James B. Grotberg

Microfluidics for flow cytometric analysis of cells and particles

This review describes recent developments in microfabricated flow cytometers and related microfluidic devices that can detect, analyze, and sort cells or particles. The high-speed analytical capabilities of flow cytometry depend on the cooperative use of microfluidics, optics and electronics. Along with the improvement of other components, replacement of conventional glass capillary-based fluidics with microfluidic sample handling systems operating in microfabricated structures enables volume- and power-efficient, inexpensive and flexible analysis of particulate samples. In this review, we present various efforts that take advantage of novel microscale flow phenomena and microfabrication techniques to build microfluidic cell analysis systems.

Acoustically detectable cellular-level lung injury induced by fluid mechanical stresses in microfluidic airway systems

We describe a microfabricated airway system integrated with computerized air–liquid two-phase microfluidics that enables on-chip engineering of human airway epithelia and precise reproduction of physiologic or pathologic liquid plug flows found in the respiratory system. Using this device, we demonstrate cellular-level lung injury under flow conditions that cause symptoms characteristic of a wide range of pulmonary diseases. Specifically, propagation and rupture of liquid plugs that simulate surfactant-deficient reopening of closed airways lead to significant injury of small airway epithelial cells by generating deleterious fluid mechanical stresses. We also show that the explosive pressure waves produced by plug rupture enable detection of the mechanical cellular injury as crackling sounds.

Insoluble surfactant spreading on a thin viscous film: shock evolution and film rupture

Lubrication theory and similarity methods are used to determine the spreading rate of a localized monolayer of insoluble surfactant on the surface of a thin viscous film, in the limit of weak capillarity and weak surface diffusion. If the total mass of surfactant increases as t(alpha), then at early times, when spreading is driven predominantly by Marangoni forces, a planar (axisymmetric) region of surfactant is shown to spread as t(1 + alpha)/3 (t(1 + alpha)/4) . A shock exists at the leading edge of the monolayer; asymptotic methods are used to show that a wavetrain due to capillary forces exists ahead of the shock at small times, but that after a finite time it is swamped by diffusive effects. For alpha < 1/2 (alpha < 1), the diffusive lengthscale at the shock grows faster than the length of the monolayer, ultimately destroying the shock; subsequently, spreading is driven by diffusion, and proceeds as t1/2. The asymptotic results are shown to be good approximations of numerical solutions of the governing partial differential equations in the appropriate limits. Additional forces are also considered: weak vertical gravity can also destroy the shock in finite time, while effects usually neglected from lubrication theory are important only early in spreading. Experiments have shown that the severe thinning of the film behind the shock can cause it to rupture: the dryout process is modelled by introducing van der Waals forces.

The dynamics of a localized surfactant on a thin film

We investigate the flow induced by a localized insoluble surfactant on a thin film. This problem is intended to model the behaviour of the lungs thin-film lining after an aerosol droplet lands on its surface. The surfactant-induced surface-tension gradients drive convection (Marangoni convection) within the film, disrupting the film surface and causing the surfactant to spread. The surfactant may also spread on the films surface by surface diffusion without inducing convection. Gravity provides a restoring force that decreases film disturbances. Lubrication theory is employed to derive equations that describe the evolution of the film thickness and surfactant concentration. A nonlinear surface-tension equation of state describes the relationship between the surfactant concentration and the surface tension. Solutions of the evolution equations are found numerically using the method of lines and analytically under limiting cases of small and large surface diffusivity. The results elucidate the behaviour of the thin-film/surfactant system. We find that surface-tension-induced convection creates film disturbances that increase the film thickness near the surfactants leading edge, and thins the film in the central region. Surface diffusion causes more rapid spreading of the surfactant, and decreases the film disturbances. Gravity decreases the film disturbances by creating bi-directional flow in the form of a ring vortex. This behaviour may have implications for the delivery of medications or toxins by aerosol inhalation.

The spreading of heat or soluble surfactant along a thin liquid film

The spreading of a localized distribution of surfactant on a thin viscous film is considered, in the situation in which the surfactant is soluble in the bulk layer and the boundary beneath the fluid is impermeable to surfactant. The surfactant distribution is controlled by advection and diffusion both at the surface of the film, where the surfactant forms a monolayer, and in the bulk. The bulk and surface surfactant concentrations are related by linearized sorption kinetics. The surfactant diffuses rapidly across the thin fluid layer, and lubrication theory is used to derive evolution equations for the film height and the surface and cross‐sectionally averaged bulk surfactant concentrations. A special case of the governing equations describes the Marangoni flow induced by a locally hot region of the layer. It is shown that in comparison to the spreading of insoluble surfactant, transient desorption of surfactant from the monolayer to the bulk causes the spreading rate to diminish, although once the bulk and surface concentrations are locally in equilibrium, film deformations are more severe, with a sharp pulse in the film height created just upstream of the leading edge of the surfactant distribution.

