Session Q18: Fluids IX

Enhancing and visualising mixing between impacting droplets

Ways to efficiently mix the fluids of subsequently-deposited droplets are urgently needed to unlock the burgeoning potential of droplet-based applications such as reactive inkjet printing and open microfluidics. In our previous work, we demonstrated the potential of Marangoni flow to stretch & fold internal fluid interfaces between coalescing droplets of simple fluids, and therefore induce good advective mixing. Now, by combining color high-speed imaging with a passive color-change reaction that highlights mixed regions, we can probe (diffusive) mixing dynamics and assess the true extent of mixing. Furthermore, we use this new tool to demonstrate how surfactants can be employed as an additive to impart Marangoni flow by modifying the dynamic surface tension of coalescing droplets without changing the underlying fluid. This development offers a way to efficiently mix droplets in applications where the underlying functional fluid (e.g. a particular chemical reactant) should be maintained.

    

Stability of dynamic contact lines in three dimensions

The wetting or dewetting of a solid surface by a viscous fluid is a pervasive phenomenon in nature, and also one of industrial importance for a wide range of coating applications. The macroscopic flow is strongly influenced by the wetting dynamics of the three-phase contact line which separates the wet and dry regions of the substrate. It is well known (Snoeijer 2013) that there is a critical capillary number, Ca_crit above which the contact line is linearly unstable to shape perturbations; in the wetting case (an advancing contact line) this leads to air entrainment, and in the dewetting case (a receeding contact line) this leads to thin-film formation. It has been recently shown (Keeler 2022) that, in two-dimensions, a fold bifurcation occurs at Ca_crit where the branches of the stable and unstable steady states, which coexist below Ca_crit, meet. In this study we extend this work into three dimensions, using, as a starting point, a "Landau-Levich" geometry in which a vertical plate is withdrawn or inserted into a bath of viscous fluid. We explore the dynamic wetting transition and its bifurcation structure through a combination of a semi-analytic linear stability analysis and full-scale direct numerical simulation, and investigate the formation dynamics of three-dimensional structures at and behind the receding contact line.

    

Universality and versatility of surfactant self-assembly in liquid-in-liquid 3D printing of soft matter

Despite low viscosity and lack of required mechanical properties in soft materials, the newly emerged liquid-in-liquid 3D printing approach has enabled the fabrication of predefined architectures from these otherwise non-printable materials. In a specific group of liquid-in-liquid 3D printing, surface active components such as surfactants have proved to be the enabling factor for printing stable aqueous structures within a hydrophobic surface-active oil phase. Furthermore, the underlying ternary phase diagram that is established using both experimental and simulation techniques reveals that the geometrical transition in nanostructures (from micellar to lamellar) has enabled the stabilization of printed constructs. In this work, the versatility and universality of this printing platform are illustrated through the use of various surfactant classes (cationic, ionic, nonionic, and zwitterionic). The constructs 3D printed using all these surfactants not only show relatively high complexity in design and structural characteristics but also demonstrate other practical features such as perfusibility and self-healing properties. Furthermore, using both experimental (small-angle X-ray scattering and interfacial/bulk rheometry) and computational (mesoscale simulation) techniques, the underlying mechanism (i.e., morphology transition at the liquid-liquid interface) for all systems with different surfactants is explored. Lastly, various printing patterns are achieved by taking into account the dynamics of the printing system and tuning printing parameters. The implications of this work lie in the freedom to use various surfactants with different molecular structures and properties, which in combination with practical features and complexity of prints, opens up new opportunities for liquid-in-liquid 3D printing techniques in various fields, including bioelectronics, tissue engineering, and drug delivery systems.

    

Dynamic Measurements of sub-nL/min flows with an optofluidic flowmeter

With the increasing prevalence and miniaturization of microfluidic systems, there is a pressing need for reliable flow rate measurements at the nL/min level. State-of-the-art flowmeters can measure 100 nL/min flows with 1% uncertainty but face fundamental limits at lower flow rates due to evaporation and lack of detailed knowledge of system geometry. We have developed an optofluidic flowmeter which directs laser light into a microfluidic channel and monitors the photobleaching of a fluorophore in the fluid. The amount of photobleaching scales inversely with the flow rate. We demonstrate that this device can measure sub-nL/min flows in real-time with less than 5% uncertainty without any detailed knowledge of the channel geometry or photobleaching physics. The precision of the flowmeter is limited only by the requirement that the Peclet number be >> 1, so increasingly low flows can be measured by reducing the channel dimensions or increasing the diffusion coefficient of the fluorophores. We study the dynamic response of the flowmeter to characterize its time resolution under a variety of conditions. Finally, we use the flowmeter to measure flows induced by electrospray ionization from glass capillaries with different tip diameters, demonstrating that a distinct emission mechanism is responsible for the current generated from nanoscale capillaries.

