Esther Ventura-Medina

A model to describe flotation performance based on physics of foams and froth image analysis

A froth-based flotation description is developed that combines the physical structure and the kinetics of flowing froths. Foam physics indicates that bubbles have a polyhedral shape and consist of lamellae between bubbles and Plateau borders. Hydrophobic material is attached to bubbles in the lamellae, while both entrained hydrophobic and hydrophilic solids are in the Plateau borders, which form drainage channels where three lamellae meet. Further, hydrophobic solids that have become detached from the lamellae through coalescence or bursting also enter the Plateau borders. The flow rate of hydrophobic solids and liquid associated with the interbubble lamellae can be quantified by the total surface area of the overflowing froth and the thickness and solids concentration of the lamellae. These can be measured directly by dynamic image analysis and froth surface sampling. The amount of solids carried in the Plateau borders by the overflowing froth is determined by the concentration in, and volumetric flow rate of these channels. The Plateau borders volume depends on the channel length, determined by the bubble size, and the channel cross-sectional area, determined by the fraction of unbroken bubbles in the overflowing froth. These can also be obtained from image processing. Therefore, the total flow rate of hydrophobic and hydrophilic solids and liquid have two contributions, firstly from the interbubble lamellae, and secondly from the Plateau borders. Mass flow rate equations have been derived for each of these three components in terms of the measurable variables which allow the unknown solids concentrations in the Plateau borders to be estimated. Experimental data from an industrial flotation operation have been interpreted using the proposed model.

Calculation of the specific surface area in flotation

Different weighting functions for calculating the specific surface area and average bubble diameter in froth flotation have been studied. The weighting functions considered were number, length, area and volume. Using bubble size distribution data obtained from image processing of batch flotation froth, specific surface area and average equivalent diameter were calculated. It was found that weighting by surface area was the most appropriate method to determine both specific surface area and average equivalent diameter. The equivalent ellipsoidal diameter was found to be a more appropriate average diameter than the equivalent spherical diameter.

Puzzle-based learning of mathematics in engineering

Abstract Puzzle-based Learning is under-used in the teaching of mathematics to engineers. It is argued here that embedding puzzles in the teaching of other subjects enhances students’ learning by developing their problem-solving and independent-learning skills, whilst increasing their motivation to learn mathematics. The authors have defined a puzzle to be a problem that is perplexing and either has a solution requiring considerable ingenuity – perhaps a lateral thinking solution – or possibly results in an unexpected, even a counter-intuitive or apparently paradoxical solution. Engineering specific puzzle variants may help student learning, but specificity can also conflict with desirable simplicity, undermining the pedagogic value of a puzzle. It is not easy to categorize puzzles by level of difficulty, whether of the puzzle as a whole or the underlying mathematics, because this depends on the background and experience of the student. Classroom experiences of using puzzles in engineering teaching are described here, with some puzzles that illuminate these issues.

Knowledge disagreement formulations in problem-based learning tutorials: balancing pedagogical demands with 'saving face'

ABSTRACT As a pedagogical approach that aims to develop students’ group-working skills and to challenge their current knowledge, problem-based learning (PBL) provides a unique setting in which to examine disagreements in interaction. Previous research on disagreements in classrooms has typically examined tutor–student interaction or student–student interaction in which a tutor is present. This paper, however, examines tutorless PBL tutorials and focuses specifically on those moments in which knowledge claims are challenged by other students. The data comprise 30 h of video recordings from 24 chemical engineering PBL tutorials in a Scottish university. Conversation analysis was used to identify 101 disagreement formulations, many of which follow the format seen in other classroom settings (e.g. agreement-prefaced disagreements). A subset of disagreement formulations manage epistemic responsibility through invoking expert sources (e.g. tutor-provided worksheets and academically superior out-group members). Through invoking an expert source in this way, students attend to the pedagogical activities – without tutor assistance – while minimising the conversational trouble associated with the act of ‘doing’ disagreement (i.e. indirectly enacting disagreements whilst maintaining a neutral stance). This paper thus contributes to CA literature on disagreements, while providing a unique insight into PBL tutorial interaction. Directions for future research are suggested.

LIQUID PHASE MIXING IN A SLURRY BUBBLE COLUMN WITH DRAFT TUBE

Abstract In this work we characterize liquid phase mixing in a 150 L bubble column with a draft tube (internal airlift configuration) for a water-air-sand system at high solid concentrations. Liquid mixing is assessed by measuring the evolution of sodium chloride concentration after a pulse of concentrated NaCl solution is injected. Tracer concentrations were measured by means of electrical conductivity probes. The experimental set up consists of a 0.29 m internal diameter, 3 m length Plexiglas column with a conical bottom (cone apex angle of 60°) and a concentric draft tube with 0.14 m internal diameter and 2 m length. The gas superficial velocity based on the cross section of the column vaired from 0.057 to 0.22 m/s. Sand particles of 280 μm in average size were used, with slurry concentrations ranging from 120 to 500 kg/m3. From the tracer outputs, circulation time (time between peaks of the response curve) and mixing time (time required to achieve a 95% homogeneous solution) were determined after the ...