R. Savino

A benchmark study on the thermal conductivity of nanofluids

This article reports on the International Nanofluid Property Benchmark Exercise, or INPBE, in which the thermal conductivity of identical samples of colloidally stable dispersions of nanoparticles or “nanofluids,” was measured by over 30 organizations worldwide, using a variety of experimental approaches, including the transient hot wire method, steady-state methods, and optical methods. The nanofluids tested in the exercise were comprised of aqueous and nonaqueous basefluids, metal and metal oxide particles, near-spherical and elongated particles, at low and high particle concentrations. The data analysis reveals that the data from most organizations lie within a relatively narrow band (±10% or less) about the sample average with only few outliers. The thermal conductivity of the nanofluids was found to increase with particle concentration and aspect ratio, as expected from classical theory. There are (small) systematic differences in the absolute values of the nanofluid thermal conductivity among the various experimental approaches; however, such differences tend to disappear when the data are normalized to the measured thermal conductivity of the basefluid. The effective medium theory developed for dispersed particles by Maxwell in 1881 and recently generalized by Nan et al. [J. Appl. Phys. 81, 6692 (1997)], was found to be in good agreement with the experimental data, suggesting that no anomalous enhancement of thermal conductivity was achieved in the nanofluids tested in this exercise.

Oscillatory Marangoni convection in cylindrical liquid bridges

Oscillatory Marangoni convection in silicon–oil liquid bridges, sustained by two circular coaxial disks with prescribed time‐dependent temperature profiles and bounded by cylindrical free surfaces, is investigated by direct three‐dimensional (3‐D) and time‐dependent simulation of the model equations, using finite difference methods explicit in time and a staggered spatial mesh in cylindrical coordinates. It is shown that, for low enough values of the dimensionless rate of ramping, the time‐dependent nature of the boundary conditions becomes unimportant and the computed critical Marangoni numbers approach the values obtained with steady stability analyses. For typical microgravity experiments, involving unsteady boundary conditions, the computed critical Marangoni numbers and the oscillation frequencies agree with available experimental data of sounding rockets and Spacelab experiments. The 3‐D thermo‐fluid‐dynamic oscillatory regime structures are depicted, discussed, and compared with previous experiment...

Transient Marangoni convection in hanging evaporating drops

A combined experimental and numerical analysis has been carried out to study Marangoni effects during the evaporation of droplets. The experiments are performed with pendant drops of silicone oils (with different viscosities) and hydrocarbons. The temperature of the disk sustaining the drop is rapidly increased or decreased in order to study transient heating or cooling processes. The velocity field in the droplet is evaluated monitoring the motion of tracers in the meridian plane, using a laser sheet illumination system and a video camera. Surface temperature distributions of the drops are detected by infrared thermocamera. The numerical model is based on axisymmetric Navier–Stokes equations, taking into account the presence of Marangoni shear stresses and evaporative cooling at the liquid-air interface. Marangoni flows cause a larger, more uniform surface temperature, increasing heat transfer from disk to droplet, as well as evaporation rate. When Marangoni effects are negligible, larger surface tempera...

Three-dimensional numerical simulation of Marangoni instabilities in non-cylindrical liquid bridges in microgravity

Instability of Marangoni convection in non-cylindrical (convex or concave) liquid bridges of low Prandtl number fluids is investigated by direct three-dimensional and time-dependent simulation of the problem. Body-fitted curvilinear coordinates are adopted; the non-cylindrical original physical domain in the (r,z,φ) space is transformed into a cylindrical computational domain in a (ξ,η,φ) space. The geometry of the domain is transformed using a coordinate transformation method by surface fitting technique. The field equations are numerically solved explicitly in time and with a finite difference technique in a staggered grid. The numerical results are analyzed and interpreted in the general context of the bifurcations theory. The computations show that for semiconductor melts the first bifurcation is characterized by the loss of spatial symmetry rather than by the onset of oscillatory flow and that it is hydrodynamic in nature. The flow field azimuthal organization related to the critical wave number, depends on the geometrical aspect ratio A=L/D of the liquid bridge and on the shape factor S (convex S>1, concave S<1) of the free surface. The critical azimuthal wave number increases when the geometrical aspect ratio of the bridge is decreased and, for a fixed aspect ratio, can be shifted to higher values by increasing the volume (convex bridges) or to lower values by decreasing the volume (concave bridges). This behavior is explained on the basis of the relation between the typology of the azimuthal disturbances and the structure of the fluid-dynamic field. A generalized law is found to correlate the critical azimuthal wave number of the instability to the geometrical aspect ratio and to the shape factor. A second oscillatory (Hopf) bifurcation occurs when further increasing the Marangoni number. Experimental results available in literature on this second bifurcation are considered for comparison. The experimental and numerical results show a good agreement.

