Fluid Mechanics and Waves Seminar - Spring 2021

February 16

Ofer Manor, Chemical Engineering, Technion – Israel Institute of Technology, Haifa, Israel

*Special Seminar: Tuesday, 11:00 AM*

Strange Dynamics of Wetting

The dynamic wetting of a solid or a liquid body by another liquid is an abundant mechanism, traversing applications in coating, mass deposition, drying, micro- and nano-fluidics, and biology -- most notably in the lungs and eyes. Here, I will use both experiment and theory to show and explain strange wetting effects in two systems: The first is the convective pattern deposition of polymer from a volatile solvent. The second is the climb of liquid against gravity in the presence of surface acoustic waves.

I will commence the seminar by considering recent experimental and theoretical work on the convective pattern deposition of polymer (polymethylmethacrylate) from a volatile toluene solvent in a micro-chamber. Similar processes are employed nowadays for the fabrication of simple macro- and micro-electronic platforms and for the identification of biological and chemical agents. The evaporation of the solvent gives rise to the receding motion of the meniscus between the polymer solution and vapor phase in the chamber. During this dynamic event, the meniscus is known to undergo slip or stick-slip motions, which monotonically de-wet the solid substrate, and leave behind a smooth coating or repeating patterns of the polymer. We show that under a certain parametric regime the motion of the meniscus becomes more complicated. The meniscus undergoes a periodic wetting-dewetting motion. This newly found motion of the meniscus in this system is a product of mass conservation and Marangoni flow. 

I will further consider the climb of silicon oil and aqueous surfactant solutions on a vertical substrate from a reservoir in the presence of a MHz-frequency surface acoustic wave (SAW). The process is reminiscent of the Landau-Levich coating (or dip coating procedure), which is widely employed in the industry; albeit, in our case, instead of the liquid coating a moving substrate, the liquid is pulled onto a static substrate by the acoustic wave. I will show that a balance between capillary, acoustic, and gravitational forces support the climb of partially wetting aqueous solutions onto the substrate to a finite height. Silicon oil films, who fully wet the substrate (vanishing three phase contact angle), climb the vertical substrate continuously in what appears to be a complete disregard of gravity. We will show that acoustic resonance effects in the nearly flat oil films balance the contribution of gravity, which let the oil spread over the substrate as if the latter was horizontal.

March 1

Siddhartha Das, Department of Mechanical Engineering, University of Maryland, College Park

Ionics and Electroosmosis at Polyelectrolyte-Brush-Functionalized Interfaces

Functionalizing solid-liquid interfaces by grafting them with polyelectrolyte (PE) molecules (which are long and charged polymer molecules) has been extensively employed for multiple applications ranging from drug delivery and oil recovery to sensing, water harvesting, and fabrication of nanofluidic diodes and transistors. Polymers and polyelectrolytes (PEs), when grafted on the solid-liquid interfaces at close-enough separation, attain “brush”-like configuration resembling the bristles of a toothbrush. Over the past four decades, fundamentals and applications of such polymer and PE-brush-grafted interfaces have been extensively probed. 

In this talk, I shall present all-atom Molecular Dynamics (MD) simulation-based exploration of the structure, ionics, and electroosmotic flows (electric-field-driven flows) at interfaces grafted with such PE brushes. First, I shall present unexplored details of PE-brush-supported counterions and water molecules resolved across atomistic scales. Ultraconfinement effect (introduced by the densely grafted PE brushes) induced massive reduction in the mobility of these counterions and water molecules will be discussed. Furthermore, the onset of the remarkable water-in-salt–like scenarios, where the water molecules in the hydration shell of the counterions get replaced by the negative functional group of the PE brushes, will be discussed. 

Second, I shall discuss the PE brush structure and the properties of the brush-supported water molecules and counterions for the case where the brushes are grafted to the walls of a nanochannel and there is an external salt. The discovery of the overscreening (OS) within the PE brush layer, caused by an interplay of nanoconfinement and counterion sizes, will be discussed. 

Finally, I shall discuss how in presence of an external electric field this OS effect can be leveraged to trigger highly non-intuitive nanoscale electroosmotic (EOS) liquid flows. At smaller electric fields, the OS effect is retained leading to a larger concentration of coions in the bulk and an EOS transport in the direction of coion migration. At larger electric fields, on the contrary, the brush height reduces, the OS effect disappears, and the EOS transport occurs in the direction of migration of the Na+ ions. This also implies a remarkable reversal in the direction of the EOS transport by merely changing the strength of the applied electric field. 

