Time-dependent viscosity

Last updated
Blue: With increasing shear rate the system is breaking down Green: With decreasing shear rate the system is building up Flow curve of thixotropic systems with and without Shear.jpg
Blue: With increasing shear rate the system is breaking down Green: With decreasing shear rate the system is building up

In continuum mechanics, time-dependent viscosity is a property of fluids whose viscosity changes as a function of time. The most common type of this is thixotropy, in which the viscosity of fluids under continuous shear decreases with time; the opposite is rheopecty, in which viscosity increases with time.


Thixotropic fluids

Some non-Newtonian pseudoplastic fluids show a time-dependent change in viscosity and a non-linear stress-strain behavior in which the longer the fluid undergoes shear stress, the lower its viscosity becomes. A thixotropic fluid is one that takes time to attain viscosity equilibrium when introduced to a step change in shear rate. When shearing in a thixotropic fluid exceeds a certain threshold, it results in a breakdown of the fluid's microstructure and the exhibition of a shear thinning property.

Certain gels or fluids that are thick (viscous) under static conditions will begin to thin and flow as they are shaken, agitated, or otherwise stressed. When stress ceases, they regress to their more viscous state after a passage of time. Some thixotropic fluids return to a gel state almost instantly, such as ketchup, and are called pseudoplastic fluids. Others, such as yogurt, take much longer and can become nearly solid. Many gels and colloids are thixotropic materials, exhibiting a stable form at rest but becoming increasingly fluid when agitated.

Examples and Applications

Cytoplasm, synovial fluid (found in joints between some bones), and the ground substance in the human body are all thixotropic, as is semen. [1] Some varieties of honey (e.g.heather honey)can exhibit thixotropy under certain conditions.

Some clays (including bentonite and montmorillonite) exhibit thixotropy, as do certain clay deposits found in caves (slow flowing underground streams tend to layer fine-grained sediment into mudbanks that initially appear dry and solid but then become moist and soupy when dug into or otherwise disturbed). Drilling muds used in geotechnical applications can be thixotropic.

Semi-solid casting processes such as thixomoulding use the thixotropic property of some alloys (mostly light metals, e.g. bismuth) to great advantage. Within certain temperature ranges and with appropriate preparation, these alloys can be injected into molds in a semi-solid state, resulting in a cast with less shrinkage and other superior properties than those cast in normal injection molding processes.

Solder pastes used in electronics manufacturing printing processes are thixotropic.

Many kinds of paints and inks (e.g. the plastisols used in silkscreen textile printing) exhibit thixotropic qualities. In many cases it is desirable for an ink or paint to flow sufficiently fast to form a uniform layer, but then resist further flow (which on vertical surfaces can result in sagging). Thixotropic inks that quickly regain a high viscosity are used in CMYK-type printing processes; this is necessary to protect the structure of the dots for accurate color reproduction.

Thread-locking fluid is a thixotropic adhesive that cures anaerobically.

Thixotropy has been proposed as a scientific explanation of blood liquefaction miracles such as that of Saint Januarius in Naples. [2]

Other examples of thixotropic fluids are gelatine, shortening, cream, xanthan gum solutions, aqueous iron oxide gels, pectin gels, hydrogenated castor oil, carbon black suspension in molten tire rubber, many floc suspensions, and many colloidal suspensions.

Rheopectic fluids

Basically the mirror of thixotropy, rheopectic fluids are an even rarer class of non-Newtonian fluids that exhibit a time-dependent increase in viscosity; they thicken or solidify when shaken or agitated. The longer they undergo a shearing force, the higher their viscosity becomes, [3] as the microstructure of a rheopectic fluid builds under continuous shearing (possibly due to shear-induced crystallization).

Examples and Applications

Examples of rheopectic fluids include some gypsum pastes, printer inks, and lubricants.

There is also aggressive ongoing research into rheopectic materials especially with regard to potential uses in shock absorption. In addition to obvious potential military applications, rheopectic padding and armor could offer significant advantages over alternative materials currently in use in a wide range of fields from sporting goods and athletic footwear to skydiving and automobile safety.