    

Time-averaged dynamics of rigid and elastic particles in oscillatory flow

Oscillatory flows are powerful tools for manipulating suspended particles and biological cells in microfluidic settings. In particular, soft biological cells may deform under the large oscillatory stresses typical of applications. We present a comprehensive theory of the dynamics of spherical particles suspended in oscillatory flow, including the effects of particle deformation, which are modeled through linear elasticity. The particle responds to the flow by producing a primary oscillatory disturbance, which is coupled with elastic deformations. The inertia of this primary flow drives a secondary disturbance that is near impossible to calculate. However, by applying the Lorentz reciprocal theorem, we are able to relate the secondary force on the particle with its time-averaged velocity using information of the primary (oscillatory) flow and elastic deformation only. We discuss how the density contrast between particle and fluid, the frequency of oscillation, and the stiffness of the particle influences its motion. For rigid particles, we show that the direction of particle motion can be reversed for certain combinations of frequency and density ratio. For elastic particles, the dynamics depend additionally on a dimensionless compliance that characterizes the ratio of elastic to viscous stresses. We find that the force-velocity relations are modified considerably from the strictly rigid case, even for modestly compliant particles. Finally, we apply the theory to compute the motion of rigid and compliant particles in some canonical oscillatory flows.   

Three-dimensional streaming around a cylinder in slender microchannels

When oscillatory flow is driven past an obstruction, its inertia produces a secondary steady flow known as streaming. Although streaming has been utilized in a variety of microfluidic applications, a systematic understanding of streaming in highly confined microfluidic environments remains missing. Here, we study three-dimensional streaming flows by conducting experiments involving a cylindrical obstacle sandwiched in a microchannel with one dimension (channel depth) much shorter than the other two dimensions. Notably, we find that the flow changes direction across the channel depth, distinct from previous observations of three-dimensional microstreaming flows. We understand the observations by applying inertial lubrication theory to solve the incompressible Navier-Stokes equations for small oscillation amplitudes. We show that for slender channels, the streaming is produced by Stokes layers at the confining top and bottom walls of the channel, and reverses direction to maintain zero channel-averaged flux. Finally, we use particle tracking measurements from the experiments of streaming around cylinders with different aspect ratios at different driving frequencies, and find a streaming speed that decays as the inverse cube of distance from the cylinder, in quantitative agreement with our theory. The agreement between our theory and experiments is promising for the control of three-dimensional flows in microfluidic particle trapping and micromixing applications.   

How much of the latent heat of melting is explained by vibrational dynamics?

Atomic vibrations dominate the entropy of solids and liquids. Less is known about the latent heat, L=T_mΔS, which is determined by the melting temperature, T_m, and the entropy of fusion, ΔS. Here, we used inelastic neutron scattering to probe changes in vibrations of Ge, Sn, Pb, Bi, and Zn on an energy scale of ~5-50 meV through the melt. Our analyses, informed by vibrational-transit theory and supported by machine-learned molecular dynamics simulations, show a distinct contribution of atomic dynamics for each element. In Ge, which has an anomalously high entropy of fusion, preliminary results show a vibrational component of ~50%. In Bi, Sn, Pb, and Zn, the role of atomic motion decreases approximately in accordance with the total entropy of fusion to a value of ~5%. We will discuss what these findings imply for the physics of melting by taking a decomposition of the latent heat into electronic, configurational, and vibrational components.   

Collective Diffusion of Multi-Component Liquids

The collective diffusion of simple liquids is understood in terms of thermal diffusivity in the hydrodynamic limit. However, the collective diffusion of multi-component liquids has not been reported, especially at the local molecular length scales where the continuous and isotropic symmetries are broken. We studied the collective diffusion of a series of liquids with an increasing number of constituents. By analyzing the structural and dynamic correlation functions of the systems, we revealed the role of mixing entropy and elemental fluctuations in determining the collective diffusion of multi-component liquids.   

