Session L19: Micro/Nano Flow: Solid/Liquid Interface

Capillary flow in open rectangular microchannels with surface modification

Capillary flow in microchannels is important for many technologies such as microfluidic devices, heat exchangers, and fabrication of printed electronics. Due to a readily accessible interior, open rectangular microchannels are particularly attractive for these applications. Here, we develop modifications of the Lucas-Washburn model to explore how a spatially varying contact angle influences capillary flow in open rectangular microchannels. Four cases are considered: (i) different uniform contact angles on channel sidewalls and channel bottom, (ii) contact angle varying along channel cross section, and (iii) contact angle varying monotonically along channel length, and (iv) contact angle varying periodically along channel length. For case (i), it is found that the maximum filling velocity is more sensitive to changes in the wall contact angle. For case (ii), the contact angles can be averaged to transform the problem to that of case (i). For case (iii), the time evolution of the meniscus position no longer follows the simple square-root law at short times. Finally, for case (iv), the problem is well described by using a uniform contact angle that is a suitable average. These results provide insight into how to design contact-angle variations to control capillary filling, and into the influence of naturally occurring contact-angle variations on capillary flow.   

Capillary imbibition in lubricant-coated channels

We present a theoretical and computational analysis of the  imbibition in a lubricant-coated pore. This simplified, schematic geometry is relevant for slippery liquid-infused porous surfaces (SLIPS) and lubricant-impregnated surfaces (LIS), where a lubricant film eliminates direct contact of the invading and displaced fluids with the solid. The study has clarified the relevance of the asymmetric distribution of dissipation among the  fluid phases in the imbibition process.  We identify two well defined spontaneous imbibition regimes: if dissipation is  more relevant in the displacing liquid, we recover the  diffusive advancing of the front corresponding to the well-known limit in which there is no lubricant. On the contrary, if dissipation takes place preferentially on the lubricant liquid, we find a linear advancing of the front through the entire channel

We present a  simplified mathematical model  that  captures these limiting regimes and quantifies the crossover between them. The model build on  a recent theoretical framework that identifies the relevant advancing regimes both for spontaneous and forced imbibition, as well as the corresponding crossovers.

This work provides a combined simulational and theoretical approach that paves the way into further scenarios of similar materials like lubricant-infused surfaces.  

    

Pinning and its role in the control of droplet motion on solid substrates

Pinning of liquid droplets on solid substrates is ubiquitous and plays an essential role in many applications, especially in various areas such as microfluidics and biology. Although pinning can often reduce the efficiency of various applications, a deeper understanding of this phenomenon can actually offer possibilities for technological exploitation. Here, by means of molecular dynamics simulation, we identify the conditions that lead to droplet pinning or depinning and discuss the effects of key parameters in detail, such as the height of the physical pinning barrier and the wettability of the substrates. Moreover, we describe the mechanism of barrier crossing by the droplet upon depinning, identify the driving force of this process, and, also, elucidate the dynamics of the droplet. Not only does our work provide a detailed description of the pinning and depinning processes but also it explicitly highlights how both processes can be exploited in nanotechnology applications to control the droplet motion. Hence, we anticipate that our study will have significant implications for the nanoscale design of substrates in micro- and nanoscale systems and will assist with assessing pinning effects in various applications.   

Quantifying heat transfer trade-offs related to fluid-solid interfaces with nanoscale texturing

Tailoring the thermal transport properties across fluid-solid interfaces has broad impacts on thermal management in a wide range of electronic and biomedical applications. In this work, we study the role that nanoscale texturing of the fluid-solid interface plays on heat transfer across a nanofluidic device. We perform molecular-dynamics (MD) simulations of a simple fluid, investigating thermal transport properties as a function of surface patterning and fluid thermodynamic conditions. We show that patterning can induce solid-like structure and dynamics in the vicinity of the fluid-solid interface, thereby shifting the vibrational modes supported by fluid in the vicinity of the interface and reducing interfacial thermal resistance. However, in contradistinction to classical fin theory, we demonstrate that nanoscale fins do not necessarily improve the overall heat transfer coefficient across a nanofluidic device employing these fins. We rationalize this observation by considering the role of surface patterning on the thermal conductivity of a thin film. We present a thermal resistance network analysis that highlights the operating conditions under which nanoscale fins can lead to improved thermal transport across a nanofluidic device.   

Microscopic insights into the onset of slip in Lennard-Jones fluids

The phenomenon of hydrodynamic slip of simple fluids at a fluid-solid interface is well-described by Molecular-Kinetic Theory (MKT), which relates slip velocity to the fluid shear rate and various thermodynamic and fluid-specific parameters. In this work, we perform extensive molecular-dynamics (MD) simulations of slip in fluids consisting of Lennard-Jones chains of varying lengths, with the goal of elucidating the role played by a kinetic length scale that is present within the MKT formalism. By performing non-linear model fits to our MD data, we demonstrate that MKT is a strong candidate to describe slip in Lennard-Jones chains. In particular, we show that the onset of slip varies as a function of chain length and molecular weight, which we rationalize in terms of the MKT framework. We close by briefly comparing our results with experimental studies of hydrodynamic slip in polymeric liquids.   