Buoyancy and Marangoni Effects in an Evaporating Drop

Experiments and numerical simulations are carried out to study Marangoni and buoyancy effects in a hanging evaporating drop. The liquids investigated are n-octane, which exhibits Marangoni effect, and water, which does not exhibit thermal Marangoni effect. The disk sustaining the drop (diameter of a few millimeters) is held at a constant temperature. A temperature difference arises in the droplet as a consequence of the energy exchange with the ambient and of the evaporative cooling. In the presence of surface tension gradients (Marangoni effect), convective flows are established, and small surface temperature differences are measured at the drop-ambient interface. When the thermal Marangoni effect is absent (as in the water droplet), the surface temperature is stratified, and much larger surface temperature differences are established over the drop surface. The velocity field inside the droplet is evaluated by monitoring the motion of tracers within the drop, in the meridian plane, using a charge-coupled device (CCD) camera. The surface temperature distribution is detected by an infrared camera

Buoyancy and surface-tension-driven convection in hanging-drop protein crystallizer

Abstract This paper deals with natural and Marangoni convection in hanging (or sitting) drop protein crystallizers. In the pre-nucleation phase the drop is modelled as a mixture of water, precipitating agent and protein, bounded by an undeformable interface with a surface tension exhibiting a linear dependence on the concentrations; axial symmetry is assumed with respect to the drop axis. The post-nucleation phase is modelled assuming a given location of the crystal and appropriate boundary conditions for the concentrations of protein and precipitating agent in the neighbourhood of the crystal and at the drop surface. The final state of the pre-nucleation is used as the initial condition for the post-nucleation phase. The field equations, written in a suitable spherical co-ordinates system, are solved, with appropriate boundary and symmetry conditions, by a numerical algorithm based on finite-difference schemes. The study cases refer to the crystallization of lysozyme in a solution of sodium chloride in water, for two configurations, full-size and half-size geometries. The computations indicate that for these configurations solute transport is dominated by convection and that the convection velocities are one or even two orders of magnitude larger than the characteristic diffusion velocities. In the pre-nucleation phase solute Marangoni effects are negligible for the half-zone geometry but in the full-size geometry they are comparable to buoyancy driven flows. Calculations of buoyancy flows around a growing crystal show that in ground conditions non-uniform concentration gradients may have a detrimental effect on the growth kinetics.

Experimental and Numerical Investigation of Martian Atmosphere Entry

A numerical and experimental investigation was performed to study the aerothermodynamic problems of entry into the Martian atmosphere. The mathematical and physical model used to study the flowfield around a capsule entering a CO 2 environment is described. Computational fluid dynamics tools have been applied to solve the system of governing equations. The importance of surface catalycity effects on the stagnation-point heat transfer and on the heat load in Martian atmosphere is highlighted. Stagnation-point heat flux levels applied to models of different materials in a plasma wind tunnel are shown, and numerical correlations are presented. The different role played by surface catalycity in Earth and Mars environments is shown.

Marangoni flotation of liquid droplets

Flotation of liquid droplets on pool surfaces, in the presence of temperature differences, is studied experimentally and numerically. Coalescence or sinking of the droplet is prevented by the thermal Marangoni motion, owing to the surface tension imbalance at the pool surface. The mechanism is the same as that investigated in previous works on coalescence and wetting prevention in the presence of temperature differences. If the droplet is colder than the liquid surface, the flow is directed radially towards the drop; this radial flow field drags the ambient air under the drop, thus creating an air film and avoiding a direct contact between the droplet and the pool molecules. The surface velocities are measured visually with a CCD camera to image the motion of tracers floating on the pool surface; the surface temperature distributions along the pool and the droplet surfaces are measured by an infrared thermocamera. The experimental results are correlated by numerical results obtained under the assumption of spherical drop and axisymmetric flow regime

Influence of buoyancy forces on Marangoni flow instabilities in liquid bridges

The influence of buoyancy forces on oscillatory Marangoni flow in liquid bridges of different aspect ratio is investigated by three‐dimensional, time‐dependent numerical solutions and by laboratory experiments using a microscale apparatus and a thermographic visualisation system. Liquid bridges heated from above and from below are investigated. The numerical and experimental results show that for each aspect ratio and for both the heating conditions the onset of the Marangoni oscillatory flow is characterized by the appearance of a standing wave regime; after a certain time, a second transition to a travelling wave regime occurs. The three‐dimensional flow organization at the onset of instability is different according to whether the bridge is heated from above or from below. When the liquid bridge is heated from below, the critical Marangoni number is larger, the critical wave number (m) is smaller and the standing wave regime is more stable, compared with the case of the bridge heated from above. For the critical azimuthal wave number, two correlation laws are found as a function of the geometrical aspect ratio A.

Microgravity Experiment Acceleration Tolerability on Space Orbiting Laboratories

Residual gravity and g jitter aboard space orbiting laboratories induce disturbing effects on fluid and material science experiments. A nondimensional scaling analysis of the field equations, under the assumption of high frequencies and small amplitudes of g jitter, was carried out to assess the tolerability criteria for microgravity experiments in the presence of oscillatory and time-averaged fluid thermodynamic distortions induced by multiplefrequency excitation. The most important result is that the tolerability limits, imposed by the presence of timeaveraged distortions, are substantially lower than those corresponding to oscillatory distortions. The tolerability domains, in the plane of frequency vs acceleration, were numerically computed for a specific test case consisting of a directional solidification process of binary alloys or semiconductors. Nomenclature b = amplitude of the sinusoidal displacement, cm c = mass concentration measured with respect to its reference value c.v = solute concentration at the crystal-melt interface in a solid GO = solute concentration at the crystal-melt interface in a