Computational Micro and Nanofluidics Laboratory - Research
Research
Micro and nano fluidics deals with the behavior, control and manipulation of fluids that are geometrically constrained to micro and/or nanoscale. As dimensions shrink, forces at interfaces become more important due to the increasing ratio of interfacial area and volume. Electrical force offers advantages relative to the conventional pressure-driven flows in macroscale. Our research focuses on understanding the electrokinetic transport phenomena in micro and nano scale channels and pores.
Electrokinetic phenomena includes: Electroosmosis, Electrophoresis, Streaming Potential and Sedimentation Potential.
Electroosmosis
When in contact with electrolytes, many solid substrates acquire a surface charge and attract oppositely charged ions, creating thin layers of charges next to it, called electrical double layers (shown below). Under an external electric field, the fluid in these electrical double layers acquires a momentum and drags the fluid in the bulk by virtue of its viscosity. The resulting fluid motion is calledas electro-osmotic flow (Probstein, 2003).
Electrophoresis
Electrophoresis is the most known electrokinetic phenomena. It refers to the motion of charged particles related to the fluid under the influence of an applied electric field.
Streaming Potential
When an electrically conducting fluid is passed through a channel or tube under an imposed pressure drop, there is an electrical potential difference set up as a result since the net current in the channel must vanish(i.e. there are no upstream and downstream electrodes). This potential is called streaming potential. The streaming potential is usually very small and it tends to oppose the fluid flow.
Sedimentation Potential
The sedimentation potential also called the Dorn effect is the potential induced by the fall of a charged particle under an external force field. It is analogous to electrophoresis in the sense that a local electric field is induced as a result of its motion. Just as in electroosmotic flow the fall ofa particle induces a streaming current caused by the distortion of the electric double layer and is similar to that described in the section on electrophoresis.
Reference
Probstein RF (2003), Physicochemical Hydrodynamics: An Introduction, 2nd edn. Wiley-Interscience.
We have developed analytical models and CFD models for electroosmotic flow (EOF) in micro/nano-channels. The models were compared to experimental data and molecular simulations. iMEDD, Inc. and Oak Ridge National Laboratory (ORNL) provided us with the experimental data we compared our results to. The iMEDD experiments were performed on a nanochannel membrane made up of approximately 47,500 nanochannels in parallel. SEM images of a section of the membrane are shown below. Each channel has the same height (which varies), a length of 3.5 microns, and a width of 44 microns, with the fluid flowing through the 44 micron channel height surface.
The reservoir and the channels in iMEDDs’ experiments. The iMEDD membrane with nanochannels across it is located in the center of the reservoir. Through the nanochannels, the liquid in one side of the reservoir is driven to the other side by electroosmosis.
Nanopore membranes fabricated by iMEDD inc. Arrays of membranes are fabricated on a silicon wafer; on each membrane, there are vertical nanochannel arrays fabricated. The width of the channels is 44μm, and the distance between two arrays is 6μm.
Comparison of our theoretical flow rates with the iMEDD experimental results. 1xPBS, 0.1xPBS and 0.01xPBS refer to original PBS, 10 folds diluted PBS and 100 folds diluted PBS, in respective.
The second set of data for comparison is the experimental results obtained by Ramsey et. al. at Oak Ridge National Laboratory. Ramsey et. al. measure the electroosmotic mobility of sodium tetraborate aqueous/methanol solution flowing through different single rectangular silicon nanochannels.
Comparison between the mobilities measured in ORNL experiments and the results from the model. The mobilities are drawn against the channel heights, which vary form 83nm to 1080nm. The mobilities Ramsey et.al obtained from their experiment agreed very well with the model.
In Georgia Institute of Technology, Dr. M. Yoda et. al. uses Nano-PIV technique to study the flows at the nano- to micrometer scale experimentally. The velocity profile and mobility of fluids are measured in their experiments.
