Surface Roughness and Effective Stick-Slip Motion

The effect of random surface roughness on hydrodynamics of viscous incompressible liquid is discussed. Roughness-driven contributions to hydrodynamic flows, energy dissipation, and friction force are calculated in a wide range of parameters. When the hydrodynamic decay length (the viscous wave penetration depth) is larger than the size of random surface inhomogeneities, it is possible to replace a random rough surface by effective stick-slip boundary conditions on a flat surface with two constants: the stick-slip length and the renormalization of viscosity near the boundary. The stick-slip length and the renormalization coefficient are expressed explicitly via the correlation function of random surface inhomogeneities. The effective stick-slip length is always negative signifying the effective slow-down of the hydrodynamic flows by the rough surface (stick rather than slip motion). A simple hydrodynamic model is presented as an illustration of these general hydrodynamic results. The effective boundary parameters are analyzed numerically for Gaussian, power-law and exponentially decaying correlators with various indices. The maximum on the frequency dependence of the dissipation allows one to extract the correlation radius (characteristic size) of the surface inhomogeneities directly from, for example, experiments with torsional quartz oscillators.Comment: RevTeX4, 14 pages, 3 figure

Electroosmotic flow of biorheological micropolar fluids through microfluidic channels

An analysis is presented in this work to assess the influence of micropolar nature of fluids in fully developed flow induced by electrokinetically driven peristaltic pumping through a parallel plate microchannel. The walls of the channel are assumed as sinusoidal wavy to analyze the peristaltic flow nature. We consider that the wavelength of the wall motion is much larger as compared to the channel width to validate the lubrication theory. To simplify the Poisson Boltzmann equation, we also use the Debye-Hückel linearization (i.e. wall zeta potential ≤ 25mV). We consider governing equation for micropolar fluid in absence of body force and couple effects however external electric field is employed. The solutions for axial velocity, spin velocity, flow rate, pressure rise and stream functions subjected to given physical boundary conditions are computed. The effects of pertinent parameters like Debye length and Helmholtz-Smoluchowski velocity which characterize the EDL phenomenon and external electric field, coupling number and micropolar parameter which characterize the micropolar fluid behavior, on peristaltic pumping are discussed through the illustrations. The results show that peristaltic pumping may alter by applying external electric fields. This model can be used to design and engineer the peristalsis-lab-on-chip and micro peristaltic syringe pumps for biomedical applications

Inkjet Metrology: High-Accuracy Mass Measurements of Microdroplets Produced by a Drop-on-Demand Dispenser

We describe gravimetric methods for measuring the mass of droplets generated by a drop-on-demand (DOD) microdispenser. Droplets are deposited, either continuously at a known frequency or as a burst of known number, into a cylinder positioned on a submicrogram balance. Mass measurements are acquired precisely by computer, and results are corrected for evaporation. Capabilities are demonstrated using isobutyl alcohol droplets. For ejection rates greater than 100 Hz, the repeatability of droplet mass measurements was 0.2%, while the combined relative standard uncertainty (uc) was 0.9%. When bursts of droplets were dispensed, the limit of quantitation was 72 μg (1490 droplets) with uc = 1.0%. Individual droplet size in a burst was evaluated by high-speed videography. Diameters were consistent from the tenth droplet onward, and the mass of an individual droplet was best estimated by the average droplet mass with a combined uncertainty of about 1%. Diameters of the first several droplets were anomalous, but their contribution was accounted for when dispensing bursts. Above the limits of quantitation, the gravimetric methods provided statistically equivalent results and permit detailed study of operational factors that influence droplet mass during dispensing, including the development of reliable microassays and standard materials using DOD technologies