NANO LETTERS
Enhanced Mass Transport in Nanofluids S. Krishnamurthy, P. Bhattacharya, and P. E. Phelan*
2006 Vol. 6, No. 3 419-423
Arizona State UniVersity, Department of Mechanical & Aerospace Engineering, Building ECG, Room 346, Tempe, Arizona 85287-6106
R. S. Prasher† Intel Corporation, CH5-157, 5000 West Chandler BouleVard, Chandler, Arizona 85226-3699 Received November 14, 2005; Revised Manuscript Received January 26, 2006
ABSTRACT Thermal conductivity enhancement in nanofluids, which are liquids containing suspended nanoparticles, has been attributed to localized convection arising from the nanoparticles’ Brownian motion. Because convection and mass transfer are similar processes, the objective here is to visualize dye diffusion in nanofluids. It is observed that dye diffuses faster in nanofluids compared to that in water, with a peak enhancement at a nanoparticle volume fraction, O, of 0.5%. A possible change in the slope of thermal conductivity enhancement at that same O signifies that convection becomes less important at higher O. The enhanced mass transfer in nanofluids can be utilized to improve diffusion in microfluidic devices.
Nanofluids are a class of heat transfer fluids created by dispersing solid nanoparticles in traditional heat transfer fluids. Repeated experiments by several groups around the world have demonstrated that the effective thermal conductivity of nanofluids, knf, is higher than can be explained by a mean-field conduction-based model, such as the MaxwellGarnett theory, as reviewed in refs 1-3. The mechanism(s) leading to this enhancement are still under scrutiny, but recently several authors have proposed models that rely on the Brownian motion of the nanoparticles to yield the observed enhancement.4-7 Two of the models5,6 postulate that nanoscale convection induced by the Brownian motion of the nanoparticles causes enhanced mixing and hence increased heat transfer beyond what simple conduction-based theories predict. The other two studies,4,7 however, proposed that although Brownian motion is important, it is the coupling between particles, as promulgated by the interparticle potential function, which is primarily responsible for the observed enhancement in knf. To date, these competing theories have not been reconciled. An unambiguous visualization of nanoscale convection induced by the nanoparticles would clarify its role in the enhancement of knf. Truly nanoscale flow visualization, however, is an exceedingly difficult task. Instead, in this study we choose to observe the microscale mass transfer (i.e., effective mass transport) of a dye droplet in a water-based nanofluid and compare that to its mass diffusivity in pure * Corresponding author. Tel: (480)965-1625. Fax: (480)965-1384. E-mail:
[email protected]. † Adjunct Professor, Arizona State University, Department of Mechanical & Aerospace Engineering. 10.1021/nl0522532 CCC: $33.50 Published on Web 02/07/2006
© 2006 American Chemical Society
Figure 1. Schematic diagram of the experimental setup for measuring the mass diffusivity of nanofluids.
water to determine if mass transport is changed by the presence of the nanoparticles. Because convective heat and mass transfer are analogous processes,8 if we observe an enhancement in the effective mass diffusivity of a nanofluid, Dnf, compared to that of pure water, then we can conclude that an enhancement in heat convection must be occurring
Figure 2. Time-dependent images, in seconds, of diffusion of fluoresein dye in (a) pure water and (b) 0.5% Al2O3 nanofluid.