The picture (left) and sketch (right) of the crossing microchannel chip used in the Georgia tech experiments, the region of interest (ROI) is indicated in the sketch plot; and the direction of flow is from top to bottom in the sketch plot, as shown by the arrow.
Comparison of the mobility measured in the Georgia Tech experiments and the average mobility calculated from the asymptotic model.
One of the recent applications of nanopores is the possibility to use them as detectors and even analyzers for (bio)molecules. A hydrodynamic model is established to investigate the translocation velocity of an electrokinetically driven DNA through a nanopore. There is an electroosmotic flow inside the nanopore and the velocity field inside the nanopore is calculated. The force balance on the DNA is used as an additional condition to determine the translocation velocity. The numerical results compare well with experimental data.
DNA translocation in a cylindrical nanopore
Channel modeled as negatively charged cylindrical channel, with length >> radius.
DNA modeled as negatively charged rigid cylinder along channel axis.
Forces on particle – electric field & viscous drag.
DNA motion direction may be with or against the bulk flow.
Current drops due to individual translocation events.
DNA translocation in a conical nanopore
Flow field inside the nanopore
Particle Transport in Micronozzles
Micro/nano nozzles and diffusers have been used for ionic transport, drug and gene delivery. A mathematical model is developed to simulate the electroosmotic flow (EOF) and particle transport in micro/nano nozzles/diffusers. Particle motion is found to be dependent primarily on the particle charge and the wall charge. The calculated particle velocities compare well with experimental data.
Experiments have been done by Prof. J. L. Lee’s group to investigate particle transport in micronozzles. The Polymethyl Methacrylate (PMMA) nozzle is fabricated by photolithography, followed by replica molding and wet etching respectively. Negatively charged and fluorescence-labeled polystyrene (PS) beads of size from 3 nm to 40 nm were used to examine the transport of particles in micro-nozzles.
Modeling results for electroosmotic flow in the experimental microdiffuser. The height of the diffuser is 20 μm at the inlet and 130 μm at the outlet and the length of the diffuser is 650 μm. In this case, the EDLs are thin compared to the diffuser. The imposed electric field is 8,000 V/m and the ζ -potential is −15 mV.
Comparison of the analytical results and the experimental data. The length of the micro-diffuser is 650μm; the inlet height is 20μm and the outlet height is 130μm. The electric field is 80 V/cm. The ζ-potential of the PMMA walls are −15mV (Kirby and Hasselbrink, 2004). Both the particles and the walls are negatively charged.
Membrane Sandwich Electroporation
Nanotips can be used for drug/gene delivery. The aperture of nanotips can carry a specific dosage of drugs/genes and leave them inside cells. The short penetration of these tiny nanotips would not cause permanent damage to cells.
Single Cell in a DC Field
Experiments on gene delivery(left): A sigle cell is fixed in a micronozzle and the dots shows the pathlines of polystyrene beads. Modeling result for the applied electric field(right).
Design of the device for gene delivery using micro/nano nozzle arrays.
A theoretical model for filtration of large solutes through a nanopore in the presence of transmembrane pressures, applied/induced electric fields, and dissimilar interactions at the entrance and exit to the nanopore is developed to characterize the experimental performance of a hemofiltration membrane designed for a proposed implantable Renal Assist Device (RAD). The model reveals that the sieving characteristics of the nanopore membrane can be improved by applying an external electric field, and ensuring a smaller ratio of the pore-feed and pore-permeate equilibrium partitioning coefficients when diffusion is present. The model is then customized to study filtration of both charged and uncharged solutes in the slit-shaped nanopores of the hemofilter for the RAD. Experimental data on the sieving coefficient of serum proteins are reported and compared with the theoretical predictions. Both steric and electrostatic partitioning are considered and the comparison suggests that in general electrostatic effects are present in the filtration of proteins though some data, particularly those recorded in a strongly hypertonic solution (10×PBS), show better agreement with the steric partitioning theory.
Filtration of biomolecules through a synthetic membrane-based device concieved to functionally substitute native kidney in End-Stage Renal Disease Patients.
