Microfluidics ENGR 1182 03 Pre Lab Review hydrostatic

Microfluidics ENGR 1182. 03 Pre Lab

Review: hydrostatic pressure Pa The pressure at the bottom of an open container filled with liquid: h P

Example: for water (r = 1000 kg/m 3) at sea level (g = 9. 80 m/s 2) the hydrostatic pressure at a depth of h =10 m is: Pressure conversion factors: 1 atm = 1. 01325 × 105 N/m 2 = 14. 696 psi

Surface tension concave meniscus § When a glass tube is immersed in water, liquid rises inside the tube due to surface tension and a concave meniscus forms. § Surface tension can be thought of as a force, acting along the air/water/glass contact line, that “pulls” the liquid up the tube. § Surface tension is caused by intermolecular forces.

Capillary flow ¡Surface tension can therefore cause fluid to flow in a capillary channel. Important factors are: § tube orientation and the gravitational constant (g) § diameter of tube § density (r) and surface tension (g) of the liquid § chemical nature of the tube walls

A capillary “valve” ¡ If a tube initially filled with water is allowed to slowly drain, not all of the liquid drains out. ¡ In addition to surface tension at the top of the liquid, surface tension also acts to counter the expansion of surface area at the exit, and therefore prevents further flow. ¡ This is the basic principle behind a capillary check valve; undesired flow can be resisted by introducing a sudden expansion in a flow channel.

Let’s take another look at a vertical capillary tube immersed in liquid. Liquid spontaneously rises until it reaches an equilibrium height. P 1 ¡ The hydrostatic pressure at height h. A is: P 2 ¡ P 1 - P 2 = ρgh. A ¡ P 2 = P 1 – ρgh. A where ρ is density of fluid P 1 ¡ Note that pressure P 2 (just beneath the surface) is not equal to P 1! This is a consequence of this interface being curved.

P 1 Now let’s take another look at a capillary tube that is initially filled and allowed to slowly drain until it reaches the equilibrium state shown here. P 2 ¡ At equilibrium, ¡ P 3 = P 2 + ρgh. B ¡ Substituting equation for P 2: ¡ P 3 = P 1 – ρgh. A + rgh. B ¡ P 3 – P 1 = ρg(h. B – h. A) P 3 P 1 (P 3– P 1) is the pressure rating of this capillary valve. A pressure > (P 3– P 1) is required to make liquid flow through this valve.

Capillary check valves can be used to prevent undesired flow into or out of a fluid reservoir in a device with micronsized channels.

Learning Objectives of Lab ¡Understand capillary flow and how a capillary valve works. ¡Explore how the flow of fluid in a micro-channel depends on pressure and geometry. ¡Practice delivering and cleansing mock samples.