as well. This would lend support for the models in refs 5 and 6 that are premised on localized convection being the primary mechanism behind the observed enhancement in knf. Another equally important result of such mass diffusion measurements in nanofluids is to determine if Dnf is enhanced relative to that in pure water. If so, then it opens up numerous additional applications for nanofluids where mass diffusion is important. For example, many microfluidic devices, such as “lab-on-a-chip” type of systems, suffer from the limited mass transfer available at low Reynolds numbers. If the mass transfer could be improved by the incorporation of passive nanoparticles, that is, nonreacting nanoparticles, then this could prove to be a convenient and inexpensive technique to improve the performance of microfluidic devices. For the experiments, a well with a diameter of 4 mm and a height of 2 mm was prepared by cutting a capillary tube and mounting it on a microscope slide with vacuum grease. This was followed by filling the well with water or nanofluid. The entire setup was then placed under a stereo microscope (Leica) for visualization purposes, as shown schematically in Figure 1. Once this was done, a small drop of dye was inserted on top of the nanofluid/water sample using a specially designed dip pin that is used to achieve highly accurate sample volumes and spot sizes. The size of the drop in the present experiment was found on average to be 250420
300 µm. The well was exposed to Hg-Ne light, and images of the sample with the dye were taken with a Magnafire camera attached to the microscope at time intervals of 20 s. Bleaching of the dye was avoided by not continuously exposing the sample to the Hg-Ne light, and images were recorded for a total time of 3 min. The dye solution was prepared by dissolving 332 mg of fluoresein powder in 0.5 mL of methanol, followed by the addition of 9.5 mL of water to the dye concentrate. This initial dye concentration was further diluted by a factor of 100. Nanofluid of the desired volume fraction was prepared by suspending appropriate quantities of 20-nm Al2O3 nanoparticles in deionized water at volume fractions of 0.1%, 0.25%, 0.5%, 0.75%, and 1%. To make the suspension stable, 0.5% Tween-80 surfactant was added, and the solution was stirred using an ultrasound sonicator for 30 min. The last step of the experimental procedure was the postprocessing of the images obtained from the experiments. In this step, the intensity of the image was first measured using Image-Pro Plus software (or a similar image editor) and then the planar area of the die was calculated using our own numerical code. The effective mass diffusivity of the dye in both deionized water and in nanofluid is determined by measuring the frontal variation of the dye, that is, the spread of the planar area, Nano Lett., Vol. 6, No. 3, 2006
Figure 4. Time-variant r 2 for water and 0.1% and 0.25% nanofluid containing 20-nm Al2O3 nanoparticles.
Figure 3. Time-dependent images, in seconds, of diffusion of fluoresein dye in 1% nanofluid.
with respect to time. The characteristic displacement of a Brownian particle, or for that matter any physical quantity like mass or heat, is governed by the mean displacement equation 〈(∆r)2〉 ) 2Dt
(1)
where 〈(∆r)2〉 is the mean square displacement (m2), D is the mass diffusivity of the Brownian particle/transport quantity (m2/s), and t is the time taken to travel the mean displacement in seconds. Because the mean displacement of the dye front can be measured from recorded images, the diffusion coefficient of dye in water or nanofluid can be determined from the slope of the mean displacement versus time plot, assuming that 〈(∆r)2〉 varies linearly with time, t. For water, the mean displacement of the dye is determined by measuring the radius of the circle at every time step. In nanofluid, because of the nonlinearity in dye diffusion, as shown in Figure 2b for 0.5% Al2O3 nanofluid and in Figure 3 for 1.0% Al2O3 nanofluid, the mean displacement of the dye is determined by equating the area of the diffused dye Nano Lett., Vol. 6, No. 3, 2006
A to an effective circular area, Aeff, of radius Reff, where A is determined from postprocessing the fluorescent signal. Figures 2 and 3 are a series of sequential images taken at time intervals of 20 s for pure water (Figure 2a) and for the 0.5% (Figure 2b) and 1% (Figure 3) Al2O3 nanofluid. The images show that the dye is transported radially outward through the medium. Because the height of the well is small relative to its diameter, what is being observed is primarily two-dimensional radial transport. Figures 2 and 3 also show that although dye diffuses in a circular manner in water, in nanofluid the transport is nonlinear in nature. It is evident from these images that for the same initial concentration of dye in water and nanofluid, dye is transported to a greater extent in nanofluid. To quantify the dye transport in water and in nanofluid, we plotted the square of the dye front (r 2) as a function of time. Figure 4 shows r 2 for pure water and the two lowest concentrations of nanofluid (0.1% and 0.25%), whereas Figure 5 shows r 2 for the three highest concentrations of nanofluid (0.5%, 0.75%, and 1.0%). Two important points can be made from the data in Figures 4 and 5: (i) the rate of mass transport, as represented by the approximate slope of the r 2 versus t curves, varies depending on the nanofluid volume fraction, φ, and (ii) some of the curves show a linear dependence of r 2 on time, which is expected for pure diffusion processes, whereas others show a nonlinear dependence. For pure water and the lowest volume fractions of nanofluid (Figure 4), mass transport appears to be primarily diffusive in nature and increases with increasing φ. For all values of φ, the rate of mass transport in nanofluid is higher than that in pure water, but a maximum mass transport rate is apparently reached for φ ) 0.5%, which will be discussed later. Two of the curves in Figure 5, those for φ ) 0.5% and φ ) 1.0%, demonstrate a 421
Figure 5. Time variant r 2 for 0.5%, 0.75%, and 1% nanofluid containing 20-nm Al2O3 nanoparticles.