Membrane provides better filtration (lower sieving coefficient S) when it has narrow and charged pores.
Aerodynamics
Professor Conlisk has also worked in the area of helicopter aerodynamics since 1989, with funding from the Army Research Office and the Geogia Tech Rotorcraft Center of Excellence.
Modern aerodynamic phenomena are extremely complex and thus pose significant problems for the computation of the flow fields of interest. The ability to model such flows is crucial to the efficient and accurate design of aerodynamic surfaces. Indeed, the ability to generate dynamic load data may be significant in extending the life of a given surface.
We are involved in several different aspects of these flows including the resolution of large-amplitude, high-frequency suction peaks on surfaces caused by vortex collisions and the prediction of the characteristics of tip-vortices shed from fixed and rotary wings. The author is an expert in developing computational schemes associated with the motion of three-dimensional vortices.
Much of the computational work is performed at the Ohio Supercomputer Center and the data reduction is performed at the Computational and Visual Fluid Dynamics Laboratory in the Department of Mechanical Engineering at Ohio State University. Visualization capabilities include on-line and interactive animation of both two and three-dimensional flow phenomena. In what follows several different projects presently ongoing at the Ohio State University are summarized. Most of the work on helicopter flows is done jointly with Professor Narayanan Komerath and at the Rotorcraft Center of Excellence at Georgia Tech.
Tip-Vortex-Airframe Interactions
The flow field generated by a helicopter in flight is extremely complex and it has been recognized that interactions between different components can significantly affect helicopter performance. Recent experimental results indicate that significant impulsive loads may be exerted on a helicopter airframe due to the influence of the tip-vortex and a simplified model for this interaction has been developed. The numerical calculations for the vortex position and the pressure indicate that a large adverse pressure gradient develops under the vortex on the fuselage causing a rapid drop in the pressure there; this large suction peak is removed within milliseconds as the vortex core flow is essentially destroyed. On the left figure is a sketch of a single bladed rotor showing how the tip-vortex will impinge on the airframe. On the right is a sketch of the local behavior as the vortex collides with the airframe. Present work suggests that the process is essentially inviscid.
Vortex-Surface Collisions
We use the term ``collision'' to describe the physical process in which the core structure of the vortex defined as a specified region of large vorticity surrounded by irrotational fluid is substantially and permanently altered; most often the core is locally destroyed. This is illustrated on the right figure just above. Characteristic of collisions is that the dominant flow features occur on local length and time scales different from those before the collision. There are various types of collisions and these are discussed is an AIAA paper 98-2858 ``A Theory of Vortex-Surface Collisions'', presented at the 2nd Theoretical Fluid Mechanics Meeting in Albuquerque in June 1998. Helicopter aerodynamics problems always involve three-dimensional collisions and the axial flow in the core of the vortex is a critical feature and generally the primary cause of the collision. Experiments suggest that a strong suction peak persists on the side of the airframe where the axial flow in the vortex is directed away from the surface and is removed where the axial flow in the vortex is directed toward the surface. We are presently working on the full 3D collision, but these basic experimental results may be explained by the solution of a much simpler problem.
The 90o Collision
Lee et al. (1998) (see the reference below) has solved the axisymmetric and incompressible Euler equations for the case where a vortex is split instantaneously at a right angle by a thin flat plate. The figures below show the swirl velocity and the axial vorticity on the wall as a function of radius for a number of times. We start with a Lamb vortex and watch as the swirl velocity in the core of the vortex gets progressively weaker. At the same time, the axial vorticity gets progressively weaker in the core of the vortex as well. This is shown in the figures below which are sketches of the swirl velocity, the axial vorticity and the pressure. These figures are for an axial velocity in the vortex of the same order of magnitude as the swirl and directed toward the surface. Note that there is no collision unless the axial velocity in the vortex is non-zero.
