Session MN: Micro Fluids VI

Study on the rise time of electroosmotic flow in microcapillary tubes

We studied the rise time of electroosmotic flow (EOF) in microcapillary tubes using laser induced fluorescence photobleaching anemometer (LIFPA) developed recently. This method can measure flow velocity with high temporal resolution. Theoretical estimation of the rise time of EOF is in the order of O(10$^{-7})$ s. However, to our knowledge, this has never been experimentally validated. We leverage the high temporal resolution of the LIFPA to measure the rise time of EOF. For a microcapillary tube of 50 microm inner diameter and 50 mm long, with a neutral dye in methanol, the initial data shows that the rise time of EOF under a pulsed electric field, is in the order of O(10$^{-4})$ s, much longer than theoretical prediction. Possible influence of different parameters such as tube diameter, length, electric field, buffer concentration, on the rise time of EOF has been studied as well.   

Break-up of drops in microfluidic T-junction

We propose a mechanism of droplet break-up in a symmetric microfluidic T-junction driven by pressure decrement in a narrow gap between the droplet and channel wall. This mechanism works in a two-dimensional setting where the capillary (Rayleigh- Plateau) instability of a cylindrical liquid thread suggested earlier [Phys. Rev. Lett. 92, 054503 (2004)] as the cause of break-up is not operative, but is likely to be responsible for the breakup also in three dimensions. We derive a dependence of the critical droplet extension on the capillary number Ca by combining a simple geometric construction for the interface shape with lubrication analysis in a narrow gap where the surface tension competes with viscous drag. The theory, formally valid for Ca$^{1/5}<<1$, shows a very good agreement with numerical results when it is extrapolated to moderate values of Ca.   

Multilayer Liquid Spreading on Superhydrophilic Nanostructured Surfaces

Superhydrophilic surfaces with nanoengineered structures have received recent interest due to the ability to manipulate fluids for applications in thermal management and microfluidics. However, the interactions of the liquid and nanostructures are complex, and unique wetting behavior on such surfaces exists. In this work, we investigated the spreading of water on silicon nanostructures with diameters ranging from 500 nm to 800 nm, separated by spacings of 500 nm. During the spreading process, the liquid was consistently separated into multiple layers of varying thicknesses. Experimental characterizations were performed to determine the thickness of the layers and a model based on surface energy minimization was developed to obtain increased understanding of the observed phenomenon. The model suggests that energy barriers from the scalloped side walls of the nanostructures, which were created by the deep reactive ion etching fabrication process, lead to disruptions in the spreading of the liquid film. A relationship between geometry and the energy barriers was obtained, which provides insight and opportunities to control the thickness of the liquid layers for a variety of microfluidic systems.   

Intrinsically Pulsating Electrohydrodynamic Cone-Jets

When the flow rate of an electrohydrodynamic cone-jet is self-regulated, the jet typically pulsates intrinsically due to the imbalance between the liquid supplied to the cone and that discharged through the jet. We used high-speed microscopic imaging and oscilloscopic current measurements to characterize these intrinsic pulsations. The measured kHz-range pulsation frequency compares favorably to a model we developed drawing an analogy between pulsating cone-jet on a supported meniscus and that on an isolated charged drop. The scaling law is expected to be applicable to electrohydrodynamic drop formation and miniaturized electrospray systems.   

Between microdroplets and microfluidics: Liquid/liquid interfaces do not brake up at a junction of hydrophilic microchannels

The intermediate state between microdroplets and microfluidics in two immiscible fluids is described. It was found that Y-shaped two-phase flow is formed with a stable liquid/liquid interface at a cross-junction in a hydrophilic microchannel. A velocity vector map, obtained by micro-particle image velocimetry, reveals the Y-shaped flow consists of aqueous phase flow along the edge of the channel and an acrylate monomer phase flow penetrating the center. The transition from the Y-shaped flow to other flow patterns can be characterized by a state diagram that depends on the capillary number and the Weber number of each injecting phase. The Y-shaped flow again has provided us the importance of the balance among viscous force, surface tension force, and inertia force in microscopic scale.   

