Mechanical vibrations of magnetically levitated viscoelastic droplets

Oscillations of a soft viscoelastic drop

A soft viscoelastic drop has dynamics governed by the balance between surface tension, viscosity, and elasticity, with the material rheology often being frequency dependent, which are utilized in bioprinting technologies for tissue engineering and drop-deposition processes for splash suppression. We study the free and forced oscillations of a soft viscoelastic drop deriving (1) the dispersion relationship for free oscillations, and (2) the frequency response for forced oscillations, of a soft material with arbitrary rheology. We then restrict our analysis to the classical cases of a Kelvin-Voigt and Maxwell model, which are relevant to soft gels and polymer fluids, respectively. We compute the complex frequencies, which are characterized by an oscillation frequency and decay rate, as they depend upon the dimensionless elastocapillary and Deborah numbers and map the boundary between regions of underdamped and overdamped motions. We conclude by illustrating how our theoretical predictions for the frequency-response diagram could be used in conjunction with drop-oscillation experiments as a "drop vibration rheometer", suggesting future experiments using either ultrasonic levitation or a microgravity environment.

Elastocapillary Transition in Gel Drop Oscillations

We report experimental observations of surface oscillations in an ultrasoft agarose gel drop. Ultrasonic levitation is used to excite shape oscillations in the gel drop and we report the natural frequency of the drop as it depends upon a nondimensional elastocapillary number, which we define as the ratio of the elastocapillary length to drop size. Our experiments span a wide range of experimental parameters and we recover the appropriate scaling laws in the elastic and capillary wave limits. The crossover between these two limits is observed and agrees well with a proposed frequency relationship.

Monitoring of blood coagulation with non-contact drop oscillation rheometry

BACKGROUND

Thromboelastography is widely used as a tool to assess the coagulation status of critical-care patients. It allows observation of changes in the material properties of whole blood brought about by clot formation and clot lysis. However, contact activation of the coagulation cascade at surfaces of thromboelastographic systems leads to inherent variability and unreliability in predicting bleeding or thrombosis risks, while also requiring large sample volumes.

OBJECTIVES

To develop a non-contact drop oscillation rheometry (DOR) method to measure the viscoelastic properties of blood clots and to compare the results with current laboratory standard measurements.

METHODS

Drops of human blood and plasma (5-10 μL) were acoustically levitated. Acoustic field modulation induced drop shape oscillations, and the viscoelastic properties of the sample were calculated by measuring the resonance frequency and damping ratio.

RESULTS

DOR showed sensitivity to coagulation parameters. An increase in platelet count resulted in an increase in the maximum clot stiffness. An increase in the calcium ion level enhanced the coagulation rate prior to saturation. An increase in hematocrit resulted in a higher rate of clot formation and increased clot stiffness. Comparison of the results with those obtained with thromboelastography showed that coagulation started sooner with DOR, but with a lower rate and lower maximum stiffness.

CONCLUSIONS

DOR can be used as a monitoring tool to assess blood coagulation status. The advantages of small sample size, the lack of contact and small strain (linear viscoelasticity) makes this technique unique for real-time monitoring of blood coagulation.

Opto-mechanical oscillator in a nanoliter droplet

Droplets are very simple physical systems, whereby surface tension shapes liquids into ideal opto-mechanical devices. This has recently enabled low-viscosity liquid samples to serve as miniature acoustic resonators harnessing optical generation of bulk vibrations, capillaries, or surface waves. Uniquely, a simple room-temperature pendant droplet can be activated as a hypersound-laser emitter when illuminated by a free-space, low-power visible laser thanks to stimulated Brillouin scattering of optical and acoustic whispering-gallery modes. Here, we demonstrate continuous operation of a liquid polymer opto-mechanical resonator and characterize its quality factor and long-term frequency stability. Our results point to the feasibility of all-liquid micro-mechanical oscillators working in the 50-100 MHz range. The stimulated generation of high-quality surface waves on nanoliter droplets gives momentum to new optical schemes for characterization of material viscous-elastic properties, laboratory investigation of atmospheric phenomena, and mass sensing for direct analysis of biological fluids based on ultrasound-hypersound coherent generation and detection.

