Solvent viscosity, pressure drop across the filter, nominal pressure, pressure gradient, flow rate, Newtonian fluid… It is not always easy to understand what lies behind these various physical parameters and fluid characteristics.
Yet to select and size the appropriate filters for specific production circuits, decipher a filter’s technical documentation, ensure maintenance of filtration systems, and replace them at the right moment, it is essential to understand what these concepts represent and how they matter in practice. Pemflow has prepared a concise introduction to applied fluid mechanics for you.
Filtration and fluid mechanics
Fluid mechanics is the branch of physics that studies the flow of liquid or gaseous fluids. When fluids are at rest, the field is referred to as fluid statics. When they are in motion—which is typically the case in filtration systems—it is referred to as fluid dynamics.
Flow
The volumetric flow rate of a fluid refers to the volume of fluid passing through a given cross-section per unit of time. It is expressed in m³/s.
In an installation using filtration systems, it is important to size the filters and pumps according to the volume of fluid to be processed per unit of time.
The geometry and structure of the filter media used (hollow fibers, woven fibers, etc.) determine the available filtration surface area and, ultimately, the fluid flow rate that can pass through it.
Pressure
Pressure
In a fluid, particles are in random motion. At any given moment, some of them collide with and rebound off the walls of the container holding the fluid. The force exerted by the fluid on the wall, perpendicular to its surface, is called the pressure force. This pressure force is proportional to the surface area considered.
A quantity called pressure is therefore defined, corresponding to the force per unit area, expressed in Pascals (1 Pa = 1 N/m²).
Compressibility
When a constraint is applied to a fluid, it will deform to a greater or lesser extent depending on its nature. A fluid’s compressibility reflects the relative decrease in its volume under the effect of pressure. Compressibility is high for gases and much lower for liquids. In other words, gases are generally easy to compress, whereas liquids are much more difficult to compress.
Viscosity
Some fluids, such as oil or glycerin, exhibit a certain resistance to flow. Other fluids, such as water, flow with far less difficulty. Oil and glycerin are therefore said to be more viscous than water.
A fluid’s viscosity characterizes its resistance to flow. It is defined as the ratio between the velocity gradient and the applied stress. It is linked to the friction forces acting between fluid particles when the fluid is set in motion.
Viscosity must be taken into account, for example, when selecting pump power and the geometry of the filters used. Dynamic viscosity is expressed in Pascal-seconds (Pa·s).
It is sometimes expressed in poise (1 Pa·s = 10 P) or centipoise (1 cP = 1 mPa·s). Viscosity dissipates the fluid’s energy and is associated with the concept of pressure drop.
Expert advice
The high viscosity of inks and paints (several hundred cP) requires the use of very specific filters.
Discover our filtration solutions for inks and solvents
Newtonian fluid
Fluids can be divided into two families depending on how their viscosity behaves under mechanical stress.
A fluid is said to be Newtonian when its viscosity is independent of the applied stress. The viscosity of Newtonian fluids, such as water, air, and most gases, is therefore constant or varies only with temperature.
When a fluid’s viscosity varies with the mechanical stress applied, it is referred to as non-Newtonian.
This is the case for most fluids: gels, slurries, pastes, suspensions, emulsions…
In some cases, their viscosity increases when mechanical action is applied; such fluids are called shear-thickening (rhéoépaississants).
A typical example is wet sand or preparations based on cornstarch: they flow like a liquid when at rest but become very hard when stirred or pressed.
Conversely, some fluids exhibit a decrease in viscosity under applied stress: these are known as shear-thinning or pseudoplastic fluids. This is the case for certain inks, varnishes, and paints. Thus, while paints spread easily under stress (the brush), they stop flowing as soon as the brush stroke is completed—that is, once no further stress is applied. This property is extremely useful in practice when carrying out painting work.
Finally, some fluids experience changes in their flow properties over time when subjected to stress. If they become increasingly fluid, like yogurt or ketchup, they are called thixotropic. Conversely, if their viscosity increases, they are referred to as antithixotropic fluids.
Pressure drop
Pressure drop refers to the dissipation, through friction, of the mechanical energy of a moving fluid. In a horizontal pipe, this energy dissipation results in a pressure decrease along the flow path.
To maintain fluid movement through a system, energy must therefore be supplied to compensate for that lost through friction. Pressure losses depend on the shape, dimensions, and roughness of the components (pipes, pumps, etc.), the flow velocity, and the fluid’s viscosity.
Pressure losses are called linear or regular when they occur along the length of the piping. They are referred to as singular when they occur at components that change the direction or cross-section of the fluid (fittings, valves, check valves, heat exchangers, etc.).
During a filtration operation, the fluid loses energy (singular pressure drop) as it passes through the filtration device, resulting in a pressure decrease. This decrease depends in particular on the filter’s structure, the nature of the filter media, and the degree of filter fouling.
Manufacturers generally indicate the pressure drop associated with flow through the filter on the corresponding product datasheet.
This is an important parameter to consider when selecting a filtration system, as it determines performance, operating costs of the installation, and so on.
Expert advice
Certain filter cartridges, such as FiberFlo® cartridges used to filter bacteria and endotoxins, offer a large filtration surface within a compact footprint. This large filtration surface allows a high fluid flow rate to pass through with a low pressure drop.
A turbulent flow, on the other hand, is a disordered flow in which fluid layers mix due to vortices created within the fluid.
Un écoulement turbulent est au contraire un écoulement qui se produit de façon désordonné. Les couches de fluide se mélangent les unes aux autres sous l’effet des tourbillons qui se créent dans le fluide.
The observed flow regime depends in particular on the fluid’s viscosity and its velocity.
Depending on the flow regime, pressure losses vary because the fluid’s behavior changes. Laminar flow is generally preferred in industry because it limits pressure losses and therefore reduces energy consumption.
Shear
A shear stress is a mechanical stress applied tangentially to the surface of a material, as opposed to normal stresses, which act perpendicular to the surface.
Consider the example of a liquid flowing between two parallel plates. If the lower plate is fixed while a force is applied to the upper plate to set it in motion, tangential stresses are exerted on the liquid, causing the fluid layers to move.
The velocity they acquire depends on the viscosity of the liquid. The liquid layers move faster the closer they are to the moving plate. A velocity gradient is then established within the fluid. The fluid is said to be sheared.
In the case of so-called complex fluids (for example, a liquid solution containing polymers, or the foams and emulsions produced in the pharmaceutical industry), viscosity generally depends on the shear rate they experience. These fluids may also be damaged if the shear is too strong.
Expert advice
For transferring fragile fluids, it is recommended to use a diaphragm pump, which minimizes shear that could damage the fluid.
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