent dynamic light-scattering technique is developed to measure the local velocity and its statistics. By employing two parallel laser beams of different colors, the technique measures the cross-correlation function of the scattered intensities from two separate illuminating volumes. Because there is no phase coherence between the two laser beams, the measured cross-correlation function is sensitive only to the intensity fluctuations caused by a seed particle that crosses the two beams in succession. The flow velocity is obtained from the measured particle transit time. We frame the scattering theory so as to account for the two-beam scattering geometry. Our experiment verifies the calculation and demonstrates applications of the technique. The method has the unique feature of being able to measure simultaneously the local velocity in two opposite directions perpendicular to the incident laser beams. Its advantages are high spatial resolution and accuracy, fast temporal response, and ease of use. The technique is useful in studies of turbulent flows, sedimentation of heavy particles, and flow phenomena in complex fluids.
Dual-beam intensity cross-correlation spectroscopy is used to measure the viscous boundary layer ... more Dual-beam intensity cross-correlation spectroscopy is used to measure the viscous boundary layer over a rough conducting surface in turbulent convection in water. It is found that the velocity boundary layer near the rough surface can be characterized by three quantities: the maximum velocity v m , the shear rate γ v and the total boundary layer thickness d + δ v ; all of them obey power laws of Rayleigh number Ra. The maximum velocity v m is located outside the rough surface and its numerical value remains the same as that in the smooth cell. The Ra-dependence of d + δ v is found to be the same as that in the smooth cell, but the power-law amplitude is increased by a factor close to 2. Because of the formation of small eddies inside the roughening grooves, the measured γ v is reduced considerably in the groove region. It is also found that the Nusselt number Nu ∼ Ra 0.35 , which is larger in both magnitude and scaling exponent as compared to the smooth case.
A new light scattering method is developed to measure scattering amplitude fluctuations resulting... more A new light scattering method is developed to measure scattering amplitude fluctuations resulting from either internal motions of flexible macromolecules or rotations of rigid particles. With a single-beam two-color cross-correlation scheme, the technique becomes insensitive to rapid phase fluctuations of the scattered light produced by translational motions of the scattering particles. We frame the scattering theory so as to encompass rotations and number fluctuations of small particles in a steady laminar flow. Experiment verifies the theory and demonstrates its applications. The technique can be used to measure the magnitudes of the local velocity and the flow vorticity. It can also be used to measure internal motions and shape fluctuations of flexible macromolecules. The advantages of the technique are its high spatial resolution, fast temporal response, and ease of use. 9256
We have measured the turbidity for a series of solutions of polymethylmethacrylate in 3-octanone ... more We have measured the turbidity for a series of solutions of polymethylmethacrylate in 3-octanone ͑PMMA/3-OCT͒ with various polymer molecular weights. The obtained correlation length ͑͒ and the osmotic compressibility ͑͒ show power law dependence on both the reduced temperature ⑀ ϭ(TϪT c )/T c and the degree of polymerization N of the polymer chains, i.e., ϳN 0.15 ⑀ Ϫ0.63 and ϳN Ϫ0.06 ⑀ Ϫ1.23 , with the associated scaling exponents in good agreement with theoretical predictions. When the results of the present experiment are combined with those from an earlier coexistence curve measurement ͓K.-Q. Xia, X.-Q. An, and W.-G. Shen, J. Chem. Phys. 105, 6018 ͑1996͔͒, it is found that the concept of two-scale-factor universality applies to systems consist of the same polymer/solvent pair but with different molecular weights.
Measurements of the coexistence curves for phase-separated polymer solutions of polymethylmethacr... more Measurements of the coexistence curves for phase-separated polymer solutions of polymethylmethacrylate in 3-octanone ͑PMMA/3-OCT͒ for six different molecular weights of PMMA have been carried out. We have tested the scaling behavior of the order parameter ⌬ ͑the difference between polymer volume fractions in the two coexisting phases͒ for its dependence on the degree of polymerization N of the polymer chains and the reduced temperature ⑀ϭ(T c ϪT)/T c . The experiments reveal that, in the asymptotic regime, the measured order parameter has power-law dependence on both N and ⑀, i.e., ⌬ϭ3.8N Ϫ0.21 ⑀ 0.34 . Furthermore, when the symmerization procedure of Sanchez ͓J. Appl. Phys. 58, 2871 ͑1985͔͒ is used to analyze the data, it suggests that ⑀N 0.46 may be used as a scaling variable for phase separated polymer solutions.
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