Günter Brenn

Evaporation of acoustically levitated droplets

The rate of heat and mass transfer at the surface of acoustically levitated pure liquid droplets is predicted theoretically for the case where an acoustic boundary layer appears near the droplet surface resulting in an acoustic streaming. The theory is based on the computation of the acoustic eld and squeezed droplet shape by means of the boundary element method developed in Yarin, Pfaenlehner & Tropea (1998). Given the acoustic eld around the levitated droplet, the acoustic streaming near the droplet surface was calculated. This allowed calculation of the Sherwood and Nusselt number distributions over the droplet surface, as well as their average values. Then, the mass balance was used to calculate the evolution of the equivalent droplet radius in time. The theory is applicable to droplets of arbitrary size relative to the sound wavelength , including those of the order of , when the compressible character of the gas flow is important. Also, the deformation of the droplets by the acoustic eld is accounted for, as well as a displacement of the droplet centre from the pressure node. The eect of the internal circulation of liquid in the droplet sustained by the acoustic streaming in the gas is estimated. The distribution of the time-average heat and mass transfer rate over the droplet surface is found to have a maximum at the droplet equator and minima at its poles. The time and surface average of the Sherwood number was shown to be described by the expression Sh= KB= p !D0, where B = A0e=(0c0) is a scale of the velocity in the sound wave (A0e is the amplitude of the incident sound wave, 0 is the unperturbed air density, c0 is the sound velocity in air, ! is the angular frequency in the ultrasonic range, D0 is the mass diusion coecient of liquid vapour in air, which should be replaced by the thermal diusivity of air in the computation of the Nusselt number). The coecientK depends on the governing parameters (the acoustic eld, the liquid properties), as well as on the current equivalent droplet radius a. For small spherical droplets with a , K = (45=4) 1=2 =1 :89, if A0e is found from the sound pressure level (SPL) dened using A0e. On the other hand, if A0e is found from the same value of the SPL, but dened using the root-mean-square pressure amplitude (prms = A0e= p

Validation and application of a novel elongational device for polymer solutions

A novel elongational device is used to investigate the capillary thinning process of threads of dilute and semidilute aqueous polymer solutions. It is shown that the end regions of the threads do not play an essential role in the thinning process, so that a simple theory describing the self-thinning of the liquid thread is appropriate to describe the experiments with polymer solutions carried out with this device. Aqueous solutions of four different polymers (all polyacrylamide based) are studied using the elongational device. It is shown that the elasticity of the polymers is dominated by polyacrylamide chains and that the effect of branching and topological structure of macromolecules is negligible. The time-dependent decrease of the thread diameter can be divided into two stages. The first is a viscoelastic one where macromolecular coils are stretched by the elongational flow, and the second is a quasi-Newtonian one, where full stretching has already been achieved, resulting in a very high but constant elongational viscosity. At the first stage the rheological behavior of the solutions studied is characterized by a constant relaxation time, whereas at the second one it is by a constant elongational viscosity. For polymer macromolecules of relatively low stability, mechanical degradation of the molecules is found during their stretching in a self-thinning capillary thread.A novel elongational device is used to investigate the capillary thinning process of threads of dilute and semidilute aqueous polymer solutions. It is shown that the end regions of the threads do not play an essential role in the thinning process, so that a simple theory describing the self-thinning of the liquid thread is appropriate to describe the experiments with polymer solutions carried out with this device. Aqueous solutions of four different polymers (all polyacrylamide based) are studied using the elongational device. It is shown that the elasticity of the polymers is dominated by polyacrylamide chains and that the effect of branching and topological structure of macromolecules is negligible. The time-dependent decrease of the thread diameter can be divided into two stages. The first is a viscoelastic one where macromolecular coils are stretched by the elongational flow, and the second is a quasi-Newtonian one, where full stretching has already been achieved, resulting in a very high but constant...

Investigation of the elongational behavior of polymer solutions by means of an elongational rheometer

An elongational rheometer is used to measure the relaxation times λ and the steady terminal elongational viscosities ηE,t of aqueous solutions of ionic and nonionic polymers at various concentrations in Θ and in good solvents. In the corresponding ηE,t/λ nomogram the results yield two typical limiting curves—one for solutions of nonionic polymers and another for solutions of ionic polymers. The curves characterize the elongational behavior of the polymer solutions. The elongational flow results in data that are intermediate to the two limiting curves for polymers in aqueous salt solutions and for aqueous solutions of mixtures of ionic and nonionic polymers. By means of an empirical correlation, the relaxation time and the steady terminal elongational viscosity are normalized such that the nomogram can be applied to polymers in various solvents. Thus a simple and reliable method for determining the behavior of polymer solutions in elongational flows is achieved.