Figure 6. Mass diffusion and thermal conductivity enhancement in a nanofluid containing 20-nm Al2O3 nanoparticles.
nonlinear dependence of r 2 on time, which indicates nondiffusive behavior. To validate the results of the experiments, a handbook value of the dye diffusion coefficient in pure water is compared with the present experimental results. The diffusion coefficient for dye in pure water from the experiments is determined to be 7.6 × 10-10 m2/s, which is in reasonable agreement with its handbook value of 5.2 × 10-10 m2/s.9 The difference may possibly be attributed to self-absorption by the dye, because of the relatively high dye concentration. For the 0.5% volume fraction nanofluid, the diffusion coefficient is found to be 1.1 × 10-8 m2/s, or more than 1 order of magnitude greater than that in pure water, signifying the fact that the presence of nanoparticles enhances mass transport. To investigate the reason for the observed enhancement in mass transport, we conducted an order-ofmagnitude analysis to envisage the phenomenon clearly. The time for the dye to diffuse through a distance equal to the diameter, d, of the nanoparticle, tm, is given by10
motion of the particles does not contribute directly to the mass transport enhancement; that is, the particles do not “push” the dye from one point to another. Rather, in accord with the models of enhanced nanoscale heat convection in nanofluids,5,6 the enhancement in diffusivity is likely due to the increased nanoscale stirring of the liquid, caused by the nanoparticles’ Brownian motion. Further, the time required for convection currents to travel a particle diameter, tc, is given by
tm )
d2 2D
(2)
where D is the diffusion coefficient of dye in water (m2/s). In water, the time taken by the dye is tm ) 3.8 × 10-7 s, and must be even less for nanofluid. The time required for a Brownian particle to travel its diameter, tb, is given by the mean displacement equation in conjunction with the StokesEinstein diffusivity tb )
3πη d3 2kbT
(3)
where η is the viscosity of water (N‚s/m2), kb is the Boltzmann constant (J/K), and T is the temperature (K). For a 20-nm Al2O3 particle, tb ) 8.1 × 10-6 s. From the above calculations, it is clear that tb > tm, and hence the Brownian 422
tc ) d2/2υ
(4)
At 300 K, for a 20-nm particle tc ) 2.0 × 10-10 s, which is much smaller than both tb and tm, thus underlying the fact that convection currents (like mass diffusion) travel much faster than the particle itself. Thus, the disturbance field created by the motion of the nanoparticles in the fluid can be a possible reason for the increase in the rate of mass transport Dnf, as well as for the increases in knf observed previously. Intuition suggests that increasing the number of nanoparticles, that is, increasing the volume fraction, φ, should therefore increase Dnf because of the increased number of disturbance fields in the fluid. Figure 6, however, shows a clear peak in the enhanced diffusivity of the dye in nanofluid, Dnf, normalized by the diffusivity in pure water, Dw. Note that the values of Dnf in Figure 6 were calculated by fitting the data linearly for all of the volume fractions. The thermal conductivity enhancement for these same nanofluids, shown as the effective nanofluid thermal conductivity, knf, divided by the thermal conductivity of pure water, kf, is also presented in Figure 6. Although not enough data are given for a definitive evaluation, it appears that there is a change in slope of the knf/kf curve at φ ) 0.5%, where the peak in Dnf/Dw occurs. Figure 6 demonstrates substantially greater enhancement in Dnf/Dw relative to knf/kf, with the peak enhancement in Nano Lett., Vol. 6, No. 3, 2006
knf/kf reaching about 16%, but that for Dnf/Dw more than 1 order of magnitude. This suggests the potential application of nanofluids in applications that require high rates of mass diffusivity. One prominent example mentioned above is microfluidic devices, in which some amount of nanoparticles could be introduced to passively increase the mass diffusivity of the reacting molecules. Note that the rate of mass transfer could possibly be increased even further through the imposition of a temperature gradient via the Soret effect.11 Numerous other applications would benefit from increased mass diffusivity, such as reacting systems or sorption processes similar to those in