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"The application of telerobotics to mining is currently being introduced into production systems around the world. Mining companies in Canada, Sweden, South Africa, and Australia have tended to lead the international charge to this form of technology for mining. While this introduction is taking place, a few basic questions have yet to be answered. How many machines can a single operator run? How many types of machines can a single operator run?A Canadian Research Chair in Robotics and Mine Automation has been established at Laurentian University to investigate these questions and many more through a series of experiments in a telerobotics laboratory that connects Laurentian teleoperation workstations to model mining machines at Cambrian College’s eDome. The laboratory supports many experiments allowing researchers to physically run multiple robot scenarios differing the numbers and types of machines at one quarter scale. Further experiments are being designed to investigate the potential for managing time delays in telerobotics. This paper describes the laboratory, experiments, and some preliminary results."

Jan 1, 2005

By Bruno Lemelin

Falconbridge Ltd Raglan Mine has been in production since 1998 and has produced annually some 900 000T of ore grading 3.1% nickel, 0.9% copper and 0.06% cobalt. The mine is located in Nunavik, Northern Quebec. The current mine life is estimated at approximately 20 years. Reserves are composed of numerous small ore bodies situated across a 65 km strike length. Planning the extraction of the ten small mineralized zones represents a great challenge to optimize. The overall objective is to maximize the company?s return on net assets. Actual planning uses computerized technology tools like Automod and Mine2-4D, and a conventional discounted cash flow method (DCF) of calculating net present value (NPV). The complex setting of Raglan could benefit from advance valuation techniques such as the real options method (RO). This paper will present the characteristics if the mines that make it a good candidate to use RO to gain further insight.

May 1, 2004

By Vu Van Dong

Resource estimation is the science of determining the amount and quality of a given material in the ground that has the potential to be mined at a profit. This is because during this time computers have become more widely available and more powerful and software packages have become more comprehensive and user friendly. Over the past three years The Mining Geology Company with the support from Vinacomin Group has developed the Coal Geological Modelling and Reserve Estimation ? VMG system. The VMG system enables the geological and mining engineer to start at the reserve estimation for the mine design and planning. The VMG system enables the national and international standards (NI43-101, CIM-Canada; SAMREC Code, Africa, and JORC Code, Australia) and user friendly with menu driven thereby permitting the engineer with minimal computer training to rapidly learn and utilize the system. Geological and mining data input through digitized map files and drill-holes information files stored in the database that is an integral part of the VMG system with the main function for collection, validation, and recording, storing and processing of data will include both ?primary? (observation and measurement) and ?interpreted? data. It is recommend that data be stored digitally, using a documented, standard format and a reliable storage medium that allows for easy and complete retrieval of the data. The coal reserve estimation through standard polygon methods with the increased use of these mathematical techniques (geometrical modelling, geostatistical method, least square method, ?) over the last ten years corresponds, to some degree, to a decrease in both the amount of the coal deposit mapping and, in particular, coal seam structural interpretation and modelling, and permit rapidly evaluation of coal seam and overburden quality and quantity. The understanding of the relationship between the coal mineralization of interest and the likely related complicate geological processes and structure that govern its emplacement and geometry within the geological framework is essential to the establishment of the geological controls for coal mineralization. System outputs includes: drillholes summary reports, stratigraphy, cross-sections, isopach maps, structure, contour maps, premining and post mining topography maps, and 3D perspective view on coal seam structure.

Oct 1, 2009

By Catalin Florin Petre, Elahe Ghasemian Langeroudi, Abdelaaziz Azizi, Éric Proulx, Caroline Olsen, Paul Blatter, Faïçal Larachi, Claude Gagnon