Additional insights into rheopecty and the possible uses of rheopectic fluids can be gained through further research into the physics of hysteresis. [4]

X Axis: Viscosity Y Axis: Shear Force Different Fluids showing variation of Viscosity with Shear Force.jpg
X Axis: Viscosity Y Axis: Shear Force

See also


  1. Hendrickson, T: "Massage for Orthopedic Conditions", page 9. Lippincott Williams & Wilkins, 2003.
  2. Garlaschelli, Ramaccini, Della the swagg fights of air forces Sala, "The Blood of St. Januarius", Chemistry in Britain30.2, (1994:123)
  3. "BBC Science - How to: make a liquid that's also a solid". Bbc.co.uk. 2013-08-05. Retrieved 2015-03-08.
  4. Harlow, Francis H.; Welch, J. Eddie (1965). "Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface". Physics of Fluids. 8 (12): 2182. doi:10.1063/1.1761178 . Retrieved 2014-05-25.

Related Research Articles

In physics, a fluid is a liquid, gas, or other material that continuously deforms (flows) under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear force applied to them.

<span class="mw-page-title-main">Fluid dynamics</span> Aspects of fluid mechanics involving flow

In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics and hydrodynamics. Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.

Rheology is the study of the flow of matter, primarily in a fluid state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force. Rheology is a branch of physics, and it is the science that deals with the deformation and flow of materials, both solids and liquids.

A viscometer is an instrument used to measure the viscosity of a fluid. For liquids with viscosities which vary with flow conditions, an instrument called a rheometer is used. Thus, a rheometer can be considered as a special type of viscometer. Viscometers can measure only constant viscosity, that is, viscosity that does not change with flow conditions.

A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, that is, it has variable viscosity dependent on stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. Ketchup, for example, becomes runnier when shaken and is thus a non-Newtonian fluid. Many salt solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as custard, toothpaste, starch suspensions, corn starch, paint, blood, melted butter, and shampoo.

The Deborah number (De) is a dimensionless number, often used in rheology to characterize the fluidity of materials under specific flow conditions. It quantifies the observation that given enough time even a solid-like material might flow, or a fluid-like material can act solid when it is deformed rapidly enough. Materials that have low relaxation times flow easily and as such show relatively rapid stress decay.

A Newtonian fluid is a fluid in which the viscous stresses arising from its flow are at every point linearly correlated to the local strain rate — the rate of change of its deformation over time. Stresses are proportional to the rate of change of the fluid's velocity vector.

In continuum mechanics, a power-law fluid, or the Ostwald–de Waele relationship, is a type of generalized Newtonian fluid for which the shear stress, τ, is given by

Hemorheology, also spelled haemorheology, or blood rheology, is the study of flow properties of blood and its elements of plasma and cells. Proper tissue perfusion can occur only when blood's rheological properties are within certain levels. Alterations of these properties play significant roles in disease processes. Blood viscosity is determined by plasma viscosity, hematocrit and mechanical properties of red blood cells. Red blood cells have unique mechanical behavior, which can be discussed under the terms erythrocyte deformability and erythrocyte aggregation. Because of that, blood behaves as a non-Newtonian fluid. As such, the viscosity of blood varies with shear rate. Blood becomes less viscous at high shear rates like those experienced with increased flow such as during exercise or in peak-systole. Therefore, blood is a shear-thinning fluid. Contrarily, blood viscosity increases when shear rate goes down with increased vessel diameters or with low flow, such as downstream from an obstruction or in diastole. Blood viscosity also increases with increases in red cell aggregability.

In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed.

