Direct and non-invasive measurement of the pressure distribution in test sections of a micro-channel is a challenging, if not an impossible, task. Here, we present an analytical method for extracting the pressure distribution in a deformable microchannel under flow. Our method is based on a measurement of the channel deflection profile as a function of applied hydrostatic pressure; this initial measurement generates 'constitutive curves' for the deformable channel. The deflection profile under flow is then matched to the constitutive curves, providing the hydrodynamic pressure distribution. The method is validated by measurements on planar microfluidic channels against analytic and numerical models. The accuracy here is independent of the nature of the wall deformations and is not degraded even in the limit of large deflections, ζ max /2h 0 = O(1), with ζ max and 2h 0 being the maximum deflection and the unperturbed height of the channel, respectively. We discuss possible applications of the method in characterizing micro-flows, including those in biological systems.
The dominance of conduction and the negligible effect of gravity, and hence free convection, are verified in the case of microscale heat sources surrounded by air at atmospheric pressure. A list of temperature-dependent heat transfer coefficients is provided. In contrast to previous approaches based on free convection, supplied coefficients converge with increasing temperature. Instead of creating a new external function for the definition of boundary conditions via conductive heat transfer, convective thin film coefficients already embedded in commercial finite element software are utilized under a constant heat flux condition. This facilitates direct implementation of coefficients, i.e. the list supplied in this work can directly be plugged into commercial software. Finally, the following four-step methodology is proposed for modeling: (i) determination of the thermal time constant of a specific microactuator, (ii) determination of the boundary layer size corresponding to this time constant, (iii) extraction of the appropriate heat transfer coefficients from a list provided and (iv) application of these coefficients as boundary conditions in thermomechanical finite element simulations. An experimental procedure is established for the determination of the thermal time constant, the first step of the proposed methodology. Based on conduction, the proposed method provides a physically sound solution to heat transfer issues encountered in the modeling of thermal microactuators.
In order to understand how interstitial fluid pressure and flow affect cell behavior, many studies use microfluidic approaches to apply externally controlled pressures to the boundary of a cell-containing gel. It is generally assumed that the resulting interstitial pressure distribution quickly reaches a steady-state, but this assumption has not been rigorously tested. Here, we demonstrate experimentally and computationally that the interstitial fluid pressure within an extracellular matrix gel in a microfluidic device can, in some cases, react with a long time delay to external loading. Remarkably, the source of this delay is the slight (∼100 nm in the cases examined here) distension of the walls of the device under pressure. Finite-element models show that the dynamics of interstitial pressure can be described as an instantaneous jump, followed by axial and transverse diffusion, until the steady pressure distribution is reached. The dynamics follow scaling laws that enable estimation of a gel's poroelastic constants from time-resolved measurements of interstitial fluid pressure.
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