Derek C. Tretheway

Apparent fluid slip at hydrophobic microchannel walls

Micron-resolution particle image velocimetry is used to measure the velocity profiles of water flowing through 30×300 μm channels. The velocity profiles are measured to within 450 nm of the microchannel surface. When the surface is hydrophilic (uncoated glass), the measured velocity profiles are consistent with solutions of Stokes’ equation and the well-accepted no-slip boundary condition. However, when the microchannel surface is coated with a 2.3 nm thick monolayer of hydrophobic octadecyltrichlorosilane, an apparent velocity slip is measured just above the solid surface. This velocity is approximately 10% of the free-stream velocity and yields a slip length of approximately 1 μm. For this slip length, slip flow is negligible for length scales greater than 1 mm, but must be considered at the micro- and nano scales.

A generating mechanism for apparent fluid slip in hydrophobic microchannels

Fluid slip has been observed experimentally in micro- and nanoscale flow devices by several investigators [e.g., Tretheway and Meinhart, Phys. Fluids 14, L9 (2002); Zhu and Granik, Phys. Rev. Lett. 87, 096105 (2001); Pit et al., Phys. Rev. Lett. 85, 980 (2000); and Choi et al., Phys. Fluids 15, 2897 (2003)]. This paper examines a possible mechanism for the measured fluid slip, for water flowing over a hydrophobic surface. We extend the work of Lum et al. [J. Phys. Chem. B 103, 4570 (1999)], Zhu and Granick [Phys. Rev. Lett. 87, 096105 (2001)], Granick et al. [Nature Materials 2, 221 (2003)], and de Gennes [Langmuir 18, 3413 (2002)], who suggest slip develops from a depleted water region or vapor layer near a hydrophobic surface. By modeling the presence of either a depleted water layer or nanobubbles as an effective air gap at the wall, we calculate slip lengths for flow between two infinite parallel plates. The calculated slip lengths are consistent with experimental values when the gas layer is modeled ...

Deformation and relaxation of Newtonian drops in planar extensional flows of a Boger fluid

Abstract This paper is an experimental investigation of the deformation and relaxation of a Newtonian drop suspended in a PIB/PB Boger fluid. The suspending fluid is undergoing a planar extensional flow produced in a four-roll mill. We show that increasing elasticity of the suspending fluid has a pronounced effect on both the deformation and relaxation of a drop. For steady flows, as the strength of viscoelastic effects in the suspending fluid is increased, the drops become more deformed, with ends that are generally more pointed. This leads to a decrease in the maximum (“critical”) capillary number for the existence of a steady, deformed drop shape. In transient startup and step flows, the elasticity of the suspending fluid produces a large deformation shape that is more pointed at its ends and more tubular in its midsection than is observed for a drop in a Newtonian fluid (bulbous ends with necking at the waist). This enables a drop in the PIB/PB suspending fluid to be extended to a longer length without breaking upon flow cessation. However, at smaller deformations, the elasticity of the suspending fluid retards the relaxation of the drop. The observed viscoelastic effects on the steady and transient deformation, as well as the relaxation of drops in the PIB/PB suspending fluid, cannot be explained by viscoelastic modifications of the global, undisturbed flow field. Instead, our results suggest the existence of a non-linear coupling between the drop shape, the local disturbance flow, and the polymer configuration in the vicinity of the drop. This coupling enhances elastic effects, such that a drop can display significant non-Newtonian behavior prior to any changes in the global, undisturbed flow field.

Experimental trajectories of two drops in planar extensional flow

In this paper we map the experimental trajectories of two deformable drops in planar extensional flow and compare the experimental results with theoretical calculations for spherical drops. We examine the effects that deformation, initial position, and viscosity ratio have on the interaction of two drops and the necessity of incorporating deformation into trajectory calculations, which can be used to estimate the collision rates, the collision efficiencies, and the collision interaction times. For drops which do not come into close contact, the existing theoretical calculations for spherical drops accurately predict the symmetric trajectories and capture the increased hydrodynamic interaction for higher viscosity ratios. For drops which come into close contact, the spherical drop theory accurately predicts the approach and exit trajectories and with a slight empirical modification adequately predicts the interaction times for deformable drops with a Taylor deformation parameter up to 0.22. The experimental results show that for drops with close contact, the collision trajectories are asymmetric and irreversible with a minimum separation between the centers of mass that is less than the minimum separation of two spheres. This minimum separation corresponds to the minor axis of the deformed drop and is not captured by the spherical theory. However, overall, the modified trajectory theory based upon the hydrodynamic mobility for spherical drops does provide a reasonable estimate for the trajectories and the interaction times for two deformable drops in planar extensional flow.

An inverse method for predicting tissue-level mechanics from cellular mechanical input

Extracellular matrix (ECM) provides a dynamic three-dimensional structure which translates mechanical stimuli to cells. This local mechanical stimulation may direct biological function including tissue development. Theories describing the role of mechanical regulators hypothesize the cellular response to variations in the external mechanical forces on the ECM. The exact ECM mechanical stimulation required to generate a specific pattern of localized cellular displacement is still unknown. The cell to tissue inverse problem offers an alternative approach to clarify this relationship. Developed for structural dynamics, the inverse dynamics problem translates measurements of local state variables (at the cell level) into an unknown or desired forcing function (at the tissue or ECM level). This paper describes the use of eigenvalues (resonant frequencies), eigenvectors (mode shapes), and dynamic programming to reduce the mathematical order of a simplified cell-tissue system and estimate the ECM mechanical stimulation required for a specified cellular mechanical environment. Finite element and inverse numerical analyses were performed on a simple two-dimensional model to ascertain the effects of weighting parameters and a reduction of analytical modes leading toward a solution. Simulation results indicate that the reduced number of mechanical modes (from 30 to 14 to 7) can adequately reproduce an unknown force time history on an ECM boundary. A representative comparison between cell to tissue (inverse) and tissue to cell (boundary value) modeling illustrates the multiscale applicability of the inverse model.