<span class="mw-page-title-main">Thixotropy</span> Change in viscosity of a gel or fluid caused by stress

Thixotropy is a time-dependent shear thinning property. Certain gels or fluids that are thick or viscous under static conditions will flow over time when shaken, agitated, shear-stressed, or otherwise stressed. They then take a fixed time to return to a more viscous state. Some non-Newtonian pseudoplastic fluids show a time-dependent change in viscosity; the longer the fluid undergoes shear stress, the lower its viscosity. A thixotropic fluid is a fluid which takes a finite time to attain equilibrium viscosity when introduced to a steep change in shear rate. Some thixotropic fluids return to a gel state almost instantly, such as ketchup, and are called pseudoplastic fluids. Others such as yogurt take much longer and can become nearly solid. Many gels and colloids are thixotropic materials, exhibiting a stable form at rest but becoming fluid when agitated. Thixotropy arises because particles or structured solutes require time to organize. An overview of thixotropy has been provided by Mewis and Wagner.

<span class="mw-page-title-main">Dilatant</span> Material in which viscosity increases with the rate of shear strain

A dilatant material is one in which viscosity increases with the rate of shear strain. Such a shear thickening fluid, also known by the initialism STF, is an example of a non-Newtonian fluid. This behaviour is usually not observed in pure materials, but can occur in suspensions.

In continuum mechanics, rheopecty or rheopexy is the rare property of some non-Newtonian fluids to show a time-dependent increase in viscosity ; the longer the fluid undergoes shearing force, the higher its viscosity. Rheopectic fluids, such as some lubricants, thicken or solidify when shaken. The opposite and much more common type of behaviour, in which fluids become less viscous the longer they undergo shear, is called thixotropy.

<span class="mw-page-title-main">Thickening agent</span> Increases the viscosity of a liquid without altering its other properties

A thickening agent or thickener is a substance which can increase the viscosity of a liquid without substantially changing its other properties. Edible thickeners are commonly used to thicken sauces, soups, and puddings without altering their taste; thickeners are also used in paints, inks, explosives, and cosmetics.

Fluid mechanics is the branch of physics concerned with the mechanics of fluids and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and biomedical engineering, geophysics, oceanography, meteorology, astrophysics, and biology.

<span class="mw-page-title-main">Shear thinning</span> Non-Newtonian fluid behavior

In rheology, shear thinning is the non-Newtonian behavior of fluids whose viscosity decreases under shear strain. It is sometimes considered synonymous for pseudo-plastic behaviour, and is usually defined as excluding time-dependent effects, such as thixotropy.

<span class="mw-page-title-main">Viscosity</span> Resistance of a fluid to shear deformation

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.

Bagnold's fluid refers to a suspension of neutrally buoyant particles in a Newtonian fluid such as water or air. The term is named after Ralph Alger Bagnold, who placed such a suspension in an annular coaxial cylindrical rheometer in order to investigate the effects of grain interaction in the suspension.

An important class of non-Newtonian fluids presents a yield stress limit which must be exceeded before significant deformation can occur – the so-called viscoplastic fluids or Bingham plastics. In order to model the stress-strain relation in these fluids, some fitting have been proposed such as the linear Bingham equation and the non-linear Herschel-Bulkley and Casson models.

Biofluid dynamics may be considered as the discipline of biological engineering or biomedical engineering in which the fundamental principles of fluid dynamics are used to explain the mechanisms of biological flows and their interrelationships with physiological processes, in health and in diseases/disorder. It can be considered as the conjuncture of mechanical engineering and biological engineering. It spans from cells to organs, covering diverse aspects of the functionality of systemic physiology, including cardiovascular, respiratory, reproductive, urinary, musculoskeletal and neurological systems etc. Biofluid dynamics and its simulations in computational fluid dynamics (CFD) apply to both internal as well as external flows. Internal flows such as cardiovascular blood flow and respiratory airflow, and external flows such as flying and aquatic locomotion. Biological fluid Dynamics involves the study of the motion of biological fluids. It can be either circulatory system or respiratory systems. Understanding the circulatory system is one of the major areas of research. The respiratory system is very closely linked to the circulatory system and is very complex to study and understand. The study of Biofluid Dynamics is also directed towards finding solutions to some of the human body related diseases and disorders. The usefulness of the subject can also be understood by seeing the use of Biofluid Dynamics in the areas of physiology in order to explain how living things work and about their motions, in developing an understanding of the origins and development of various diseases related to human body and diagnosing them, in finding the cure for the diseases related to cardiovascular and pulmonary systems.