Top-down approach to liquid structure

Conventional approaches to describe the structure of simple liquid and glass are bottom-up, starting with a cluster of an atom and its nearest neighbors, and add more atoms to build the structure. But this approach fails to explain the persistence of medium-range order (MRO), the exponential decay in the pair-distribution function beyond the first neighbors, even in liquids with complex chemistry. We propose to add to the bottom-up approach the top-down approach based upon the idea of density wave instability. The interatomic potential has a strongly repulsive part, but that part is irrelevant for liquid formation because atoms never come so close to each other. We define the pseudopotential Vp(r) for which the strongly repulsive part, where V(r) >> kT, is removed and Vp(r) = Vp(r_cutoff) is assumed below r_cutoff. Surprisingly, the Fourier transform of Vp(r), Vp(Q), has a deep minimum at a wavevector Q1, close to the first peak of the structure function S(Q). The value of Q1 does not depend strongly on the cutoff energy, Vp(r_cutoff). Thus, this minimum must be the consequence of shape resonance due to atomic exclusion. This minimum stabilizes the density wave state when the pseudopotential is applied to the high-density gas state in the reciprocal space. Because liquid is isotropic, the Q1 vectors are spherically distributed forming the Bragg sphere. The coherence length of the MRO increases with decreasing temperature, and when it extrapolates to infinity such a density wave state is realized. Thus, we suggest that the pseudopotential is driving the system to such a state. But this density wave state has poor short-range order. Therefore, the two driving forces, bottom-up and top-down, are in conflict to each other, and the MRO appears as a compromise. This dual approach explains various properties of liquid and glass, including fragility and viscosity.

    

Physics-informed Deep Learning for simultaneous Surrogate Modelling and PDE-constrained Optimization

We model the flow around an airfoil with a physics-informed neural network (PINN) while simultaneously optimizing the airfoil geometry to maximize its lift-to-drag ratio. The parameters of the airfoil shape are provided as inputs to the PINN and the multidimensional search space of shape parameters is populated with collocation points to ensure that the Navier-Stokes equations are approximately satisfied throughout. We use the fact that the PINN is automatically differentiable to calculate gradients of the lift-to-drag ratio with respect to the parameter values. This allows us to use the L-BFGS gradient-based optimization algorithm, which is more efficient than non-gradient-based algorithms. We train the PINN with adaptive sampling of collocation points, such that the accuracy of the solution is enhanced along the optimization trajectory. We demonstrate this method on two examples: one that optimizes a single parameter, and another that optimizes eleven parameters. The method is successful and, by comparison with conventional CFD, we find that the velocity and pressure fields have small pointwise errors and that the method converges to optimal parameters. We find that different PINNs converge to slightly different parameters, reflecting the fact that there are many closely-spaced local minima when using stochastic gradient descent. This method can be applied relatively easily to other optimization problems and avoids the difficult process of writing adjoint codes. As knowledge about how to train PINNs improves and hardware dedicated to neural networks becomes faster, this method of simultaneous training and optimization with PINNs could become easier and faster than using adjoint codes.   

Vibrational Properties Beyond Debye Model

The vibrational density of states (VDOS, denoted g(ω)) is a fundamental property of solid materials, determining the specific heat and thermal transport. For over 100 years, the Debye model has served the fundamental law for our understanding of the vibrational properties of bulk solid materials which show a low energy relationship of g(ω) ∝ ω², where ω is the frequency and g(ω) is the number of modes within an energy/frequency interval. Upon the transition from solid to liquid phase, the conventional stable phonon vibration modes in solid phase are replaced by more complex instable vibrational modes, called instantaneous normal modes (INM) at the liquid state. The INMs are consequences of the intrinsic anharmonic interaction potentials among the atoms in liquid phase. Due to the complicated potential landscape, it has been very difficult to analytically describe the vibrational phonon density of states (VDOS) of liquids until very recently.  Zaccone and Baggioli [1] have recently developed a theoretic model based on overdamped Langevin liquid dynamics. Distinct from the Debye law, g(ω) ∝ ω², for solids, the model for liquids reveals a linear relationship, g(ω) ∝ ω, in the low-energy region. With inelastic neutron scattering, we confirmed this model on real liquid systems including water, liquid metal, and polymer liquids. We have applied this model and extracted the effective relaxation rate for the short time dynamics for these liquids [2].

