An analytic and experimental investigation into gaseous flow with slight rarefaction through long microchan- nels is undertaken. A two-dimensional (2-D) analysis of the Navier-Stokes equations with a first-order slip-velocity boundary condition demonstrates that both compressibility and rarefied effects are present in long microchannels. By undertaking a perturbation expansion in , the height-to-length ratio of the channel, and using the ideal gas equation of state, it is shown that the zeroth-order analytic solution for the streamwise mass flow corresponds well with the experimental results. Also, the effect of slip upon the pressure distribution is derived, and it is obtained that this slip velocity leads directly to a wall-normal migration of mass. The fabrication of wafer-bonded microchannels that possess well-controlled surface structure is described, and a means for accurately measuring the mass flow through the channels is presented. Experimental results obtained with this mass-flow measurement technique for streamwise helium mass flow through microchannels 52.25- m wide, 1.33- m deep, and 7500- m long for a pressure range of 1.6-4.2 atmospheres (outlet pressures at atmospheric) are presented and shown to compare favorably with the analysis. (147)

The slip effects of water flow in hydrophilic and hydrophobic microchannels of 1 and 2 μm depth are examined experimentally. High-precision microchannels were treated chemically to enhance their hydrophilic and hydrophobic properties. The flow rates of pure water at various applied pressure differences for each surface condition were measured using a high-precision flow metering system and compared to a theoretical model that allows for a slip velocity at the solid surface. The slip length was found to vary approximately linearly with the shear rate with values of approximately 30 nm for the flow of water over hydrophobic surfaces at a shear rate of ${10}^5 {\mathrm{s}}^{\text{−1}}.$ The existence of slip over the hydrophilic surface remains uncertain, due to the sensitivity of the current analysis to nanometer uncertainties in the channel height.

High-precision experimental results are reported showing the tangential momentum accommodation coefficient (TMAC) for several gases in contact with single-crystal silicon to be less than unity. A precise and robust experimental platform is demonstrated for measurement of mass flows through silicon micromachined channels due to an imposed pressure gradient. Analytic expressions for isothermal Maxwellian slip flows through long channels are used to determine the TMAC at a variety of Knudsen numbers. Results from experiments using nitrogen, argon and carbon dioxide are presented. For all three gases the TMAC is found to be lower than one, ranging from 0.75 to 0.85.

We precisely measure the force-free swimming speed of a rotating helix in viscous and viscoelastic fluids. The fluids are highly viscous to replicate the low Reynolds number environment of microorganisms. The helix, a macroscopic scale model for the bacterial flagellar filament, is rigid and rotated at a constant rate while simultaneously translated along its axis. By adjusting the translation speed to make the net hydrodynamic force vanish, we measure the force-free swimming speed as a function of helix rotation rate, helix geometry, and fluid properties. We compare our measurements of the force-free swimming speed of a helix in a high-molecular weight silicone oil with predictions for the swimming speed in a Newtonian fluid, calculated using slender-body theories and a boundary-element method. The excellent agreement between theory and experiment in the Newtonian case verifies the high accuracy of our experiments. For the viscoelastic fluid, we use a polymer solution of polyisobutylene dissolved in polybutene. This solution is a Boger fluid, a viscoselastic fluid with a shear-rate-independent viscosity. The elasticity is dominated by a single relaxation time. When the relaxation time is short compared to the rotation period, the viscoelastic swimming speed is close to the viscous swimming speed. As the relaxation time increases, the viscoelastic swimming speed increases relative to the viscous speed, reaching a peak when the relaxation time is comparable to the rotation period. As the relaxation time is further increased, the viscoelastic swimming speed decreases and eventually falls below the viscous swimming speed.

Synovial fluid is a semidilute hyaluronate (HA) polymer solution, the rheology of which depends on HA–protein interactions, and lubricin is a HA-binding protein found in synovial fluid and at cartilage surfaces, where it contributes to boundary lubrication under load. Individuals with genetic deficiency of lubricin develop precocious joint failure. The role of lubricin in synovial fluid rheology is not known. We used a multiple-particle-tracking microrheology technique to study the molecular interactions between lubricin and HA in synovial fluid. Particles (200 nm mean diameter) embedded in normal and lubricin-deficient synovial fluid samples were tracked separately by using multiple-particle-tracking microrheology. The time-dependent ensemble-averaged mean-squared displacements of all of the particles were measured over a range of physiologically relevant frequencies. The mean-squared displacement correlation with time lag had slopes with values of unity for simple HA solutions and for synovial fluid from an individual who genetically lacked lubricin, in contrast to slopes with values less than unity (α ≈ 0.6) for normal synovial fluid. These data correlated with bulk rheology studies of the same samples. We found that the subdiffusive and elastic behavior of synovial fluid, at physiological shear rates, was absent in fluid from a patient who lacks lubricin. We conclude that lubricin provides synovial fluid with an ability to dissipate strain energy induced by mammalian locomotion, which is a chondroprotective feature that is distinct from boundary lubrication.