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Computer simulation of gravity-driven granular flow.

機(jī)譯：重力驅(qū)動(dòng)的顆粒流的計(jì)算機(jī)模擬。

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We develop and use three-dimensional event-driven molecular dynamics simulations of dry gravity-driven granular flow. Our system is comprised of mono- and poly-disperse sets of spherical grains falling down a vertical chute under the influence of gravity. We observe three phases or states of granular matter: a free-fall dilute granular gas region at the top of the chute, a granular fluid in the middle and then a glassy region at the bottom.;We investigate collision time distributions as one approaches the static limit of steady-state flow of dry granular matter. The collision times fall in a power-law distribution with an exponent dictated by whether the grains are ordered or disordered. Remarkably, the exponents have almost no dependence on dimension. We are also able to resolve a disagreement between simulation and experiments on the exponent of the collision time power-law distribution. We also investigate velocity fluctuations in dry granular flow. We find three different classes of velocity distributions depending on factors such as the local density. The class of the velocity distribution depends on whether the grains are in a free-fall, fluid or glassy state. The analytic form of the distributions match those that have been found by other authors in fairly diverse systems. Here, we have all three present in a single system in steady-state. Power-law tails that match recent experiments are also found but in a transition area suggesting they may be an artifact of crossover from one class of velocity distribution to another. We find evidence that the transition from one class to another may correspond to a second order dynamical phase transition in the limit that the vertical flow speed goes to zero.;Finally, we investigate constitutive relations in dry granular flow. We examine local stresses, heat flow, and dissipation in an three phases of our system. We find a complete closed set of constitutive relations capable of describing the system in the different regions and test several proposed constitutive relations in the fluid and glassy regions. Similar to static sand piles, we find that stresses in the glassy region are almost entirely determined by directions along which collisions occur. We show that the static sand pile is the static limit of our glassy state. We also examine the strain rate and viscosity dependence on the granular temperature. While finding regimes consistent with experiments, we find that these quantifies do not exhibit a universal power-law relationship. However we do find a universal power-law relationship between the shear stress and the shear rate in the glassy region, and likewise between viscosity and shear rate in the glassy region. We show that there is a yield stress associated with our glassy system and we demonstrate the stress and energy balance in the different regions of our system. We show that Fourier's law for heat flow is obeyed in the glassy region, however care must be taken in separating energy and heat flow. In the glassy region the conductivity is equal to the volume fraction times the mean collision frequency. In the fluid region the thermal conductivity has an exponential dependence on the granular temperature. We finally close our relations by deriving an expression for the mean collision frequency in terms of the pressure and granular temperature.
機(jī)譯：我們開(kāi)發(fā)和使用三維事件驅(qū)動(dòng)的分子動(dòng)力學(xué)模擬的干重力驅(qū)動(dòng)的顆粒流。我們的系統(tǒng)由單粒和多粒球形顆粒組成，它們?cè)谥亓Φ淖饔孟聫拇怪被郎系袈?。我們觀(guān)察到顆粒物的三個(gè)階段或狀態(tài)：在滑道頂部的自由下落的稀顆粒氣體區(qū)域，在中間的顆粒流體，然后在底部的玻璃狀區(qū)域。干顆粒物穩(wěn)態(tài)流動(dòng)的靜態(tài)極限。碰撞時(shí)間屬于冪律分布，其冪由晶粒有序或無(wú)序決定。值得注意的是，指數(shù)幾乎與尺寸無(wú)關(guān)。我們還能夠解決碰撞時(shí)間冪律分布指數(shù)上的仿真與實(shí)驗(yàn)之間的分歧。我們還研究了干燥顆粒流中的速度波動(dòng)。根據(jù)局部密度等因素，我們發(fā)現(xiàn)了三種不同的速度分布類(lèi)別。速度分布的類(lèi)別取決于晶粒是否處于自由下落，流體或玻璃態(tài)。分布的分析形式與其他作者在相當(dāng)不同的系統(tǒng)中發(fā)現(xiàn)的分布形式相匹配。在這里，我們?cè)诜€(wěn)定狀態(tài)下將所有三個(gè)存在于單個(gè)系統(tǒng)中。還發(fā)現(xiàn)了與最近的實(shí)驗(yàn)相匹配的冪律尾部，但在過(guò)渡區(qū)域表明它們可能是從一類(lèi)速度分布到另一類(lèi)速度分布的交叉產(chǎn)物。我們發(fā)現(xiàn)有證據(jù)表明，從一類(lèi)到另一類(lèi)的過(guò)渡可能在垂直流速為零的極限內(nèi)對(duì)應(yīng)于二階動(dòng)力學(xué)相變。最后，我們研究了干燥顆粒流中的本構(gòu)關(guān)系。我們?cè)谙到y(tǒng)的三個(gè)階段檢查局部應(yīng)力，熱流和耗散。我們找到了一個(gè)完整的本構(gòu)關(guān)系的封閉集合，該本構(gòu)關(guān)系能夠描述不同區(qū)域中的系統(tǒng)，并在流體和玻璃狀區(qū)域中測(cè)試了幾種建議的本構(gòu)關(guān)系。與靜態(tài)沙堆相似，我們發(fā)現(xiàn)玻璃狀區(qū)域中的應(yīng)力幾乎完全由發(fā)生碰撞的方向確定。我們表明，靜態(tài)砂堆是玻璃態(tài)的靜態(tài)極限。我們還檢查了應(yīng)變速率和粘度對(duì)顆粒溫度的依賴(lài)性。在找到與實(shí)驗(yàn)相符的方案時(shí)，我們發(fā)現(xiàn)這些量化結(jié)果未顯示出普遍的冪律關(guān)系。然而，我們確實(shí)在玻璃狀區(qū)域中的剪切應(yīng)力與剪切速率之間以及玻璃狀區(qū)域中的粘度與剪切速率之間找到了普遍的冪律關(guān)系。我們顯示出與玻璃狀系統(tǒng)相關(guān)的屈服應(yīng)力，并且證明了系統(tǒng)不同區(qū)域的應(yīng)力和能量平衡。我們表明在玻璃狀區(qū)域中遵守了熱流的傅立葉定律，但是在分離能量和熱流時(shí)必須小心。在玻璃狀區(qū)域中，電導(dǎo)率等于體積分?jǐn)?shù)乘以平均碰撞頻率。在流體區(qū)域，熱導(dǎo)率與顆粒溫度呈指數(shù)關(guān)系。最后，我們通過(guò)推導(dǎo)平均碰撞頻率的表達(dá)式（根據(jù)壓力和顆粒溫度）來(lái)結(jié)束我們的關(guān)系。

著錄項(xiàng)

  • 作者

    Drozd, John Jan.;

  • 作者單位

    The University of Western Ontario (Canada).;

  • 授予單位 The University of Western Ontario (Canada).;
  • 學(xué)科 Physics Condensed Matter.;Engineering Materials Science.
  • 學(xué)位 Ph.D.
  • 年度 2009
  • 頁(yè)碼 129 p.
  • 總頁(yè)數(shù) 129
  • 原文格式 PDF
  • 正文語(yǔ)種 eng
  • 中圖分類(lèi) 工程材料學(xué);
  • 關(guān)鍵詞

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