Mixed boundary value problems in curvilinear domains relevant to microfluidic cooling using biomimetic structured surfaces
与使用仿生结构化表面的微流体冷却相关的曲线域中的混合边值问题
基本信息
- 批准号:EP/N022394/1
- 负责人:
- 金额:$ 9.43万
- 依托单位:
- 依托单位国家:英国
- 项目类别:Research Grant
- 财政年份:2016
- 资助国家:英国
- 起止时间:2016 至 无数据
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
A major challenge hindering the development of microprocessor chips capable of meeting the ongoing demand for faster processing speeds, is designing cooling systems that can accommodate the concomitant increases in chip heat production. One method, known as direct liquid cooling (DLC), is to drive liquid coolant directly through a chip via microscopic channels. However, since these channels are necessarily very narrow, the required driving pressure difference can be impractically large. One way to overcome this is to reduce the frictional forces exerted by the channel walls on the coolant. Very recently it has been proposed to do this by using microchannels lined with what are known as superhydrophobic surfaces (SS's).SS's are surfaces textured with microscopic structures which can reduce the frictional drag forces on liquids flowing over them. Essentially, cavities between the structures trap pockets of air over which the liquid flows more freely than it does over a solid substrate. Such surfaces occur commonly in nature, a well-known example being the lotus leaf. The potential for using biomimetic SS's in a wide variety of applications has been known for some time, but it is only recently that advances in microfabrication technology have made it possible for them to be manufactured. This has led to a surge in interest in them. However, in the context of DLC, whilst SS's lubricate the flow of the coolant, little is known about how they influence the flow of heat, which is the primary concern. This currently makes designing DLC devices with SS's a difficult task. What are of most use to engineers doing this, are formulae which reveal the exact (or close to exact) dependence of the flow of liquid and heat on the design parameters (e.g., the spacing of the microstructures). Such formulae make it possible to pinpoint the values of these parameters which optimise cooling much faster than, say, by numerical computations. The primary aim of this project is to find such formulae.In terms of exact solutions, the benchmark results in the field are those derived by Philip. Our first aim is to derive an extension of these results. We shall do this by using similar techniques to those applied by Philip, but with the important addition of a new set of mathematical tools arising from recently-identified, so-called secondary Schottky groups. The use of similar tools has proved to be highly effective at finding exact solutions to similar problems over the last decade.However, one limitation of Philip's results, and almost all others which have followed in the literature, is that they assume the shape of the interface, or meniscus, between the trapped pockets of air and the liquid to be flat. In reality this meniscus is generally curved, and at these microscopic scales, this curvature can have a significant effect. Our second aim is to derive solutions which account for a full range of this curvature. The construction of such solutions in terms of explicit formulae would be very hard using the tools applied in the case of flat menisci or other, traditional methods. To overcome this we shall make use of a powerful new technique, based on so-called transforms, which is specifically designed for solving problems of this type involving curved boundaries.The multiple facets of this proposal (modelling flows of both liquid and heat involving solid/liquid/gas interfaces and curvature effects), and the complexity and power of the tools to be applied (secondary Schottky groups, the new transform method), make this a mathematically rich project. In addition, the innovative application of SS's to DLC, and the current interest in SS's as a whole, combined with the novelty of the proposed mathematical techniques, make these investigations of timely significance. Furthermore, given that a number of other entirely different physical processes are governed by the same mathematical equations, the project's results will have a broad impact.