Surfactant effects on fluid-elastic instabilities of liquid-lined flexible tubes: A model of airway closure

A theoretical analysis is presented predicting the closure of small airways in the region of the terminal and respiratory bronchioles. The airways are modelled as thin elastic tubes, coated on the inside with a thin viscous liquid lining. This model produces closure by a coupled capillary-elastic instability leading to liquid bridge formation, wall collapse or a combination of both. Nonlinear evolution equations for the film thickness, wall position and surfactant concentration are derived using an extended version of lubrication theory for thin liquid films. The positions of the air-liquid and wall-liquid interfaces and the surfactant concentration are perturbed about uniform states and the stability of these perturbations is examined by solving the governing equations numerically. Solutions show that there is a critical film thickness, dependent on fluid, wall and surfactant properties above which liquid bridges form. The critical film thickness, epsilon c, decreases with increasing mean surface-tension or wall compliance. Surfactant increases epsilon c by as much as 60 percent for physiological conditions, consistent with physiological observations. Airway closure occurs more rapidly with increasing film thickness and wall flexibility. The closure time for a surfactant rich interface can be approximately five times greater than an interface free of surfactant.

Use of Air-Liquid Two-Phase Flow in Hydrophobic Microfluidic Channels for Disposable Flow Cytometers

This paper describes a disposable flow cytometer that uses an air-liquid two-phase microfluidic system to produce a focused high-speed liquid sample stream of particles and cells. The susceptibility of thin liquid columns to instabilities may suggest that focusing of sample liquids with streams of air would be difficult. The design of channel geometry, control of flow rates, and use of appropriate surface chemistries on the channel walls, however, enabled the generation of thin (15–100 μm) and partially bounded sample streams that were stable and suitable for rapid cell analysis. Using an inverted epi-fluorescence microscope with a photo-multiplier tube, we demonstrated that the system is capable of counting the number of beads and C2C12 myoblast cells. The effects of different flow rates and surface chemistries of the channel walls on the air-liquid two-phase flows were characterized using optical and confocal microscopy. Use of air instead of liquids as a sheath fluid eliminates the need for large sheath liquid reservoirs, and reduces the volume and weight requirements. The low manufacturing cost and high volumetric efficiency make the air-sheath flow cytometer attractive for use as a stand-alone device or as an integrated component of bio-artificial hybrid microsystems.

Droplet spreading on a thin viscous film

We investigated experimentally the flows induced by a localized surfactant (oleic acid) on thin glycerol films. The oleic acid creates surface-tension gradients, which drive convention on the surface and within the film. Qualitative descriptions of the Lagrangian flow field were provided by flow-visualization experiments. Quantitative measurements of surface flows were conducted using dyed glycerol markers, where the initial motion of these markers is used to define the position of the timedependent ‘ convection front ’. The flow characteristics were found to depend largely upon the magnitude of a gravitational parameter, G, representing the ratio of gravitational to surface-tension gradient (Marangoni) forces. Small G (G 0. For this reason, surface markers may not be used to measure accurately the position of the droplet’s leading edge. Finally, simulations of the Lagrangian flows conducted using the theory of Gaver & Grotberg (1990) compare favourably with these experimental results in the limit of dilute surfactant concentrations, and thus experimental verification of that theory is provided by this work. The results of this study may be useful for understanding the behaviour of the lung’s thin-film lining after an aerosol droplet of insoluble exogenous surfactant lands upon its surface.

Fluid-elastic instabilities of liquid-lined flexible tubes

The dynamics of a thin film of Newtonian fluid coating the inner surface of an elastic circular tube is analysed. This problem is motivated by an interest in the closure of small airways of the lungs either by formation of a liquid bridge, the collapse of the airway wall or a combination of both processes. Liquid bridge formation is due to the destabilization of the liquid film that coats the inner surface of airways, while wall collapse can be due to either the high surface tension of the air–liquid interface or the flexibility of the wall. Nonlinear evolution equations for the film thickness and wall position are derived using lubrication theory, but an accurate representation of the curvatures of both the liquid and wall interfaces is employed which is valid for thick films. These approximations allow closure to be predicted. In addition, these approximations are justified by comparison with rigid-wall results obtained by solving the full Navier–Stokes equations and because fluid inertia only becomes important in the very late stages of closure. The linear stability of these equations is examined using normal-mode analysis for infinitesimal disturbances and the nonlinear stability is investigated by solving the governing equations numerically using the method of lines. Solutions show that there is a critical film thickness, strongly dependent on fluid and wall properties, above which unstable waves grow to form liquid bridges. The critical film thickness decreases with increasing surface tension or wall compliance since waves grow faster. Even for relatively stiff airways, the volume of fluid in the liquid lining required for closure can be approximately 70% of the volume for the rigid-tube case. Wall damping is an important effect only when the airway is sufficiently compliant. Airway closure occurs more rapidly with increasing unperturbed film thickness, surface tension and wall flexibility and decreasing wall damping.

Experiments on transition to turbulence in oscillatory pipe flow

A laser-Doppler velocimeter is used to analyse volume-cycled oscillatory flow of a Newtonian viscous fluid in a straight circular tube. The axial velocity is measured at radial positions across the diameter of the tube for a wide range of amplitude A = stroke distance/tube radius (2.4 [les ] A [les ] 21.6) and Womersley parameter (9 R δ R δ = α A √2 is the Reynolds number based on Stokes-layer thickness. The turbulence is confined to an annular region which is a few times the Stokes-layer thickness near the wall. Hot-film anemometer measurements indicate the core flow remains stable when the boundary layer becomes turbulent for R δ up to 1310.