Technology

Background

Flotation is an important separation technique which has been used for a century in the mining industry for recovery of valuable minerals. Flotation has also been adapted by other industries, e.g. the pulp and paper industry for separation of ink, toner, and other unwanted contaminants from wood fibers during waste paper recycle operations. In Canadian oil sands operation, flotation has been used to recover bitumen from oil sands. Air-particle or air-bitumen attachment is an essential step for a successful flotation and is strongly dependent on the chemistry of a flotation system. The attachment process involves thinning and rupture of the intervening film and formation of a stable three-phase contact line in a liquid. In a broader sense, induction time (t) is defined as the minimum times required for film thinning, film rupture and three-phase contact line expansion.

Since it is fairly difficult to accurately measure these times separately, in practice, they have been measured collectively and referred to as the induction time. The induction time plays a critical role in flotation. Under a given hydrodynamic condition, the shorter the induction time is, the higher is the flotation recovery.


Theoretical studies on film thinning, film rupture and three-phase contact line also showed that the induction time measured by moving an air bubble toward and then away from a mineral bed in a liquid is a function of physical properties of the solid particles (e.g. size, density and contact angle), physical properties of the liquid (viscosity, density and surface tension) and the three-phase contact line tension. The key factors controlling the attachment of air bubble-solid particles in a liquid are surface and interfacial properties of the intervening phases, e.g. surface energy of the solid
, surface tension of the liquid, interfacial tension of the solid-liquid as well as contact angle of the liquid contacting the solid surface. Only the contact angle and surface tension are directly measurable, all other surface and interfacial properties are derived from these two properties. It is desirable to have an instrument capable of measuring induction time, surface and interfacial properties. 
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Normally, studying the effect of flotation chemicals on flotation performance requires a Denver Flotation Cell test to obtain a froth followed by a series of assays of the recovered froth. This set of experiments at least takes 1-2 days to complete, it also need a few instruments to characterize surface/interfacial properties of both the solids  and the liquid, e.g. goniometer for contact angle measurement, tensiometer for surface/interfacial tension/energy and contact angle measurements, and drop shape analyzer also for surface/interfacial tension/energy and contact angle measurements. The multifunctional induction timer is an excellent tool for studying the effect of flotation chemicals on flotation performance. It just takes 1-2 hours to do an induction time measurement, whereby reducing overall cost and accelerating technological advancement.

Working principle of the instrument

Figure 1 is a 3D view of the instrument for measuring induction time, surface and interfacial properties, including a motorized vertical main stage holding the main drive (a voice coil motor or a speaker), a gas bubble or liquid drop generation system, an advanced image system including a high speed camera, a regular (or telecentric) zoom lens and a telecentric illuminator, a sample stage with a three-way manual translation, a precision micro (or submicro) displacement sensor, a multifunctional software, Floatimer, that controls all motors, monitors the displacement sensor’s feedback, records and analyzes images to make multifunctional measurements, and a control box enclosing all required electronics. With the gas bubble or liquid drop generation system, an air bubble of controllable size can be generated at the end of a capillary tube using a micro-syringe. The advanced image system is used to assist viewing the precise positioning and contacting process between the air bubble and solids particles, and to provide high quality images for edge detection and digital image processing.

induction-timer-3d-main-body

 Figure 1.  3D view of the Induction Timer’s main body.

Induction time measurement

A layer of testing solid particles is placed in a testing liquid (or solution) held in a square glass cell, a small air bubble is generated at the tip of the glass capillary using the gas bubble generation system. Induction time measurement comprises using a controller to send a square (or a ladder) wave instruction with a preset time period, tn, from the computer to an amplifier enclosed in the control box and observing whether attachment can be established between the air bubble and the solid particles in the testing liquid, the amplifier then applies a current to the drive, whereby to move the air bubble down to and make contact with the particle bed for the preset time period, tn, then retract to its original place as shown in Fig. 2(a). Induction time, tind, is defined as the minimum contact time required to establish attachment between the air bubble and the solid particles. When a few solid particles are observed at the bottom of the air bubble after the air bubble retracts to its original place, the attachment is established, the preset contact time, tn, is considered longer than the induction time, tind, a shorter time, tn-1, shall be preset and do another try. Contrarily, when no solid particle is observed at the bottom of the air bubble after the air bubble retracts to its original place, the attachment is not established, the preset contact time (tn) is considered shorter than the induction time (tind), a longer time, tn+1, shall be preset and another try shall be carried out. This testing procedure shall be performed as many times as possible till the incremental value (tn+1tn) is close or equal to the decremental value (tntn-1) and falls an acceptable error range, then the, tn, is considered as its induction time, tind.