The formation of satellite droplets by unstable binary drop collisions

Experimental investigations on the process of satellite droplet formation by unstable binary drop collisions are presented. The experiments are carried out using two monodisperse streams of drops of equal size. A systematic variation of the parameters influencing the collisions leads to an extended version of the stability nomogram which involves the numbers of satellite droplets formed by stretching separation after off-center collisions. The time scales for the formation of liquid filaments and their breakup into the satellites are measured and, in the case that a single satellite is formed, the satellite size is measured by means of a phase-Doppler anemometer. Furthermore, a theoretical model for the breakup of cylindrical liquid filaments in head-on and off-center collisions is presented. The model is based on a linear stability analysis of the filament formed after the collision. The critical wavelength associated with the largest deformation energy is calculated and identified with the disturbance w...

Drying of acoustically levitated droplets of liquid-solid suspensions: Evaporation and crust formation

Measurements on the drying behavior of droplets of aqueous suspensions of glass beads are carried out in a tube levitator at varying drying conditions. The experimental results show that there exist two distinct drying stages. At stage I the droplet diameter decreases. At stage II it is constant, while solvent evaporation still proceeds, as it follows from the permanent upward motion of the drop toward the pressure node. A theory for describing the evaporation of a liquid/solid suspension droplet in the acoustic field at the first drying stage is developed and validated with the measurement data. The theory solves the mass transfer problem of liquid vapor from the droplet surface. It takes the convective influence of the acoustic field on the mass transfer into account, using results from the earlier work of the authors on the evaporation of acoustically levitated droplets. Comparison of the theory with the experiments supports the idea that at the first drying stage solvent evaporation proceeds from the wetted surface of suspension droplets. The acoustically driven mechanism of the evaporation process is related to the acoustic streaming flow. The present work does not propose any theory for the second drying stage. It presents only some physical estimates, suggesting that stage II begins from a relatively fast precipitation of the suspended particles (glass beads) in the outer layers of the droplet, and crust formation. The estimates also suggest that the further solvent evaporation proceeds through the pores of the crust. Liquid evaporation in the pores, according to the estimates, proceeds according to the ordinary diffusion-driven mechanism, which is a limiting process in this case.

Linear analysis of the temporal instability of axisymmetrical non-Newtonian liquid jets

Abstract The temporal instability behavior of non-Newtonian liquid jets moving in an inviscid gaseous environment is investigated theoretically for axisymmetrical disturbances. The corresponding dispersion relation between the wave growth rate and the wave number is derived. The linearized stability analysis shows that a jet of a viscoelastic fluid exhibits a larger growth rate of axisymmetric disturbances than a jet of a Newtonian fluid with the same Ohnesorge number, indicating that non-Newtonian liquid jets are more unstable than their Newtonian counterparts. This is a well-known effect for small perturbations of the jet surface. For non-Newtonian liquid jets the instability behavior is influenced by the interaction of the liquid viscosity and elasticity effects, in which the liquid viscosity tends to dampen the instability, whereas the elasticity results in an enhancement of instability for small perturbations. The validity of the theoretical results for the growth rate spectra and breakup lengths of viscoelastic liquid jets is tested against experimental results from the literature. The comparisons confirm that the linearized theory fails to describe the nonlinear phenomena involved in viscoelastic jet breakup correctly, but it yields good results for the growth rate of disturbances in a regime of low jet Weber numbers and small deformations. The limits of validity of linear theories for viscoelastic jet instability are quantified, taking also into account the onset of non-axisymmetric deformations due to bending.

Shear and extensional rheological investigations in solutions of grafted and ungrafted polysaccharides

Many polysaccharides with varying shear stability have been grafted with polyacrylamide branches to enhance their turbulent drag-reducing and flocculating characteristics. Their aqueous solutions have been studied by shear and extensional rheometric techniques. All the solutions of grafted carboxymethyl cellulose, guar gum, starch, and sodium alginate exhibit shear-thinning non-Newtonian behavior. The viscosities are higher than those of ungrafted polysaccharides. The solutions of grafted carboxymethyl cellulose, guar gum and sodium alginate are spinnable. When subjected to uniaxial stretching in a stretching device, the formation of a thread and reduction of the thread diameter with time were observed. The stretching device was used to measure the relaxation time, which was found to be the largest (∼26 ms), on the order of flexible polyacrylamide, for the grafted carboxymethyl cellulose. Though a polyacrylamide solution degrades through nozzle flow and completely loses its extensional properties, a solution of grafted carboxymethyl cellulose retains about half its relaxation time because of the shear stability of polysaccharide chains and their structure.