"The recovery of gold from ores is often accompanied by the release of other species in the leach solution. This state of affairs leads to depleted free cyanide levels in the slurry. Therefore, separation and quantification of these cyanicides and free cyanide at different stages of the cyanidation process as well as in waste solutions is crucial to provide mitigation tools by preventing leaching of deleterious metals for environmental considerations.COREM and the research group of Prof. Larachi have been working together on the control of gold passivation and cyanicides during cyanidation for several years. Previously, a first capillary electrophoresis (CE) protocol for the speciation of sulfur and cyanicides (SCN-, Cu, Fe) during cyanidation of gold complex sulfide ores was developed and validated for assessing industrial process water.The separation of zinc cyanide complexes used to be confronted with a number of difficulties due to the weak and/or undetectable cyanocomplexes in formally available CE protocols. Moreover, according to our knowledge, no direct CE protocol exists to separate free cyanide. Therefore, a new study aimed at developing a second CE protocol for the detection and quantification of cyanide complexes of zinc and nickel as well as of free cyanide in the cyanidation process water.To achieve this goal, six common carrier electrolytes such as pyridine, trimellitic acid, 4-methylbenzylamine, sodium chromate, phthalic acid and tris base were studied, using an indirect UV detection method. The best results were obtained using sodium chromate for which all ions were successfully separated and quantified. In addition, the effect of electric field strength, injection volume, electro-osmotic flow (EOF) modifier and background electrolyte (BGE) concentration were examined, while peak height, peak area and noise were considered for optimization.As a result, the new protocol is expected to complete the initial CE protocol by detecting cyanide complexes of zinc and nickel as well as free cyanide. Moreover, analytical determination of free cyanide in the presence of weak cyanide complexes achieved by the new protocol was also compared to conventional titration using silver nitrate solution. This new CE protocol will contribute to applied research and help plants to better understand and eventually control the behaviour of cyanidation circuits."

Jan 1, 2011

By R. Jackman, D. Koningen, G. Wilcox

"Gowest Gold Ltd. is in the process of developing the Frankfield East gold deposit located along the largely undeveloped Pipestone fault northeast of Timmins, Ontario. In addition to resource development and environmental permitting work the company has had an ongoing program of metallurgical and engineering studies aimed at evaluating options for processing the Frankfield East ore. Mineralization at the Frankfield project contains arsenopyrite and pyrite as the major sulphide minerals. Bulk flotation of all sulphides results in extremely high gold recovery. However, the gold is almost entirely associated with the arsenopyrite fraction of the ore and is refractory in nature requiring preoxidation treatment. Selective flotation was investigated to recover a gold-arsenopyrite concentrate thereby reducing the mass which would be subjected to further gold processing. As part of this work, a pyrite concentrate low in arsenic content was also recovered that would be suitable as a source of sulphur for a smelter (or other pyrometallurgical facility). Production of separate arsenopyrite and pyrite concentrates is frequently examined but rarely adopted due to the distribution of gold between the two products or the inability to achieve adequate separation. Several flowsheet options were investigated in the study. The best results were achieved following a sequential flotation flowsheet. The flowsheet configuration was key to meeting the targets for the two products. In this paper, the various options investigated are reviewed and the results of the final flowsheet are presented. The overall plan by Gowest was to evaluate all process options to bring the Frankfield East deposit into production. The ability to effectively separate the arsenopyrite and pyrite components in the ore provides Gowest with added opportunities to pursue both short and long term production scenarios."

Jan 1, 2012

By Nick D. Rose

Outline ?Background ?History of inverse-velocity for failure prediction ?Methodolog ?Case Histories ?Three case examples of predicted slopefailure to actual date of occurrence ?One case example of mitigated slope failure using inverse-velocity to forecast failure time and schedule remedial measures ?Conclusions

May 1, 2006

By M. Kalin

"Ecological Engineering and Biological Polishing technology is a decommissioning approach for inactive coal, uranium and base metal operations. To improve acid mine drainage water some fundamental aspects of wetland ecology and sediment microbiology are combined, to provide conditions to allow for biomineralization of the contaminants.This paper summarizes the first records of microbial alkalinity generation in acid mine drainage through the utilisation of the ARUM process. The process requires that the seepage is at pH 4.5 where sulphate reducers utilize sulphate to produce hydrogen sulphide, which in turn precipitates with metals. The pH increase is brought about by alkalinity generating microbes.The ARUM process has been successful in increasing the pH from 2.5 to 7.0. Flow through reactors operated in the laboratory continuously for more than 60 days have removed Ni from 13 mg/L to < 0.01 mg/L. Design parameters are being developed for low flow rates of 5 L/min in a test system receiving seepage from a tailings.1.0 INTRODUCTIONAcid mine drainage associated with mining wastes poses a significant environmental problem. Conventional means to treat acid mine drainage (AMD) use chemical treatment system. Ecological Engineering technology uses natural biological means to curtail and ameliorate AMD during mine operations and at the time of decommissioning. The premise underlying Ecological Engineering technology is that AMD is the result of a natural process enhanced by mining activities. Therefore, in nature, a process providing a natural balance to AMD has to exist, which, when assisted through appropriate means, can counteract the detrimental effects of AMD on the environment. This process is microbial alkalinity generation which is known to occur in wetlands, lake and ocean sediments (Baas Becling et al, 1960)."

