With the aim to set an objective approach of how to evaluate this “resistance to flow” it is necessary to previously resort two concepts:<\/p>\n
\u00a0 <\/p>\n
- \n
- Shear stress<\/strong><\/li>\n
- Speed of deformation<\/strong><\/li>\n<\/ul>\n
[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row][et_pb_column type=”4_4″][et_pb_text _builder_version=”3.21″]<\/p>\n
Shear Stress<\/h2>\n
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In a fluid that is in circulation and confined in a certain geometry, the velocity of each particle will be in general different from that of the rest of the particles and will depend on the distance from the particle with respect to the walls of the pipe. For example, in a fluid<\/strong> flowing with laminar flow <\/strong>inside a circular pipe, the velocity profile has a parabolic shape:<\/p>\n
[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row][et_pb_column type=”1_3″][\/et_pb_column][et_pb_column type=”1_3″][et_pb_image _builder_version=”3.21″ src=”https:\/\/www.sacome.com\/wp-content\/uploads\/2019\/05\/Regimen-laminar-por-el-interior-de-una-tuberia-circular.png” alt=”Laminar Flow” title_text=”Laminar Flow” \/][\/et_pb_column][et_pb_column type=”1_3″][\/et_pb_column][\/et_pb_row][et_pb_row][et_pb_column type=”4_4″][et_pb_text _builder_version=”3.21″]<\/p>\n
This difference between the velocity of a particle and the adjacent one is due to the internal force F<\/strong><\/i> (called shear force) that acts in the plane in which the particle is moving. The shear stress is then obtained by dividing this force between the surface A<\/strong><\/i> on which it acts.<\/p>\n
[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row][et_pb_column type=”1_4″][\/et_pb_column][et_pb_column type=”1_2″][et_pb_image _builder_version=”3.21″ src=”https:\/\/www.sacome.com\/wp-content\/uploads\/2019\/05\/Ecuacion-del-esfuerzo-de-cizalla.png” alt=”Rheology in the design of food processing plants” title_text=”Shear stress” \/][\/et_pb_column][et_pb_column type=”1_4″][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section bb_built=”1″ fullwidth=”off” specialty=”off” prev_background_color=”#000000″ next_background_color=”#000000″][et_pb_row][et_pb_column type=”4_4″][et_pb_text _builder_version=”3.21″]<\/p>\n
Shear Rate<\/h2>\n
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The deformation \u00fd<\/strong><\/i> is understood as the change in size or shape experienced by a body subjected to a stress. Thus, the shear rate \u00fd<\/strong><\/i> is defined as the variation of this deformation with respect to time.<\/p>\n
[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row][et_pb_column type=”1_4″][\/et_pb_column][et_pb_column type=”1_2″][et_pb_image _builder_version=”3.21″ src=”https:\/\/www.sacome.com\/wp-content\/uploads\/2019\/05\/Velocidad-de-deformacion.png” alt=”The Importance of rheology in the design of food plants” title_text=”Strain Rate” \/][\/et_pb_column][et_pb_column type=”1_4″][\/et_pb_column][\/et_pb_row][et_pb_row][et_pb_column type=”4_4″][et_pb_text _builder_version=”3.21″]<\/p>\n
In the case of a fluid<\/strong>, the shear rate<\/strong> is calculated by dividing the velocity by a characteristic length of the geometry in which the fluid circulates. For example, in a pipe of circular section it is:<\/p>\n
![\"null\"](\"https:\/\/www.sacome.com\/wp-content\/uploads\/2019\/05\/Velocidad-de-deformacion-en-un-fluido.png\")
<\/p>\nbeing U<\/strong><\/i> the average speed and D<\/strong><\/i> the inside diameter.<\/p>\n
In this way, the rheological behaviour of a fluid is characterized by the relationship that exists between the shear rate, \u00fd<\/i><\/strong> and the shear stress, \u03c4<\/i><\/strong> necessary to produce it, disclosing the internal structural changes that the product suffers during processing.<\/p>\n
![\"\"](\"https:\/\/www.sacome.com\/wp-content\/uploads\/2019\/05\/Relacion-entre-la-velocidad-de-deformacion-y-el-esfuerzo-de-cizalla.png\")
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With this in mind, a fluid can be classified as follows:<\/p>\n
<\/p>\n
- \n