The induction time of solid-air bubble can be measured either using an air bubble to attach a solid particle bed in a testing liquid as shown in Fig. 2(a) or using a drop of the testing liquid to attach the solid particles bed exposing in the air directly as shown in Fig. 2(b). The method 2(a) involves the liquid receding process (solid-air interface replacing solid-liquid interface), hence provides a receding induction time, treceding, while the method 2(b) involves the liquid advancing process (solid-liquid interface replacing solid-air interface), hence provides an advancing induction time, tadvancing.

The induction time of solid-air bubble in the testing liquid can also be measured using a solid substrate with a flat surface as shown in Fig. 2(c), attachment between the solid surface and the air bubble is believed to have been established when the air bubble is sticking on the solid surface after the capillary tube retracts to its original place. The induction time of solid-air bubble in the testing liquid can also be measured using a drop of the testing liquid to contact the solid substrate in the air environment as shown in Fig. 2(d), attachment between the solid surface and the testing liquid drop is believed to have been established when the drop of the testing liquid is sticking on the solid surface after the capillary tube retracts to its original place.  The method shown in Fig. 2(c) provides a receding induction time, while the method shown in Fig. 2(d) provides an advancing induction time.
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Figure 2. Illustrations of induction time measurement in different situations. (a) An air bubble attaching surface of solid particles in a testing liquid; (b) A drop of testing liquid attaching surface of solid particles exposing in the air; (c) An air bubble attaching surface of a solid substrate in a testing liquid; (d) A drop of testing liquid attaching surface of a solid substrate exposing in the air.

 

Measurements of contact angle, surface and interfacial tension

Surface and interfacial properties can be measured using drop methods (sessile drop method and pendant drop method) and probe methods (Du Noüy ring method, Du Noüy-Padday rodmethod and Wilhelmy plate method).

The sessile drop method
is used for characterization of solid surface energies, and in some cases, aspects of liquid surface energies as shown in Fig. 3(a). The shape of a liquid-vapor interface is determined by the Young-Laplace equation, with the contact angle playing the role of a boundary condition via Young’s Equation. The shape profile of the sessile drop is digitized and analyzed using Young-Laplace equation for contact angle calculation.

sessile-pandent-drop-methods-cropFigure 3. A schematic illustration of the drop methods: (a) the sessile drop and (b) the pendant drop methods, where θ is the contact angle, and γsg, γlg and γsl represent the solid-gas, liquid-gas, and solid-liquid interfacial energies, respectively, d is the capillary tube diameter, m is the weight of the pendant drop.

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If the solid-vapor interfacial energy is denoted by γsg, the solid-liquid interfacial energy by γsl, and the liquid–vapor interfacial energy (i.e. the surface tension) by γlg, then the equilibrium contact angle θc is determined from these quantities by Young’s Equation:

γ
sg  = γlg cosθ +  γsl,          (1)
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The main premise of the method is that by placing a drop of liquid with a known surface energy, the shape of the drop, specifically the contact angle, and the known surface energy of the liquid are the parameters which can be used to calculate the surface energy of the solid sample. The liquid used for such experiments is referred to as the probe liquid, and the use of several different probe liquids is required.