 

[1]. A. Zaccone and M. Baggioli, Proc. Natl. Acad. Sci, USA 118, e2022303118 (2021).

[2]. C. Stamper, D. Cortie, Z. Yue, X. L. Wang and D. H. Yu, J. Phys. Chem. Lett. 13, 3105 (2022).   

X-ray free-electron laser heating of water at picosecond time-scale

Split-pulse X-ray photon correlation spectroscopy using X-ray free-electron laser is a promising tool to probe atomic dynamics in liquid and soft-matter in pico-second timescale, which has been accessible only by spectroscopy. However, sample heating by X-ray beam is a major obstacle for this technique. Using molecular dynamics and the two-temperature model we examine the atomic level response of water to X-ray laser pulse and compare with recent experiments. We investigate the effects of the sample heating and the heat dissipation on the structure and dynamics of water through the atomic density correlation and the dynamic structure factor. Our results indicate, in agreement with experiment, that, in addition to the beam energy, the time delay between the two pulses is a critical factor for obtaining reliable information on the atomic level dynamics of water. 

    

Band gap formation in internal gravity waves propagating in periodically stratified fluids

In the ocean, the interplay between heat diffusion and salt diffusion can drive double diffusive instability and lead to the formation of spatially periodic density profiles. These periodic structures, called thermohaline staircases, can persist over large regions and have also been suggested to exist in astrophysical bodies, such as in giant planet interiors. In this talk, we show that such periodically stratified fluids can host internal gravity waves with properties reminiscent of photonic crystal and topological insulator physics. Combining experimental, numerical and analytical modeling, we show the formation of band gaps and surface states that are exponentially localized near interfaces and controlled by boundary conditions. We also find that these internal wave states are robust to perturbations and can be observed in numerical simulations performed with geophysical stratification profiles from the Arctic Region. Our results suggest that energy transport by internal waves could be profoundly altered by the presence of periodic stratifications naturally occurring in the ocean, and could therefore influence large-scale circulation patterns.   

Velocity distributions of inelastically interacting ice floes driven by stochastic winds

The motion of sea ice on the ocean surface is driven primarily by stochastic winds and is resisted by water drag. However, observations show that the velocity distribution of sea ice is much broader than that of the driving winds. Here, we identify the quantitative mechanistic underpinnings of this observation by developing a stochastic dynamics framework of interacting ice floes. We model the wind as the superposition of a mean and a normally distributed single-correlation-time noise. This wind drives a dynamical system for the motion of sea ice floes that interact with each other through inelastic collisions. Through numerical particle-dynamics simulations, we find that the broadened velocity distribution of the ice is a direct and generic consequence of collisions. We rationalize these numerical results by developing a coarse-grained kinetic theory based on the Boltzmann equation for granular flows with drag, leading to analytic expressions for the velocity distributions. Extracting all physical inputs to the model from observational data, we show that both the simulations and the kinetic theory are in good quantitative agreement with observations of ice in the Fram Strait.   

Flowing fibers in the presence of obstacles: toward a sorting device

Flowing suspensions of rigid and flexible particles in structured media are encountered in many biological and industrial systems. The motion of the particles results from the complex interplay between the surrounding flow, internal elastic forces, as well as hydrodynamic and steric interactions with obstacles. In this work, we study numerically and experimentally the dynamics of flexible and rigid fibers interacting with triangular obstacles in a microchannel. We identify various types of fiber trajectories around a single obstacle depending on their mechanical and geometrical properties. Long and rigid fibers are found to be more laterally shifted in the presence of obstacles while short and flexible fibers tend to remain on the same streamline with no visible deviation. In the rigid case, the trajectories are highly sensitive to the initial orientation of the fibers. We also show that the channel height and width strongly affect the flow field around the obstacle, and therefore the fiber motion. We finally suggest how these findings could be used to optimize a microfluidic device to sort fibers by length and/or deformability.