Jan 1, 1991

By L. Vollert

In-situ recovery of metals is presently experiencing a revival not seen since early applications in amenable copper oxide deposits, uranium and generally applications where neither, porosity and permeability, nor process chemistry have been prohibitively difficult. With ever decreasing grades in current mining operations or Greenfields projects and ever increasing capital and operating costs, in-situ recovery is looked to as the processing option that will both unlock these deposits as well as potentially derive revenue from mineralised waste remaining in the ground once traditional mining and processing methods become uneconomical. In-situ recovery is also being looked to as a mining method that minimises the environmental impact sustained in the application of traditional energy and water intensive mining and processing operations where millions of tonnes of ore are mined from the earth, processed on surface and then disposed of in both waste dumps and tailings facilities. The key challenge facing companies like Newcrest is that these low-grade deposits or remnant mines are generally hard rock applications that require costly methods to liberate the valuable minerals. A further challenge includes identifying suitable chemistries that both facilitate the economic recovery of gold and copper and that may be considered environmentally acceptable. This paper presents a desktop study whereby the issues of access creation and chemical extraction are discussed and evaluated with a view to driving future research in the area and unlocking this application as a real processing option. INTRODUCTION Mining companies are increasingly challenged by low grade, deep and complex ore deposits which are no longer economically exploitable by current methods. The large footprint of current open pit operations can present obstacles for permitting and social acceptance. For these reasons in-situ recovery (ISR) technologies are receiving renewed attention as a technology which could be used to exploit these more complex deposits economically and with less environmental impact. The environmental impact may be further reduced if emphasis is placed on use of renewable energy sources rather than traditional grid power, gas turbine or diesel generators are employed to drive the operation. A potential renewable energy driven ISR mine of the future is shown in Figure 1.

Jan 1, 2019

By Maureen E. Lipkewich

Education builds long term awareness, acceptance and support for responsible mineral resource development. The MABC Education Program is an award winning education partnership with British Columbia classroom teachers that has helped over 5400 teachers with resources and other learning opportunities. Each year, thousands of students begin, and continue, to learn about our modern mineral industry as a result of this teacher-written program. The CIM network has an integral role in the future of mineral education in today?s classrooms in Canada and programs of this caliber are vital to our future. The industry needs help in raising awareness of the benefits of modern mining and teachers need help in acquiring that information.

May 1, 2002

By C. Cornejo, C. Schuffeneger, J. Rosas

"At the end of 2010 the AMSA Esperanza Concentrator started commissioning. Located in the Atacama Desert this project is the first of several large size concentrators developed recently to operate in Northern Chile. In addition to the new operations to be implemented in the short term, many existing installations are planning expansions. The use of large size equipment is one of the common characteristics of the new concentrators, but also new technologies are being considered and innovation is present in most cases. Sea water or desalinated water will be required to process large tonnages of sulphide copper ores as well as gold bearing ores, since process water supply from the Andes will no longer be available. The high cost of sea water or desalinated water supply and the high cost of energy are not a limitation as the current metal market scenario allows obtaining an attractive NPV even from installations designed to process relatively low grade ores. A review of the current concentrators being developed in Chile is presented, including a description of the main design issues related to technology and innovation. An analysis of the Chilean mining industry is also presented, detailing mine and plant capacities as well as expected final products.INTRODUCTION The mining sector in Chile has become a reference when analysing the large concentrator plants projected or currently in operation all over the world. At present and as a consequence of the high price of metal commodities, most South American countries have an active mining sector. Chile is known as a major producer of metals. First records of copper production exported to Spain are dated to the early XVII century. Since then Chile has produced over 13% of the total copper ever produced in the world. After 1990 Chilean mining and the associated cluster of activities has substantially grown to levels never reached before, especially in the production of copper, gold and other non-metallic minerals. This dramatic increase is the result of an economic policy based on delivering comparative advantages and incentives for the admission of foreign capital to offset the weak domestic investment in previous decades. Massive mining of its huge mineral resources has allowed Chile to be a world leader in the production of copper and other base metals and mineral products."