Modeling of Heat Transport and Wafer Heating Effects during Plasma Etching

Uniformity of plasma etching and deposition processes critically depends on the wafer temperature and its spatial variation across the wafer. The goal of this work is to use mathematical modeling to investigate the key factors that determine the wafer temperature and its radial uniformity during plasma etching. Toward this end, a mathematical model of energy transport in and out of a Si wafer in a piasma etching reactor that employs a substrate platen with a He back side cooling arrangement was developed. The possibility of wafer bowing due to high He back side pressure was considered and the effects of ion bombardment flux uniformity, He back side pressure, and different wafer clamping arrangements were studied. While an increase in He back side pressure increases the rate of heat transfer from the wafer to the electrode, excessive He pressure causes the wafer to bow. Bowing increases the electrode-wafer gap, decreases the heat transfer rate, and adversely affects the temperature uniformity. These effects are most pronounced for large diameter wafers (>200 mm) and are predicted to be very important in the processing of 300 and 400 mm substrates. The manner in which the wafer is clamped to the cooled electrode is another key factor that determines the heat transport at the wafer edge and the radial temperature profile across the wafer. The uniformity of the wafer temperature depends on the heat transport at the wafer edges. Poor thermal contact at the wafer edge leads to a high but uniform wafer temperature ; on the other hand, if a good thermal contact is made at the wafer edge, the average temperature is lower but less uniform. Model predictions compared well with the available experimental data.

The μPIVOT: an integrated particle image velocimeter and optical tweezers instrument for microenvironment investigations

A novel instrument to manipulate and characterize the mechanical environment in and around microscale objects in a fluidic environment has been developed by integrating two laser-based techniques: micron-resolution particle image velocimetry (μPIV) and optical tweezers (OT). This instrument, the μPIVOT, enables a new realm of microscale studies, yet still maintains the individual capabilities of each optical technique. This was demonstrated with individual measurements of optical trap stiffness (∼70 pN μm(-1) for a 20 μm polystyrene sphere and a linear relationship between trap stiffness and laser power) and fluid velocities within 436 nm of a microchannel wall. The integrated device was validated by comparing computational flow predictions to the measured velocity profile around a trapped particle in either a uniform flow or an imposed, gravity-driven microchannel flow (R(2) = 0.988, RMS error = 13.04 μm s(-1)). Interaction between both techniques is shown to be negligible for 15 μm to 35 μm diameter trapped particles subjected to fluid velocities from 50 μm s(-1) to 500 μm s(-1) even at the highest laser power (1.45 W). The integrated techniques will provide a unique perspective toward understanding microscale phenomena including single-cell biomechanics, non-Newtonian fluid mechanics and single particle or particle-particle hydrodynamics.

Examination of the Slip Boundary Condition by µ-PIV and Lattice Boltzmann Simulations

This work examines the slip boundary condition by Lattice Boltzmann simulations, addresses the validity of the Navier’s hypothesis that the slip velocity is proportional to the shear rate and compares the Lattice Boltzmann simulations to the experimental results of Tretheway and Meinhart (Phys. of Fluids, 14, L9-L12). The numerical simulation models the boundary condition as the probability, P, of a particle to bounce-back relative to the probability of specular reflection, 1P. For channel flow, the numerically calculated velocity profiles are consistent with the experimental profiles for both the no-slip and slip cases. No-slip is obtained for a probability of 100% bounce-back, while a probability of 0.03 is required to generate a slip length and slip velocity consistent with the experimental results of Tretheway and Meinhart for a hydrophobic surface. The simulations indicate that for microchannel flow the slip length is nearly constant along the channel walls, while the slip velocity varies with wall position as a results of variations in shear rate. Thus, the resulting velocity profile in a channel flow is more complex than a simple combination of the no-slip solution and slip velocity as is the case for flow between two infinite parallel plates.

Single Pixel Evaluation of Microchannel Flows

Recently a new μPIV interrogation algorithm has been proposed in which the interrogation window size is reduced to a single pixel. Such small interrogation window sizes are possible using correlation averaging to increase the effective particle concentration to levels required for correlation analysis to succeed. The random error exhibits the expected behavior of decreasing roughly in proportion to N−1/2 while the bias error exhibits unexpected peak-locking behavior with zero bias error at integer and half integer pixel displacements and maximal errors at one-quarter and three-quarter pixel displacements. Accompanying experiments show the potential of this technique but have not yet been sufficiently refined to confirm this unexpected bias error behavior.Copyright

Effects of Absolute Pressure on Fluid Slip in a Hydrophobic Microchannel

This work examines the effects of absolute pressure on fluid slip in a hydrophobic microchannel. Previous experiments with hydrophobic surfaces have indicated the presence of an apparent fluid slip. The mechanism responsible for the apparent fluid slip observed by Pit. et. al. (Phys. Rev. Lett., 85 , 980–983), Zhu and Granick (Phys. Rev. Lett., 87 , 096105), and Tretheway and Meinhart (Phys. of Fluids, 14 , L9-L12) is unknown. Recently, Tyrell and Attard () have observed the presence of nanobubbles on a hydrophobic surface. Modeling these nanobubbles as a thin gas layer and solving for the velocity profile between two infinite parallel plates yields an apparent fluid slip consistent with the experimentally observed results. As the slip length is highly dependent on the nanobubble or gas layer thickness, increases in absolute pressure should decrease the bubble size and reduce the measured slip. This work explores the proposed mechanism by measuring velocity profiles and calculating slip lengths at varying absolute pressures.Copyright