Acoustically levitated drops: Drop oscillation and break-up driven by ultrasound modulation

Abstract The behaviour of drops in an acoustic levitator is simulated numerically. The ultrasound field is directed along the axis of gravity, the motion of the drop is supposed to be axisymmetric.The flow inside the drop is assumed inviscid (since the time intervals considered are short) and incompressible. First, as a test case, we consider a stationary ultrasound wave. We observe, as in previous experimental and theoretical works, that stable drop equilibrium shapes exist for acoustic Bond numbers up to a critical value. The critical value depends on the dimensionless wave number of the ultrasound. Beyond the critical value, we still observe equilibrium drop shapes, but they are not purely convex (i.e. “dog-bone” shaped) and found to be unstable. Next we modulate the ultrasound pressure level (SPL) with a frequency ω2, which is comparable to the first few drop resonance frequencies, and a small modulation amplitude. Simulations and experiments are performed and compared; the agreement is very good. We further on investigate numerically the more general case of an arbitrary ω2 (still comparable to the first few drop resonance frequencies, yet). A very rich drop dynamics is obtained. We observe that a resonant drop break-up can be triggered by an appropriate choice of the modulation frequency. The drop then disintegrates although the acoustic Bond number remains below its critical value. Finally we change the modulation frequency linearly with time, sweeping over a window containing the drops first eigenfrequency ω2(res). After ω2 has crossed ω2(res), in the range of validity of the inviscid approximation, the drop equatorial radius oscillates between well-defined saturation values. For small modulations the range of oscillation grows linearly with the modulation amplitude. For larger modulations, however, a substantial increase in the oscillation range of the drop equatorial radius is observed in the case of down-sweep; the increase does not occur in up-sweeps of the modulation frequency. We compare our results with experimental findings and in particular the so-called jump phenomenon, as well as with experimental and numerical results from the literature.

The acoustic tube levitator : A novel device for determining the drying kinetics of single droplets

An acoustic tube levitator was developed and used for investigating the drying behavior of single droplets (d D,0 ≃1.0 mm) containing water and a certain fraction of inert, solid material such as glass beads with a mean diameter of d s =30 μm. A glass tube surrounds the transducer and reflector of the acoustic tube levitator, hence increases the radial stability of the droplet and shields it against disturbances from outside. A CCD camera and a back-light illumination are used to observe the evolution of the droplet diameter and the vertical position of the droplet. Ambient temperature, initial volume and initial solid mass fraction of the droplet were systematically varied. From the measured droplet diameter and the position of the mean density, the moisture content and the mean porosity of the drying droplet/grain can be determined as a function of time.

A new apparatus for the production of monodisperse sprays at high flow rates

Abstract A spray generator was constructed for the production of monodisperse liquid sprays at industrially relevant liquid flow rates. The operation of the generator is based on the Rayleigh-type breakup of multiple liquid jets. Laser drilled nozzle holes (diameters 41 or 76 μm) in the nozzle plate (diameter 105 mm) produce 613 individual laminar liquid jets; liquid mass flow rates of up to 170 kg/h are thus obtained. The breakup of these liquid jets is controlled by a piezoceramic oscillator which is driven by a square wave excitation signal. The operation of the spray generator was characterized using video imaging. The spray generator provides a well controlled monodisperse spray with a fairly wide operation envelope with respect to nozzle Reynolds number and wave number ( Re = 600–1200, k = 0.3–1.0). The liquid jet velocities at different positions of the nozzle plate were found to be equal. Furthermore, the excitation proved to affect all the liquid jets emerging from the nozzle properly. The relative standard deviation of drop diameters in the spray was typically 2–4%. With increasing downstream distance from the nozzle plate, the interaction between the spray and the surrounding gas leads to the loss of monodispersity through collisions and subsequent coalescence of neighbouring droplets in the jets. Some preliminary investigations about the influence of an amplitude modulated excitation signal on the operation of the spray generator were also conducted.