Jan 1, 2012

By Michel Fontaine, Bruno St-Cyr

"The mission of the CENTRE DE RECHERCHE INDUSTRIELLE DU QUEBEC (CRIQ) is to stimulate economic development by guiding businesses in their pursuit of innovation.With a comprehensive approach to their needs, CRIQ provides businesses with expertise based on the most recent developments and insights in the fields of:Research and Development ServicesAutomation and production processesDevelopment of industrial equipmentEnvironmental biotechnologiesTesting and Product Qualification Services Industrial and Technological Information ServicesConsultancy and competitive intelligence servicesIndustrial information bankStandardization ServicesElaboration of standards and product certificationSystems registrationEXPERTISE COMPETENCE, INNOVATIONSince its founding in 1969, CRIQ has been involved in over 100,000 projects. The results of its research and development services have enabled it to build over one hundred pieces of equipment, almost all still in operation today. CRIQ has been and remains the driving force of innovation and expertise on the industrial scene, offering highly competitive solutions to a clientele from numerous industrial sectors.CRIQ became a crown corporation operating on a commercial basis on June 30, 1997. This change in its corporate structure has enabled it to put a marked emphasis on trade and implement an array of new operational practices.The formation of marketing companies with private partners, the opening up to corporate business and international markets, the new directions for internal research and the strengthening of its marketing component are among the activities CRIQ has initiated over the last fiscal year to finally reach its cruising speed."

Jan 1, 2000

By Jiwen Zhang

Abstract Due to the blocking nature at the crusher station, straightforward application of queuing theory cannot give realistic results on the performance of a shovel-truck-crusher system. A new queuing network-based model has been developed in which, the crusher station is formulated into an open queuing network and the whole shovel-truck-crusher system into a closed queuing network with the crusher station as a special server. To fully account for the influence of blocking, Monte Carlo simulation is first used to obtain the performance parameters of the open queuing network for the crusher station. The closed queuing network for the entire system is solved by applying the Extended Summation Method (ESUM), in which the crusher server is described by the simulation results. The model has been applied to the Yuanbaoshan open-pit coal mine to analyze its shovel-truck-crusher system and to improve its efficiency. Results indicate that the blocking at the crusher is an important factor affecting the crusher output and in turn the efficiency of the whole system, and prove that the model can realistically describe the behavior of such systems.

Oct 1, 2009

By Jiwen Zhang

Due to the blocking nature at the crusher station, straightforward application of queuing theory cannot give realistic results on the performance of a shovel-truck-crusher system. A new queuing network-based model has been developed in which, the crusher station is formulated into an open queuing network and the whole shovel-truck-crusher system into a closed queuing network with the crusher station as a special server. To fully account for the influence of blocking, Monte Carlo simulation is first used to obtain the performance parameters of the open queuing network for the crusher station. The closed queuing network for the entire system is solved by applying the Extended Summation Method (ESUM), in which the crusher server is described by the simulation results. The model has been applied to the Yuanbaoshan open-pit coal mine to analyze its shovel-truck-crusher system and to improve its efficiency. Results indicate that the blocking at the crusher is an important factor affecting the crusher output and in turn the efficiency of the whole system, and prove that the model can realistically describe the behavior of such systems.

Oct 1, 2009

By Denis Labrie

Le minage en profondeur sous contrainte modérée à élevée présente de nombreux défis aux opérateurs et aux ingénieurs de mine notamment au niveau du contrôle de terrain et de l?environnement minier souterrain, pour assurer la sécurité des travailleurs sous terre et la continuité du cycle d?opération. Des conditions de contrainte élevée signifient une pression accrue au front de taille et sur les structures minières tels les piliers de mine et les fins de zone, un risque de rupture violente ou de coup de toit plus élevé, des zones de rupture plus grandes au pourtour des excavations, des charges accrues sur le support de terrain, etc. Le présent article fournit un aperçu du travail fait à l?intérieur du Programme de Contrôle de terrain de CANMET au cours des sept (7) dernières années, entre 1995 et 2001, pour comprendre et suivre l?évolution des niveaux de contrainte à l?intérieur des structures minières. Les propriétés déterminées en laboratoire sur des échantillons rocheux et les prévisions effectuées au moment de la conception sont comparées avec les observations effectuées en chantier à la paroi des excavations et à l?intérieur de la masse rocheuse. La plupart des cas discutés ici montrent une corrélation satisfaisante entre les observations effectuées en chantier d?une part, et les résultats d?essai obtenus en laboratoire et les calculs réalisés lors de la conception d?autre part. Ces observations peuvent donc être considérées comme des moyens relativement sûrs pour vérifier et suivre l?évolution des niveaux de contrainte présents à l?intérieur des structures minières.