absorption refrigerators. The reason for the Dnf/Dw peak, and the change in slope of the knf/kf curve, is not clear at this time. One possible mechanism is the effect of aggregation, the probability of which increases with decreasing particle-to-particle separation. For nanoparticles of constant size, like the 20-nm Al2O3 nanoparticles considered here, an increase in the volume fraction, φ, means a decrease in the particle-to-particle separation, and hence a greater possibility of aggregation. Aggregation would tend to produce, in effect, fewer larger particles of greater mass. The effect of these larger, more massive particles can be understood through a recently introduced Brownian Reynolds number6
Re )
1 υ
x
18kbT πFnd
(5)
where Fn is the density of the nanoparticle. The Re definition in eq 5 is based on the root-mean-square velocity of a Brownian particle, νn ) x3kbT/mn, where mn is the mass of the nanoparticle and quantifies the contribution of the nanoparticles’ Brownian motion to enhanced convective transport. From these two expressions, larger aggregated particles (greater d), which equivalently have larger mass, mn, move more slowly and hence contribute less to convective motion than do smaller, less massive nanoparticles. In conclusion, experiments were conducted to investigate the effect of the presence of nanoparticles in a fluid on mass diffusion by visualizing the mass transport of dye in water and nanofluids. The results from the experiments show that the mass transport is enhanced by the presence of nanoparticles in the fluid. For some nanoparticle volume fractions, the mass transport is diffusive in nature, but for others it is nondiffusive. An order-of-magnitude analysis suggests that
Nano Lett., Vol. 6, No. 3, 2006
the Brownian motion of the nanoparticles is not directly responsible for the observed mass transport enhancement. Rather, it is the velocity disturbance field in the fluid, created by the motion of the nanoparticles, that could be responsible for such enhancement. An optimum volume fraction of nanoparticles delivers the greatest enhancement in mass transport rate and causes a change in slope of the thermal conductivity enhancement. Although the reasons for this peak enhancement are still not clear, we hypothesize that with increasing volume fraction there is a greater likelihood for particle aggregation, producing in effect larger, more massive particles with reduced capacity to promote localized convection and increased heat transfer and mass diffusion. This result suggests that at higher volume fractions of nanoparticles, some other mechanism for enhanced heat transport, such as increased conduction through aggregates, or particleto-particle coupling through their interparticle potentials, may become increasingly important. Acknowledgment. We gratefully acknowledge the support of the National Science Foundation, through a GOALI award to Arizona State University and to the Intel Corporation (Award No. CTS-0353543), and the direct support provided by Intel. Experimental assistance provided by A. Vuppu, helpful discussions by P. Keblinski with R.P., and the reviewer’s comments are all gratefully acknowledged. References (1) Eastman, J. A.; Phillpot, S. R.; Choi, S. U. S.; Keblinski, P. Annu. ReV. Mater. Res. 2004, 34, 219. (2) Keblinski, P.; Eastman, J. A.; Cahill, D. G. Mater. Today 2005, 8, 36. (3) Phelan, P. E.; Bhattacharya, P.; Prasher, R. S. Annu. ReV. Heat Transfer, in press, 2005. (4) Bhattacharya, P.; Saha, S. K.; Yadav, A.; Phelan, P. E.; Prasher, R. S. J. Appl. Phys. 2004, 95, 6492. (5) Jang, S. P.; Choi, S. U. S. Appl. Phys. Lett. 2004, 84, 4316. (6) Prasher, R. S.; Bhattacharya, P.; Phelan, P. E. Phys. ReV. Lett. 2005, 94, 025901-1. (7) Wang, J.; Chen, G.; Zhang, Z. ASME Summer Heat Transfer Conference, Paper no. HT2005-72797, San Francisco, CA, 2005. (8) See, e.g., Goldstein, R. J. Mass Transfer Systems for Simulating Heat Transfer Processes. In Measurement Techniques in Heat and Mass Transfer; Hemisphere Publishing Corp.: Washington, D.C., 1985; pp 215-229. (9) Mills, A. F. Mass Transfer; Prentice Hall, New Jersey, 2001. (10) Einstein, A. InVestigations on the Theory of Brownian MoVement; Dover Publications: New York, 1956. (11) Cerbino, R.; Mazzoni, S.; Vailati, A.; Giglio, M. Phys. ReV. Lett. 2005, 94, 064501.
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