Experimental Investigation of Wetting with Magnetic Fluids
Experimental Investigation of Wetting with Magnetic Fluids Selin Manukyan*, Marius Schneider** *Merck KGaA, Frankfurter Str. 250, 64283 Darmstadt, Germany **Technische Universität Darmstadt, Institute of Gas Turbines and Aerospace Propulsion, Otto-BerndtStraße 2, 64287 Darmstadt, Germany e-mail: [email protected]
Supplementary Information This information is available free of charge via the Internet at http://pubs.acs.org/. Nguyen defines the magnetic fluids in three groups, ferrofluids, magnetorheological fluid and magnetophoresic fluids, respectively (see table S1) [19]. According to these definitions, we can cluster the investigated liquids in ferrofluid and magnetophoresic fluid. Table S1: Effect of magnetic particle size on the characterization of the magnetic liquid [1]. Groups
Size of Magnetic Particle in the Carrier Liquid
Ferrofluids
Smaller than 10nm
Magnetorheological Fluids
ranging from 10 nm to 10 µm
Magnetophoresic Fluids
in the order of several microns or larger
Characterization The thermal energy dominates over the magnetic energy induced by an external magnetic field. Particles interact and react to the external magnetic field changing the viscosity of the fluid. Particles are considered as individual entities.
In figure S1 the internal and external body forces are sketched. The yellow arrows indicate the direction of movement of the three points observed in the experiments. The behavior of both droplets is opposite. The gravitational and pressure forces act in the same way in both cases: The gravitational force is always aligned with the gravitational field and the pressure force is directed towards the droplet’s surface. The forces resulting from surface tension are also equally directed in all points apart from the contact line. The surface tension acts in different directions at the contact lines due to the different initial contact angles of each liquid. For the ferrofluid, with a contact angle below 90°, the surface tension is directed towards the droplet’s central axis. For the water based magnetic paint droplet, with a contact angle above 90°, the surface tension is directed towards the outside. This results in the contact line being pulled towards the center of the droplet for the ferrofluid, i.e. a decrease of the diameter at the contact line, and vice versa for water based magnetic paint. Table S2 shows a simple relationship diagram of the force components applying on the both droplets. In figure S2 a sketch of the assumed magnetic particle orientation in both liquids under applied magnetic field is shown.
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Figure S1: Free body diagrams of the ferrofluid and magnetic paint drops. Table S2: Relationship of the force components on the magnetic liquids [1]. Case 1 (B=0)
Relationship of the Force Components Case 2 (B>0)
where θ is the contact angle and surface force is the product of droplet diameter and surface tension, the magnetic force is the product of magnetic force field, volume of the droplet, permeability of the vacuum, susceptibility difference between the liquid and magnetic particle [1].
Figure S2: Accumulation structure of the spherical and magnetic flake particles in ferrofluid and in magnetic paint under magnetic field (assumption).
References: 1. Nguyen N. Micro-magnetofluidics: interactions between magnetism and fluid flow on the microscale, Microfluidics and Nanofluidics 2012, 12 (1), 1-16.
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Supplementary Information This information is available free of charge via the Internet at http://pubs.acs.org/. Nguyen defines the magnetic fluids in three groups, ferrofluids, magnetorheological fluid and magnetophoresic fluids, respectively (see table S1) [19]. According to these definitions, we can cluster the investigated liquids in ferrofluid and magnetophoresic fluid. Table S1: Effect of magnetic particle size on the characterization of the magnetic liquid [1]. Groups
Size of Magnetic Particle in the Carrier Liquid
Ferrofluids
Smaller than 10nm
Magnetorheological Fluids
ranging from 10 nm to 10 µm
Magnetophoresic Fluids
in the order of several microns or larger
Characterization The thermal energy dominates over the magnetic energy induced by an external magnetic field. Particles interact and react to the external magnetic field changing the viscosity of the fluid. Particles are considered as individual entities.
In figure S1 the internal and external body forces are sketched. The yellow arrows indicate the direction of movement of the three points observed in the experiments. The behavior of both droplets is opposite. The gravitational and pressure forces act in the same way in both cases: The gravitational force is always aligned with the gravitational field and the pressure force is directed towards the droplet’s surface. The forces resulting from surface tension are also equally directed in all points apart from the contact line. The surface tension acts in different directions at the contact lines due to the different initial contact angles of each liquid. For the ferrofluid, with a contact angle below 90°, the surface tension is directed towards the droplet’s central axis. For the water based magnetic paint droplet, with a contact angle above 90°, the surface tension is directed towards the outside. This results in the contact line being pulled towards the center of the droplet for the ferrofluid, i.e. a decrease of the diameter at the contact line, and vice versa for water based magnetic paint. Table S2 shows a simple relationship diagram of the force components applying on the both droplets. In figure S2 a sketch of the assumed magnetic particle orientation in both liquids under applied magnetic field is shown.
Page 1 of 2
Figure S1: Free body diagrams of the ferrofluid and magnetic paint drops. Table S2: Relationship of the force components on the magnetic liquids [1]. Case 1 (B=0)
Relationship of the Force Components Case 2 (B>0)
where θ is the contact angle and surface force is the product of droplet diameter and surface tension, the magnetic force is the product of magnetic force field, volume of the droplet, permeability of the vacuum, susceptibility difference between the liquid and magnetic particle [1].
Figure S2: Accumulation structure of the spherical and magnetic flake particles in ferrofluid and in magnetic paint under magnetic field (assumption).
References: 1. Nguyen N. Micro-magnetofluidics: interactions between magnetism and fluid flow on the microscale, Microfluidics and Nanofluidics 2012, 12 (1), 1-16.
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