May 1, 2002

By Brian Hart, Stamen Dimov

"The Time of Flight Secondary Ion Mass Spectrometer (ToF-SIMS) is unique in that it measures the outermost atomic layers of any material. The technique is particularly suited for determining surface chemical composition of mineral particles. It is most commonly used as a diagnostic tool to measure mineral surface chemical variability in plant and bench top flotation separation processes. Recently, research towards understanding the full capability of the instrument has resulted in the development of new diagnostic applications related to various Au extraction technologies and the development of the ToF-SIMS as a predictive tool for assessing the chemical reactivity of the ore.In this paper we will present a brief review of the ToF-SIMS technique with recent advances in instrumentation and methodologies including:•,?recent developments and advances towards a semi-quantitative approach to the evaluation of mineral surface modifiers (ex. Cu),•,?flotation case studies investigating activator, depressant and collector loading variability within a flotation process,•,?the recently developed chemical reactivity test which we believe has the potential to predict the behaviour of minerals in a flotation test in response to chemical transfer during grinding,•,recent applications for determination of surface Au preg-robbed in carbonaceous materials.A portion of this material has been recently presented at the COM 2009 meeting and at SIMS XVII (see Dimov et al 2009 and Hart et al, 2009).INTRODUCTIONIn flotation seperation surface chemistry is the principal determinant for selective separation of the various mineral phases (Ralston, 1994, Smart et al, 2003). Determination of this hydrophobic/hydrophilic balance by particle therefore requires correct identification and selection of the particular mineral phase(s) followed by a statistical analysis of the surface chemical characteristics of the particles with an estimation of the spread of values (Smart et al, 2003)."

Jan 1, 2010

By David R. Macedon

"Through the years, a wide variety of dust control methods have been utilized at mineral processing operations. While some have been successful, many have been highly ineffective. Dust Control systems currently in use include baghouse systems, fog systems, surfactant spray systems, and foam dust suppression. While baghouse systems can be effective, they are capitalintensive and costly to operate and maintain. Chemical dust control programs can be very effective. However, if applied incorrectly, they can have detrimental effect on mineral recovery. Thus, many operations utilize a combination of baghouses and water, often with limited success.Recent advancements in surfactant and polymer chemistry have resulted in substantially improved chemical dust suppression programs. These products range from non-corrosive surfactant/humectant combinations for road dust control to foam-based systems for crushers and transfer points, to advanced polymers for pile binding and soil stabilization. These advances are discussed in detail, citing results from fieldwork in the precious and base metals industries.INTRODUCTIONThe global nature of the mineral processing industry presents a unique set of challenges. Traditional thinking would tell us what works in one place should work in another. This could not be further from the truth in the area of dust control. We learn very quickly that there are a number of factors that can affect the efficiency and success of a dust control program and that these factors are not all chemical or equipment related. Some of these factors include facility maintenance, product selection, water quality and characteristics, and economic considerations.What has been learned from past experience is that each mineral processing plant presents a unique set of factors that will affect the ability to create an optimal dust control program. This paper presents a myriad of treatment options that will highlight the advancements in chemical dust suppression products and equipment."