The Molecular Origin of Slip

Liquid flow adjacent to a solid surface can slip resulting in a finite liquid velocity at the solid/liquid interface. However, how this liquid slip occurs is poorly understood. Here, we study liquid films driven over a solid surface. We show that slip over the surface is not simply the result of independent molecular hops over the solid substrate. Rather, much of the velocity at the solid/liquid interface results from correlated motion of several molecules which propagate as nonlinear waves similar to solitons. Solitons are fundamentally important in the fluid mechanics of slip. Understanding their dynamics may suggest new methods of designing low drag surfaces and new technologies for chemical separations.

    

Experimental study of fluid slip on drag reducing polymeric surfaces patterned by CO2 laser system

Lotus leaf bio-inspired drag reducing surfaces have been a topic of interest

for many researchers due to their application in field of anti-icing, self cleaning, drag

reducing surfaces. The aforementioned surfaces achieve their low surface drag by

reducing contact between solid and liquid by using micro-structures that trap air

between the structures and allow fluid to flow over them with reduced shear. So far

the application of these surfaces in various fields are well known along with the drag

reducing mechanism. However, when it comes to fabricating these micro-patterned

surfaces artificially, the techniques used like photolithography, dry reactive ion

etching (DRIE) etc), are quite cumbersome and require many additional resources. This

limits the use of these drag reducing surfaces to just the laboratory environment and

hence, there is a need to find fabrication method that would allow for much simpler and

faster fabrication of drag reducing surfaces. To solve this problem, we use CO₂ laser

system and micro-patterned polymer surfaces. CO₂ laser system fabrication method

is a single step surface patterning method that allows for both easy and large scale

production of these surfaces. Combined with low surface energy of polymeric

surfaces, drag can be reduced dramatically.   

Slipping on grooves: an analytic study of flow over liquid-infused surfaces (LIS)

We describe the construction of explicit solutions to a two-phase fluid problem relevant to modelling flow over a liquid-infused surface. In the longitudinal configuration, these surfaces typically comprise a periodic array of fluid-filled grooves in a no-slip surface over which flows a different working fluid. The fluid-filled grooves help to lubricate the flow of the working fluid leading to useful reduction in viscous drag. This drag reduction is quantified by explicit formulas for the slip length extracted from the analytical solutions. The case where the fluid filled grooves are closed, perhaps using ``baffles'', causing a back-pressure that deforms the fluid-fluid interface, is also analyzed.

    

A multiscale model to describe the wetting of solid surfaces

Interface properties between liquids and solids determine the adhesion, friction, and wettability response of surfaces in various applications of engineering interest. However, the multiscale nature of these phenomena limits bottom-up prediction of the resulting surface properties.

In this work, we use computational experiments to characterize solid surfaces and reproduce the dynamics of a droplet on a surface. First, we adopt molecular dynamics simulations to compute the work of adhesion (Wad), solid-liquid interface tension (γsl), and slip length using the free energy perturbation (FEP) approach and the Green-Kubo relation, respectively. The obtained results are validated against experiments and then used as boundary conditions for a continuous model based on the phase field method in terms of the wetted wall and friction coefficient in the Navier slip. We explore the impact and spread of the droplet on the surface and compare the results with experiments.

This numerical approach allows us to understand and decouple the different mechanisms governing the wetting properties of solid surfaces. The goal is to propose a multiscale framework for the computational characterization of surfaces, which is necessary for the optimal design of materials with tailored surface properties.   

How to reconcile non-equlibrium with equilibrium measurements of slip length

We show that slip measurements in molecular dynamics simulations using non-equilibrium and equilibrium (Green-Kubo) methods can be reconciled by properly accounting for the hydrodynamic wall location. The latter is an integral part of the Green-Kubo (GK) formulation and denotes the location at which the slip boundary condition is to be applied, typically inside the fluid. In contrast, non-equilibrium methods measure the slip at the fluid-solid interface. Although GK expressions for calculating the hydrodynamic wall location have been developed, statistical noise as well as the lack of a well-defined plateau in the associated GK integral has made them imprecise and cumbersome to use, and as a result, led to their neglect. Unfortunately, the distance between the actual and the hydrodynamic wall location can be sufficiently large that if their difference is not taken into account, the equilibrium and non-equilibrium measurements appear to diverge. Here we propose an alternative approach for calculating the hydrodynamic wall location that is not subject to the above limitations. Extensive molecular dynamics simulations are used to validate our approach.