Though medical devices rarely use hydraulics, many devices employ microfluidic systems that contain liquids with very little extra room for expansion. Fluids can also be present in larger medical devices that utilize water chambers or contain human fluid samples for a variety of applications. Typically, none of these situations involve fluids under extreme pressures; however, it is common that sealed fluidic systems undergo thermal fluctuations. This can result in very intense pressures that can cause the chamber, or microfluidic pathway, to burst. For example, an increase from room temperature (20o C) to body temperature (35o C) of 10 ml of sealed water results in a pressure increase of 872 atm. This can present a risk to human health either through direct contamination (the liquid touches the patient) or false outputs (the diagnostic system loses accuracy, or the treatment system fails to effectively deliver treatment).
This article examines a two-step method to estimate the direct effects the thermal expansion of water will have on your system, and help to understand what you’re dealing with.
Background on the Thermal Expansion of Water
As water changes across a range in temperature, it will either expand or shrink, depending on where it is in Graph 1. You may also have heard water is unique in that its frozen form is larger (less dense) than its liquid form. This is true assuming we’re only comparing liquid water (0-100o C) to frozen water (less than 0o C). Even extremely cold ice is larger (less dense) than liquid water at any temperature (the curve on the left of the graph levels off as the ice gets colder). If water is contained to a sealed fluidic pathway and the volume is rising due to temperature effects, then something has to give, which will either be the liquid compressing or the wall expanding. The wall of the container will certainly burst if it isn’t able to contain the pressure by force or flexing.
Step 1: Calculating the Volumetric Effect on the System—Is It Significant?
The first step to understanding the effects of thermal expansion on your system is to calculate volumetric expansion. The simplest way to determine volume change is to use a chart like Graph 1 (others are available for other ranges), and a simple formula:
Water has very intense pressure expansion per unit of temperature. Fortunately, that also means a little bit of “give” in the container can reduce the internal pressure enormously. At this point in your calculations, you’ll want to stop and determine if the change in volume being imparted on your system is worrying or negligible. To do this, pretend that water is incompressible and envision the effect of this volume change on your pressure vessel. If the change in volume could cause failure, you’ll want to actually consider compressibility and carry on to determine pressure.
Step 2: Estimating the Pressure Effect on the System
If you need to know the pressure imparted on your fluidic system, start by finding the compressibility of your liquid. As implied by Graph 1, water expands at a different rate depending on its temperature, meaning calculating the given compressibility at a certain temperature requires a non-trivial formula (the compressibility of water is the reciprocal of the bulk modulus), or more simply, a graph like Graph 2.
A good general value for water around room temperature is often around 45.8 x 10-11Pa-1 ml/ml.
Using the general value for water compressibility, use the following formula to determine pressure effects of thermal expansion on your fluidic system:
This simple result can be used directly to calculate material failure (i.e., check whether the pressure is higher than yield strength), but that doesn’t account for displacement. A better option is to drop the expected pressure value into a Finite Element Analysis (FEA) tool that can convert pressure loading to a resultant displacement for your closed fluidic system. Check to see if the displacement caused by the pressure is greater than the ΔVnominal; if so, the water pressure may drop off before the material fails. Remember, even though you might find yourself with an extremely highΔP, even a small volumetric expansion in the pressure vessel will result in a significant drop in pressure. Iterations in the FEA and the use of localized high-resolution zones may be required to achieve an accurate result.
Notes on Specific Effect in Microfluidics
In microfluidics, expanding water could mean the plastic walls will simply deflect and absorb the expansion with little effect on the container itself, or it could mean the bonds between layers fail. This depends on a number of factors beyond the temperature changes, including material, bonding methods, and the aspect ratio of the fluidic channels.
Besides the mechanical frame failing, liquid expansion may also affect any sensors in your system, which tend to be vulnerable to perturbations. Even if they aren’t damaged long term, changes in pressure or volume may throw off their readings and result in inaccuracies.
Don't Forget Cyclic Loading!
Almost by nature, thermal expansion loading tends to be cyclic. Your system may be able to withstand a single cycle or a handful of cycles, but numerous cycles may affect your pressure vessel differently and cause long-term issues. This is a factor well worth exploring.
Possible Mitigation Strategies
There are a number of ways to mitigate thermal expansion of liquids. Bubbles, balloons, flexible wall material, dampeners, or large aspect ratio containers can often take up the load without significant changes. Avoiding adhesive joints may also reduce the chance of long-term failure.
Choosing a material with a high coefficient of thermal expansion may also lessen the impact of liquid expansion, as the material will expand and contract along with the contained liquid (from 4o C to 100o C for water, other liquids are more consistent across larger ranges).
Another great option is to limit temperature changes in the liquid or avoid them altogether. Heaters can be useful to avoid freezing conditions and coolers can be used if the ambient system is hotter than the liquid needs to be.
Don’t ignore the effects of liquid thermal expansion on any medical device that may contain fluids. Even a cursory check of the fluidic pressure against your base material is well worth the time to review. If a more complex analysis is needed, this article and some clever FEA should provide you with a tool to estimate the potential effects.
Nigel Syrotuck is the mechanical engineer team lead at StarFish Medical. His background includes a diverse project development portfolio including sustainable power solutions, assisted living devices, and nano-satellite design.