- Newtonian fluid.<\/strong><\/li>\n
- Non-Newtonian fluid.<\/strong><\/li>\n
- Viscoelastic fluid.<\/strong><\/li>\n<\/ul>\n
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Newtonian Fluid<\/h3>\n
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In a Newtonian fluid<\/strong>, the ration \u03c4=\u03c4(\u00fd)<\/strong> is a ratio of proportionality, that is, in order to double the shear rate<\/strong>, it is necessary to double the shear stress <\/strong>as well.<\/p>\n
[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row][et_pb_column type=”1_4″][\/et_pb_column][et_pb_column type=”1_2″][et_pb_image _builder_version=”3.21″ src=”https:\/\/www.sacome.com\/wp-content\/uploads\/2019\/05\/Fluido-Newtoniano.png” \/][\/et_pb_column][et_pb_column type=”1_4″][\/et_pb_column][\/et_pb_row][et_pb_row][et_pb_column type=”4_4″][et_pb_text _builder_version=”3.21″]<\/p>\n
The proportionality constant obtained from the previous graph corresponds to the dynamic viscosity \u00b5<\/strong>.<\/p>\n
[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row][et_pb_column type=”1_4″][\/et_pb_column][et_pb_column type=”1_2″][et_pb_image _builder_version=”3.21″ src=”https:\/\/www.sacome.com\/wp-content\/uploads\/2019\/05\/Viscosidad-din\u00e1mica-\u00b5.png” alt=”The Importance of rheology in the design of food plants” title_text=”Dynamic viscosity \u00b5” \/][\/et_pb_column][et_pb_column type=”1_4″][\/et_pb_column][\/et_pb_row][et_pb_row][et_pb_column type=”4_4″][et_pb_text _builder_version=”3.21″]<\/p>\n
Non-Newtonian Fluid<\/h3>\n
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Non-Newtonian fluids<\/strong> are those that do not satisfy the above-mentioned ratio of proportionality (known as Newton’s law). In general, food products are characterized by non-Newtonian behaviour, due to the complexity of their internal structure. Some typical examples are:<\/p>\n
[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row][et_pb_column type=”1_4″][\/et_pb_column][et_pb_column type=”1_2″][et_pb_image _builder_version=”3.21″ src=”https:\/\/www.sacome.com\/wp-content\/uploads\/2019\/05\/Fluido-No-Newtoniano.png” alt=”The Importance of rheology in the design of food plants” title_text=”Non-Newtonian Fluid” \/][\/et_pb_column][et_pb_column type=”1_4″][\/et_pb_column][\/et_pb_row][et_pb_row][et_pb_column type=”4_4″][et_pb_text _builder_version=”3.21″]<\/p>\n
In view of the multiple behaviours<\/strong> that can be found in different food products<\/strong>, it is necessary to turn to the concept of apparent viscosity<\/strong>, thus developing useful engineering tools for design.<\/p>\n
The apparent viscosity is then defined as the slope of the curve \u03c4=\u03c4(\u00fd)<\/strong>, that is:<\/p>\n
[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row][et_pb_column type=”1_4″][\/et_pb_column][et_pb_column type=”1_2″][et_pb_image _builder_version=”3.21″ src=”https:\/\/www.sacome.com\/wp-content\/uploads\/2019\/05\/Viscosidad-aparente.png” alt=”Rheology in the design of food processing plants” title_text=”Apparent Viscosity” \/][et_pb_image _builder_version=”3.21″ src=”https:\/\/www.sacome.com\/wp-content\/uploads\/2019\/05\/Grafica-viscosidad-aparente.png” alt=”Rheology in the design of food processing plants” title_text=”Apparent Viscosity Chart” \/][\/et_pb_column][et_pb_column type=”1_4″][\/et_pb_column][\/et_pb_row][et_pb_row][et_pb_column type=”4_4″][et_pb_text _builder_version=”3.21″]<\/p>\n
We can find in the specialized literature many mathematical models that describe the relations \u03c4=\u03c4(\u00fd)<\/strong><\/i> and \u03b7=\u03b7(\u00fd)<\/strong><\/i>. Some examples are the Casson, Ellis, Herschel-Bulkley, Carreau, Cross or Powell-Eyring models. In general, these models fit properly only to a certain type of fluid and in a certain range of shear rate<\/strong>.<\/p>\n
- Non-Newtonian fluid.<\/strong><\/li>\n
- Speed of deformation<\/strong><\/li>\n<\/ul>\n
![\"\"](\"https:\/\/www.sacome.com\/wp-content\/uploads\/2019\/05\/Modelo-Power-Law_1.png\")
<\/p>\n![\"\"](\"https:\/\/www.sacome.com\/wp-content\/uploads\/2019\/05\/Modelo-Power-Law_2.png\")
<\/p>\n