WebEx Recording - 3/1/21

March 29

Joseph Cousins, School of Mathematics & Statistics, University of Strathclyde

Governing Equations and Solution Multiplicities for a Static Ridge of Nematic Liquid Crystal

Technological interest in nematic liquid crystal (nematic) droplets and films includes their applications for liquid crystal display manufacturing [1,2] and emerging technologies, such as microfluidics [3], adaptive lenses [4], and microelectronics [5].  Many of these complicated multiphase systems involve interfaces between the nematic, a solid substrate, and a passive gas, and include nematic--solid--gas three-phase contact lines. Theoretical studies of these systems often use well-established theories of Newtonian droplets and films [6], which fail to account for the non-Newtonian nature of nematics.

Motivated by a desire to increase understanding of nematic droplets and films, we use constrained energy minimisation of the nematic Oseen--Frank and Rapini--Papoular energy densities [1] to formulate and analyse the full governing equations for a static sessile two-dimensional ridge of nematic. We then consider the special case of a thin symmetric ridge, for which we obtain insight into the multiplicity of solutions for the free surface height and the nematic molecular orientation. In particular, depending on the values of material parameters, we find solutions for the free surface height and the nematic molecular orientation with uniform molecular orientations, with partially distorted molecular orientations, with completely distorted molecular orientation, and a wetting solution for which the nematic wets the solid substrate completely. Our findings allow us insight into the behavior of nematic droplets and films and provide a framework for future investigations.

April 12

Florencio Balboa Usabiaga, Basque Center for Applied Mathematics

Rheotaxis and Gravitaxis of Artificial Swimmers

Microorganisms have evolved to thrive in complex environments and to react to external signals such as flows, light or chemical gradients. Despite the internal complexity of the microorganisms their response to some signals, like shear flows or gravity, can be explained by simple mechanical arguments. In fact, it is possible to fabricate artificial micro-swimmers that perform rheotaxis or gravitaxis. In this seminar I will describe some experiments with phoretic particles swimming on inclined planes or under shear flows and I will show that rheotaxis and gravitaxis is strongly facilitated by interactions with solid boundaries, allowing even heavY microswimmers to climb nearly vertical surfaces or swim against strong flows.

To understand the experimental results we will use simple mathematical models and sophisticated simulations. In particular, I will introduce a robust and versatile numerical method to simulate active particles immersed on Stokes flows. Our method, well suited for many particles simulations of arbitrarily shaped colloids, is equivalent to a regularized Boundary Integral Method with the advantages that it can deal with Brownian noise and active flows easily.

April 26

Sean Carney, Department of Mathematics, UCLA

Low-Mach Number Fluctuating Hydrodynamics Model for Ionic Liquids

An ionic liquid is a liquid salt with dissociated cations and anions such as molten NaCl. Of particular interest are ionic liquids composed of complex hydrocarbons that are high-viscosity liquids at room temperature. These room temperature ionic liquids (RTILs) can exhibit intriguing physical properties useful in applications such as super-capacitors, batteries, photoelectrochemical cells, and microelectromechanical lubricants. RTIL dynamics are governed by the thermodynamic competition between electrostatic forces, interfacial tension, and short range cation-anion repulsion due to the ions’ complex molecular structures. This competition is quantified by a Gibbs free energy functional from which we derive a PDE model of RTILs. The inviscid hydrodynamics and electrostatics can be derived from the calculus of variations, while the evolution equation for ion concentration and the viscous hydrodynamic force density are derived from the Onsager reciprocal relations of nonequilibrium thermodynamics. The PDEs are further augmented with white noise flux terms modeling thermal fluctuations intrinsic to fluid mixtures at mesoscopic length scales, and a low Mach number formulation is utilized to analytically remove sound waves from the equations of motion based on the assumption that they are relatively unimportant to the system dynamics.

After calibrating the strength of the short range repulsive term based on a stability analysis of the concentration equation, we numerically demonstrate the formation of mesoscopic structuring at equilibrium in two and three dimensions. In simulations with electrode boundaries the measured double layer capacitance decreases with voltage, in agreement with theoretical predictions and experimental measurements for RTILs. Finally, we present a shear electroosmosis example to demonstrate that the methodology can be used to model electrokinetic flows.

April 12, 2021