Capillary Flows

Capillary flows are commonly encountered in microfluidic devices. For example, in bio chip designs lengthy micro channels are often used to deliver liquid solution from one place to another. An inlet channel is connected to a liquid reservoir and surface tension forces pull the liquid into the micro channel (provided the liquid is “wetting” to the chip surface). This page covers some specific applications for FLOW-3D in the analysis of such capillary flows: filling, absorption and switching.

Marangoni flow in a dish of water that is heated at its center. Flow generated by non-uniform surface tension is demonstrated by a shallow 8.0 cm diameter dish of water of depth 0.75 cm at an initial temperature of 20º C. Placed at the center of the circular dish is a cylindrical rod of diameter 0.5 cm, which is heated to a temperature of 80 Cº and is submerged into the water surface to a depth of 0.05 cm. As the water near the hot rod is heated its surface tension is reduced by an amount of 0.1678 dyne/cm/ºC causing the surface to retract toward the outer rim of the dish. The retraction is shown by massless marker particles initially sprinkled over the surface.

Capillary Absorption

Capillary absorption into the pore of a solid substance occurs because of adhesion between the liquid and the solid. A simple, yet useful, test of absorption has been suggested by Martti Toivakka of Abo Akademi University in Finland. The test pore consists of a1.0 μm wide, two-dimensional channel connected to an expanding throat whose side walls are circular arcs with 1.0 μm radii. In the absence of body forces, surface tension and wall adhesion pull liquid into the channel to a level that depends on the static contact angle between the liquid and solid. The accompanying figures show that FLOW-3D correctly computes the filling level (fluid is red) for any given contact angle.

Thermocapillary Switch

A small mass of liquid moved in or out of the path of a light beam can redirect it by refraction or reflection into a different path. This concept is particularly attractive in connection with optical fibers where once a beam enters a fiber it is trapped by internal reflections. To make optical circuits of any complexity, it is necessary to have a “switch” that can redirect light from one fiber to another.

One concept that has been proposed is based on thermo-capillarity. A small drop of liquid is placed in a micro channel that intersects a fiber-optic light beam. When the drop is moved along the channel to where the beam must pass through it, the beam is reflected into a different fiber. The drop is moved by differentially heating its two sides. This causes changes in the surface tension in the menisci on either side of the drop such that the drop is pulled toward the cooler end of the channel.

The animation above shows a FLOW-3D simulation of a drop of water in a 14mm-wide channel that is being heated at the bottom.

Capillary Filling

Understanding the capillary filling process is important to chip design. Different geometry of liquid flow pathways may result in different capillary filling behavior including the possibility of entrapping air bubbles, etc. Knowledge of the filling process guides designers in arranging internal structures of the chip such as chambers, binding pillars, splits, and valves.

The simulation below validates the analytic prediction of capillary action. The capillary fill is balanced by surface tension and gravity, which is a fundamental process accurately predicted by FLOW-3D.