Jan 1, 2004

By Mike Turner

The Otter-Juan mine was closed by WMC Resources? Kambalda Nickel Operations (WMC-KNO) in 1999 due to the combined effects of low Nickel prices and high mining costs. GBF Mining Pty Ltd purchased Otter-Juan Mine from WMC in early 2001 as part of WMC?s disinvestment from the nickel mines in the Kambalda area. Goldfields Mine Management (GMM), (a wholly owned subsidiary of GBF Pty Ltd) re-opened Otter-Juan in May 2001. The Otter-Juan mine is one of the oldest mines in the Kambalda region and is now mining at depths below 1160mbs. Stresses are very high, rock mass deformation considerable, and the mine has a history of serious seismic activity. Orebody widths in the current mining area range from 2 to 2.5m, with dips from 25° to 40°. On taking over the operation, GMM converted the mining method from the previous mechanised drift and fill method to a slot-rise and strip method using hand held airlegs. During the latter years of production under the control of WMC, production averaged around 12000 tonnes per month, with grades of 2.7% and orebody extraction of only 55 to 60%. In the last three years of operation under the control of GMM the mine has produced an average of 12000 tonnes per month of ore at an average grade of 4.2% and with an orebody extraction of 70 to 75%. The mine is now highly profitable with at least another 3 years of reserves remaining at depth. The main benefits of the current method include reduced dilution and increased extraction. In the relatively poor ground conditions experienced this has only been possible using airleg mining, with excavations designed to suit conditions, support to suit rockmass deformations, and with improved extraction sequencing. Other benefits have included improved operating conditions, reduced falls of ground incidents and a dramatic reduction in seismic activity. These achievements have only been possible by stepping back in time and using traditional airleg stoping methods to extract the maximum amount of the orebody with minimum dilution. This paper includes details of the mine history, geology, mining method, seismicity, and support.

May 1, 2004

By Paul R. Clark

Outline of Presentation ? Brief review of gasification and IGCC ? Polygenerationand its potential ? Why gasification today ? Major technology providers and their activities ? US initiatives ? Alberta Energy Resources and application of gasification ? CO2 management ? Advantages and barriers to gasification ? Conclusions

May 1, 2006

By D. Wolfe, K. Reid, T. Nunn

"The Aurora North mine has been operating for more than ten years, and is the source of over half of Syncrude’s bitumen production. In order to minimize front-end rejects, and to allow for high throughput, the ore top size at Aurora has been set at a nominal 125 mm. These relatively large lumps have a significant effect on both pump performance and pipeline pressure gradient. Current design methods underestimate the solids de-rating effect of lumpy slurries in pumps, and do not accurately describe the distribution or magnitude of the lump effect on pipeline pressure gradient. Data from the Aurora hydrotransport systems has been compiled, to quantify the effect of lumps on the pump head ratio and pipeline pressure gradient, and how this effect changes as lump ablation occurs along the length of the pipeline. A model has been built, using a logarithmic curve, which predicts the effect of 125 mm lumps on pipeline pressure gradient as a function of velocity and the distance from the start of a hydrotransport pipeline. This model is applicable only to Aurora hydrotransport operation, but similar models could be developed for other operations using the same methods. Using accurate pipeline pressure gradients and pump head ratios when designing future hydrotransport pipeline systems will help improve their reliability and operability."

Jan 1, 2014

By Bjarne Ekberg

"The most economical way of dewatering mineral concentrates is to reduce the moisture content in the material mechanically using thickeners and filtration avoiding thermal drying whenever possible. In addition to this, the dewatering process should produce low moisture cake, high quality liquid, consume little energy. As a part of the dewatering process The CERAMEC® capillary filter has been proven to meet these requirements in over 150 installations. The filtration is done by using ceramic filter plates with small pore size. The capillary action in the filter medium secures gas free filtration at good vacuum, and due to the small pore size, filtrate is crystal clean and particle free. The energy consumption is minimal. This paper will discuss results from filters installed at Pyhäsalmi Mine Oy in Finland where the technology was has been used since the late eighties. Results from more recent installations like Los Pelambres in Chile and LKAB in Sweden will also be discussed.INTRODUCTIONThe idea of using capillary action to make dewatering more efficient was invented two decades ago. Ten years later whole filter plants utilizing the new method were delivered to mine concentrators for dewatering of mineral concentrates. Further development of ceramic membrane plates made it possible to meet the requirements in iron ore dewatering. In addition to low cake moisture, high capacity and low energy consumption, there are a lot of environmental advantages in using capillary filtration. One of them is clear filtrate.CAPILLARY FILTRATIONA micro-porous filter material behaves like a large number of narrow capillaries forming a network. When a pressure difference ?P is applied over the wetted, hydrophilic pore with the radius r, the force striving to push the water out of the pore will be ?Ppr2. The force striving to hold the water in the pore will be the vector force 2pr? cosa of the surface tension ? and the cosine contact angle a. Equalling those forces and solving the equation for ?P we get"

Jan 1, 2003