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The pendant drop method is a technique by which a drop of liquid is suspended from a tube (capillary or needle) in a bulk liquid or gaseous phase. The shape of the drop results from the relationship between the surface tension or interfacial tension and gravity. In the pendant drop method, the surface tension or interfacial tension is calculated from the shadow image of a pendant drop using drop shape analysis in accordance with Young-Laplace equation as shown in Fig. 3(b). The force due to surface tension is proportional to the length of the boundary between the liquid and the tube, with the proportionality constant usually denoted, γ. Since the length of this boundary is the circumference of the tube, the force due to surface tension is given by, Fγp d γ, where d is the tube diameter, p = 3.14159.

The mass, m, of the drop hanging from the end of the tube can be found by equating the force due to gravity with the component of the surface tension in the vertical direction giving the formula,

mg =  p d γ sin θ,              (2)

where θ is the contact angle with the tube, and g is the acceleration due to gravity. The limit of this formula, as θ goes to 90°, gives the maximum weight of a pendant drop for a liquid with a given surface tension, γ.

mg =  p d γ.                        (3)

This relationship is the basis of a convenient method of measuring surface tension. More sophisticated methods are available to take account of the developing shape of the pendant as the drop grows.

 

The du Noüy ring method is one technique by which the surface tension of a liquid or the interfacial tension between two liquids can be measured as shown in Fig. 4(a). The method involves slowly lifting a ring, often made of platinum or platinum-iridium, from the surface of a liquid. The material is also chemically inert and easy to clean. The force, , required to rise the ring from the liquid’s surface is measured and related to the liquid’s surface tension, γ :

F = 2 p (Ri + Ra) γ,               (4)

where  Ri is the radius of the inner ring of the liquid film pulled and Ra is the radius of the outer ring of the liquid film.

ring-rod-plate-methods-crop

Figure 4.  A schematic illustration of the probe methods: (a) the Du Noüy ring method,  (b) the Du Noüy-Padday rod method and  (c) the Wilhelmy plate method.
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The Du Noüy-Padday rod method is a minimized version of the Du Noüy ring method replacing the large platinum ring with a thin rod (probe) that is used to measure equilibrium surface tension or dynamic surface tension at an air-liquid interface. The rod is attached to a scale or balance via a thin metal hook. The Padday method uses the maximum pull force method, i.e. the maximum force due to the surface tension is recorded while the probe is first immersed approximately one mm into the liquid and then slowly withdrawn from the interface.

γ = Fmax / (2 p D)              (5)

where D is diameter of the probe, g  is the surface tension of the liquid. The maximum pull force is obtained when the buoyancy force reaches its minimum. This is observed as a maximum in the force curve, which relates to the surface tension.

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Wilhelmy plate method is used to measure equilibrium surface and interfacial tension at an air-liquid or liquid-liquid interface as shown in Fig. 4(c). In this method, the plate is oriented perpendicular to the interface, and the force exerted on it is measured. The Wilhelmy plate is often made from filter paper, glass or platinum which may be roughened to ensure complete wetting. In fact, the results of the experiment do not depend on the material used, as long as the material is wetted by the liquid.  The plate is cleaned thoroughly and attached to a balance with a thin metal wire. The force on the plate due to wetting is measured using a microbalance and used to calculate the surface tension, γ, using the Wilhelmy equation:

γ = F / (l cos θ)                   (6)

where l is the wetted perimeter (2w + 2d, w is the plate width and d is the plate thickness) of the Wilhelmy plate and θ is the contact angle between the liquid phase and the plate.

Measurements of advancing and receding contact angles

A given static system of solid, liquid, and vapor at a given temperature and pressure has a unique equilibrium contact angle. The equilibrium contact angle reflects the relative strength of the liquid, solid, and vapor molecular interaction. However, in practice contact angle hysteresis is observed, ranging from the so-called advancing (maximal) contact angle to the receding (minimal) contact angle. The equilibrium contact is within those values, and can be calculated from them. While for a given system of solid, liquid, and vapor at a given temperature and pressure with the liquid moving quickly over the solid surface, the contact angle can be altered from its value at rest. The advancing contact angle will increase with speed, and the receding contact angle will decrease. With the advanced high speed image system, both advancing and receding contact angles can be measured using the sessile drop method.