Channel shape modifications to focus particles: A theoretical analysis

Microfluidics techniques that provide focusing of particles suspended in a stream of fluid have several applications such as cell sorting, detection, media exchange, particle removal, etc. For example, focusing can typically be achieved by the use of a stream (or sheath) or surrounding fluid, by dielectrophoresis, or by acoustic methods. In contrast, recent experimental work has shown how micro-structures can be introduced along the walls of a channel so that the suspended particles focus along a symmetry axis; the response is due to the hydrodynamic features (the pressure field) of the flow [1]. We present a model for these low-Reynolds-number flows based on an asymptotic lubrication analysis that accounts for the periodic perturbations at the boundary. We evaluate the resulting forces on suspended, large particles and discuss how the appropriate design of such obstacles at the walls can allow particles to deviate from streamlines and follow a required path.\\[0pt] [1] Choi et al. Small 4, 634-641 (2008).   

Contact Angle Dependence of Viscosity for Micro-Scale Flows

Several microchambers with different geometries and surface properties were microfabricated. Experiments were performed to fill the microchambers with different liquids (e.g., water and alcohol) at various flow rates to study the conditions for bubble formation inside the microchambers. The results indicate that contact angle plays a significant role on properties of fluids confined within small geometries, such as in microfluidic devices. On treatment of the glass with a mono-layer of Octa Tri-Chloro Silane the hydrophobic surface is formed. In the presence of the hydrophobic surface the flow characteristics for filling of the micro-chamber change drastically. On fitting a numerical model to the experimental data it is observed that the viscosity in the fluid confined close to the wall (``near wall region'') can decrease by a factor of 10-100 on treatment with OTS. This shows that the viscosity in confined fluids can depend on the contact angle.   

Enriched boundary layers for heterogeneous reaction in stirred microfluidic flows

The rate of transport of a scalar from a fluid stream to a reactive surface depends on both the character of the flow and the scalar concentration profile incident on the surface. Uniaxial flows tend to form thick regions of low concentration near the reactive surface, leading to decreased rates of scalar transport. For irreversible reactions, this effect can be mitigated through efficient mixing of the bulk. This ensures that the average concentration is incident on the reactive surface, and that concentration boundary layers are kept thin.\footnote{J. Kirtland, G. McGraw, A. Stroock. \textit{Physics of Fluids} \textbf{18}, 073602 (2006).} Coupled reversible reactions, such as those occurring at the electrodes of an electrochemical cell, can complicate the analysis of such a system. In a stirred microfluidic electrochemical cell, depletion of the reactant of the forward reaction implies enrichment of the reactant of the reverse reaction. This enriched fluid can bypass the well mixed bulk, leading to increased scaling of the overall transport process with the P\'{e}clet number \textit{Pe}, even in cases of efficient bulk mixing. We present numerical and experimental results in several such flows and discuss situations where this enrichment can be beneficial (amplification in sensors) or detrimental (quantitative concentration measurement).   

Electro-convection about conducting particles in the thick-Debye-layer limit

In recent years there is an increasing interest in electrokinetic flows about polarizable bodies and particles, where the thin-Debye-layer model is commonly employed. This model may fail for nano-size particles, where the Debye layer thickness may be comparable to the particle dimension. Using a weak-field approximation, we here analyze the limit of a thick Debye layer. We consider the simplest scenario: steady-state electrokinetic flow about an initially uncharged conducting sphere. The dimensionless problem is governed by two parameters: $\beta $, the applied field magnitude (normalized with the thermal scale), and $\lambda $, the Debye thickness (normalized with the cylinder radius). The double limit $\beta \ll 1$ and $\lambda \gg 1$ is singular: standard asymptotic expansions fail to satisfy the far-field velocity decay condition. The resolution of the flow field requires use of inner-outer asymptotic expansions. Two distinguished limits are discussed: the thick-layer limit $1\ll \lambda \ll 1/\beta $, in which the outer domain is characterized by the Debye thickness, and the ``super thick'' limit $1\ll 1/\beta \ll \lambda$, in which the $O(1/\beta$) outer domain reflects a transition form diffusionally-governed ionic concentrations to a dominant balance between diffusion and electro-migration.   

Molecular simulation of electrokinetic flows

We develop a highly accurate and efficient molecular approach to simulate micro and nano electrokinetic flows. We calculate the long range Coulombic interactions using Particle-Particle Particle-Mesh (P$^3$M) approach. The Poisson equation for charge potential is solved in physical space using an iterative multi-grid technique. We demonstrate our approach through simulation of electro-osmotic channel flows with nano roughness on the walls. By comparing the flow rate with traditional pressure driven flows, our results indicate that in electro-osmotic flow the roughness affects the flow through altering the charge density distribution in the electrical double layer (EDL).