阻碍能够满足对更快处理速度的持续需求的微处理器芯片的开发的主要挑战是设计能够适应芯片热产生的伴随增加的冷却系统。一种方法,称为直接液体冷却(DLC),是通过微观通道直接驱动液体冷却剂通过芯片。然而,由于这些通道必须非常窄,所需的驱动压差可能大得不切实际。克服这一点的一种方法是减小由通道壁施加在冷却剂上的摩擦力。最近,已经提出通过使用衬有所谓的超疏水表面(SS)的微通道来做到这一点。SS是具有微观结构的纹理化表面,其可以减少流过它们的液体上的摩擦阻力。基本上,结构之间的空腔捕获空气袋,液体在其上比在固体基底上更自由地流动。这种表面在自然界中很常见,一个众所周知的例子是荷叶。在各种各样的应用中使用仿生SS的潜力已经知道了一段时间,但直到最近,微细加工技术的进步才使它们成为可能。这导致人们对它们的兴趣激增。然而,在DLC的背景下,虽然SS润滑冷却剂的流动,但人们对它们如何影响热流知之甚少,而这是主要问题。这使得目前设计具有SS的DLC设备成为一项困难的任务。对工程师来说,最有用的是揭示液体和热量的流动对设计参数的精确(或接近精确)依赖性的公式(例如,微结构的间距)。这样的公式使得精确确定这些参数的值成为可能,这些参数的值比例如通过数值计算优化冷却快得多。这个项目的主要目的是找到这样的公式。在精确解方面,该领域的基准结果是由Philip导出的。我们的第一个目标是得到这些结果的推广。我们将通过使用与菲利普所应用的技术类似的技术来做到这一点,但重要的是增加了一套新的数学工具,这些工具来自最近发现的所谓二级肖特基基团。在过去的十年里,使用类似的工具已经被证明是非常有效的,可以找到类似问题的精确解。然而,菲利普的结果以及文献中几乎所有其他结果的一个局限性是,它们假设了被困空气和液体之间的界面或弯月面的形状是平坦的。实际上,这种弯月面通常是弯曲的,并且在这些微观尺度上,这种曲率可以具有显著的效果。我们的第二个目标是得到的解决方案,占整个范围内的曲率。使用在平面双曲正切情况下应用的工具或其他传统方法,根据显式公式构造这样的解将是非常困难的。为了克服这一点,我们将利用一个强大的新技术,基于所谓的变换,这是专门设计用于解决这种类型的问题,涉及弯曲的边界。(模拟涉及固体/液体/气体界面和曲率效应的液体和热量的流动),以及所应用工具的复杂性和能力(次级肖特基群,新的转换方法),使这成为一个数学丰富的项目。此外,创新的应用SS的DLC,和当前的利益SS的作为一个整体,结合新奇的建议的数学技术,使这些调查及时的意义。此外,鉴于许多其他完全不同的物理过程都由相同的数学方程控制,该项目的结果将产生广泛的影响。
项目成果
期刊论文数量(3)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Longitudinal shear flow over a bubble mattress with curved menisci: arbitrary protrusion angle and solid fraction
具有弯曲弯液面的气泡垫上的纵向剪切流:任意突出角和固体分数
- DOI:10.1093/imamat/hxy029
- 发表时间:2018
- 期刊:
- 影响因子:1.2
- 作者:Luca E
- 通讯作者:Luca E
Exact Formulae for the Effective Slip Length of a Symmetric Superhydrophobic Channel with Flat or Weakly Curved Menisci
具有平坦或弱弯曲弯月面的对称超疏水通道有效滑移长度的精确公式
- DOI:10.1137/17m1117185
- 发表时间:2017
- 期刊:
- 影响因子:1.9
- 作者:Marshall J
- 通讯作者:Marshall J
Analytical Solutions for an Escape Problem in a Disc with an Arbitrary Distribution of Exit Holes Along Its Boundary
出口孔沿边界任意分布的圆盘逃逸问题的解析解
- DOI:10.1007/s10955-016-1653-2
- 发表时间:2016
- 期刊:
- 影响因子:1.6
- 作者:Marshall J
- 通讯作者:Marshall J
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Jonathan Simon Marshall其他文献
Jonathan Simon Marshall的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
相似国自然基金
水稻边界发育缺陷突变体abnormal boundary development(abd)的基因克隆与功能分析
- 批准号:32070202
- 批准年份:2020
- 资助金额:58 万元
- 项目类别:面上项目
流体湍流运动的相关数学分析
- 批准号:10971174
- 批准年份:2009
- 资助金额:25.0 万元
- 项目类别:面上项目
不可压流体力学方程中的一些问题
- 批准号:10771177
- 批准年份:2007
- 资助金额:17.0 万元
- 项目类别:面上项目
关于任意截面导体壁中的环状形非圆截面等离子体稳定性的研究
- 批准号:10375050
- 批准年份:2003
- 资助金额:23.0 万元
- 项目类别:面上项目
相似海外基金
Study on the bifurcation structure of positive solutions for concave-convex mixed nonlinear elliptic boundary value problems with indefinite weights
不定权凹凸混合非线性椭圆边值问题正解的分岔结构研究
- 批准号:
15K04945 - 财政年份:2015
- 资助金额:
$ 9.43万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Efficient runge-kutta software for mixed order systems of boundary ODEs value
用于边界 ODE 值混合阶系统的高效 runge-kutta 软件
- 批准号:
946-1998 - 财政年份:2001
- 资助金额:
$ 9.43万 - 项目类别:
Discovery Grants Program - Individual
Efficient runge-kutta software for mixed order systems of boundary ODEs value
用于边界 ODE 值混合阶系统的高效 runge-kutta 软件
- 批准号:
946-1998 - 财政年份:2000
- 资助金额:
$ 9.43万 - 项目类别:
Discovery Grants Program - Individual
Efficient runge-kutta software for mixed order systems of boundary ODEs value
用于边界 ODE 值混合阶系统的高效 runge-kutta 软件
- 批准号:
946-1998 - 财政年份:1999
- 资助金额:
$ 9.43万 - 项目类别:
Discovery Grants Program - Individual
Efficient runge-kutta software for mixed order systems of boundary ODEs value
用于边界 ODE 值混合阶系统的高效 runge-kutta 软件
- 批准号:
946-1998 - 财政年份:1998
- 资助金额:
$ 9.43万 - 项目类别:
Discovery Grants Program - Individual
Mixed boundary value problems of elasticity and thermoelasticity, biomechanics and prestressed theory of thermoelasticity and thermoviscoelasticity
弹性和热弹性的混合边值问题、热弹性和热粘弹性的生物力学和预应力理论
- 批准号:
4177-1994 - 财政年份:1996
- 资助金额:
$ 9.43万 - 项目类别:
Discovery Grants Program - Individual
Mixed boundary value problems of elasticity and thermoelasticity, biomechanics and prestressed theory of thermoelasticity and thermoviscoelasticity
弹性和热弹性的混合边值问题、热弹性和热粘弹性的生物力学和预应力理论
- 批准号:
4177-1994 - 财政年份:1995
- 资助金额:
$ 9.43万 - 项目类别:
Discovery Grants Program - Individual
Mixed boundary value problems of elasticity and thermoelasticity, biomechanics and prestressed theory of thermoelasticity and thermoviscoelasticity
弹性和热弹性的混合边值问题、热弹性和热粘弹性的生物力学和预应力理论
- 批准号:
4177-1994 - 财政年份:1994
- 资助金额:
$ 9.43万 - 项目类别:
Discovery Grants Program - Individual
Mixed boundary value problems of elasticity and thermoelasticity
弹性和热弹性的混合边值问题
- 批准号:
4177-1991 - 财政年份:1993
- 资助金额:
$ 9.43万 - 项目类别:
Discovery Grants Program - Individual
Mathematical Sciences: Boundary Value Problems for Operatorsof Mixed Type on Closed Domains
数学科学:闭域上混合型算子的边值问题
- 批准号:
9206140 - 财政年份:1992
- 资助金额:
$ 9.43万 - 项目类别:
Standard Grant