Optovibrometry: tracking changes in the surface tension and viscosity of multicomponent droplets in real-time

An instrument was developed for measuring real time changes in the surface tension and viscosity of multicomponent droplets of miscible liquids and other soft materials. Droplets containing glycerol and water were supported on superamphiphobic surfaces and vibrated by applying a short mechanical impulse. Laser light was refracted through the droplets and allowed to fall on the surface of a photodiode. Time dependent variations in the intensity measured by the photodiode during vibration were used to monitor the decay of the droplet oscillations. The frequencies and spectral widths of the droplet vibrational resonances were then obtained from Fourier transforms of these time dependent intensity signals. A recently developed model of viscoelastic droplet vibration was used along with these values and measurements of the drop dimensions to extract the surface tension and viscosity of the drops as they evaporated. Collection of data was automated and values of frequency, spectral width, drop size, surface tension and viscosity were obtained with a time resolution of three seconds over a period of thirty minutes. The values of surface tension and viscosity obtained were shown to be in good agreement with literature values obtained from bulk glycerol/water solutions; thus validating the technique for wider application to other multicomponent liquids and soft matter systems.

Rheological Properties of Viscoelastic Drops on Superamphiphobic Substrates

The rheological properties of microliter sized drops of polymer solutions were investigated using measurements of their mechanical vibrational response. Drops were suspended on superamphiphobic substrates and vibrated by the application of a short mechanical impulse. Surface vibrations were monitored by refracting laser light through the drops and focusing the refracted light onto the surface of a photodiode. Time dependent variations in the photodiode output were Fourier transformed to obtain the frequency and spectral width of the mechanical resonances of the drops. These quantities were related to the frequency dependent shear storage and loss moduli (G' and G″, respectively) using a simple theoretical model. The resulting rheological properties were found to be in agreement with microrheology measurements of the same solutions. Drop vibration therefore provides a fast and accurate method of quantifying the rheological properties of single drops.

Mechanical vibrations of pendant liquid droplets

A simple optical deflection technique was used to monitor the vibrations of microlitre pendant droplets of deuterium oxide, formamide, and 1,1,2,2-tetrabromoethane. Droplets of different volumes of each liquid were suspended from the end of a microlitre pipette and vibrated using a small puff of nitrogen gas. A laser was passed through the droplets and the scattered light was collected using a photodiode. Vibration of the droplets resulted in the motion of the scattered beam and time-dependent intensity variations were recorded using the photodiode. These time-dependent variations were Fourier transformed and the frequencies and widths of the mechanical droplet resonances were extracted. A simple model of vibrations in pendant/sessile drops was used to relate these parameters to the surface tension, density and viscosity of the liquid droplets. The surface tension values obtained from this method were found to be in good agreement with results obtained using the standard pendant drop technique. Damping of capillary waves on pendant drops was shown to be similar to that observed for deep liquid baths and the kinematic viscosities obtained were in agreement with literature values for all three liquids studied.

Artificial tektites: an experimental technique for capturing the shapes of spinning drops

Determining the shapes of a rotating liquid droplet bound by surface tension is an archetypal problem in the study of the equilibrium shapes of a spinning and charged droplet, a problem that unites models of the stability of the atomic nucleus with the shapes of astronomical-scale, gravitationally-bound masses. The shapes of highly deformed droplets and their stability must be calculated numerically. Although the accuracy of such models has increased with the use of progressively more sophisticated computational techniques and increases in computing power, direct experimental verification is still lacking. Here we present an experimental technique for making wax models of these shapes using diamagnetic levitation. The wax models resemble splash-form tektites, glassy stones formed from molten rock ejected from asteroid impacts. Many tektites have elongated or ‘dumb-bell' shapes due to their rotation mid-flight before solidification, just as we observe here. Measurements of the dimensions of our wax ‘artificial tektites' show good agreement with equilibrium shapes calculated by our numerical model, and with previous models. These wax models provide the first direct experimental validation for numerical models of the equilibrium shapes of spinning droplets, of importance to fundamental physics and also to studies of tektite formation.