Locally Steady Rotor Wakes and Interactions Between Tip-Vortices
The regions over which steady and unsteady rotor wake patterns exist have been examined numerically for one and two-bladed rotors. A lifting-line theory is used to model each rotor blade and a time-stepping vortex method is used to calculate the tip-vortex motion. The velocities within the first few turns of the wake have been obtained and the results indicate a periodic nature of the wake in both time and space. Temporal aperiodicity is observed beyond the first few turns of the tip-vortex for hovering rotors, while for rotors in sufficient climb, the entire wake is steady relative to the blades and both spatially and temporally periodic. The numerical results are shown to be independent of both time step and spatial grid below clearly defined values.
The velocity field within thewake of a two-bladed rotor is shown in the plot (far right). Note that the velocity pattern in the x, y and z directions is periodic with a time period corresponding to 180o rotation of the blades. The steady, periodic nature of the wake is best illustrated in the figure (right) which shows the wake structure at increasing wake ages from 180o to 720o. Note that the geometry at wake ages of 180o and 540o are identical and so are those at 360o and 720o, displaying total spatial and temporal periodicity.
Experiments (Caradonna et al. 1997), hereafter referred to as CK, have shown that deep in the wake of a 2-bladed rotor in near-hover states, the tip vortices roll around each other, pair and eventually merge as seen in figure (far left). Similar rollup phenomena has been observed in the computed results. The situation is shown in the figure (left). The merging of the tip-vortices appears to be the process by which transition to the far wake occurs. This process is deterministic and periodic, and appears to be intrinsic to rotor wakes. It is easy to show that this vortex-vortex interaction in the wake of a rotor is to be expected based on classical vortex dynamics and that the interaction is most intense in hover and in descent.
The velocity field around and across the tip-vortex of a single rigid blade was computed and compared with experiments conducted by McAlister. Velocities induced by the entire field were computed at vertical cuts through the tip-vortex at wake ages of 30o, 60o and 100o. The figure(far right) shows the vertical velocity induced across the tip-vortex at a wake age of 60o and the figure (right) shows the horizontal velocity induced across thetip-vortex at a wake age of 60o. It should be noted that all parameters used in the computations, such as circulationand core radius, were obtained directly from experiments. The computations involve no adjustable constants.
The Formation of Rotor Tip-Vortices
The major objective of this current work is to apply classical inviscid lifting line and lifting surface theories locally near the rotor tip and describe the origin of the tip-vortex.
The x-y section view of the roll-up process for the rotor after 800 iterations at which convergency has been achieved upto 30.0 chord-lengths distance downstream from the leading edge of the blade is shown in figure (far right). The vortex lines emanating from each panel is shown. Note that the trailing vortices near the tip region roll over to form a strong tip-vortex. However, ina region away from the tip, the trailing vortices do not roll-up in distances of the order shown in the figure. They collectively form the weak inboard sheet which is shown to move inboard. The 3-D view of the roll-up process is also shown in the figure (right).
The growth of the circulation of the tip-vortex as a function of 'x' is shown in figure (far left). The circulation of the tip-vortex is obtained by summing the circulations of each individual filaments. Note that the tip-vortex circulation is approaching an asymptotically constant value far downstream of the blade. The variation of the trailing circulation - which is nothing but the derivative of the bound circulation - with spanwise distance along the blade, is shown in the figure (left). This figure is useful in noting the relative strengths of the strong tip-vortex made up of the rolled-up trailing vortices and the weak inboard vortex sheet made up ofthe non-rolled-up trailing vortices. It is found that the strength of the inboard sheet is approximately 5 percent as that of the strength of the tip-vortex and hence its role can be neglected while computing the tip-vortex circulation.
It is observed that the strength of the tip-vortex grows asymptotically to a certain value. This value is always smaller than the corresponding maximum bound circulation value as shown in the figure on the left. The reason behind this is that not all the trailing vortices emanating from the blade tip upto the spanwise location where the maximum bound circulation occurs roll up to form the tip-vortex. The ratio of the maximum tip-vortex strength to the maximum bound vortexstrength is found to lie between 0.73-0.93.