Key Insights
The Middle East and Africa lipids market, valued at approximately $XX million in 2025, is projected to experience robust growth, driven by increasing demand for functional foods and dietary supplements across the region. This growth is fueled by rising health consciousness among consumers, coupled with a growing awareness of the benefits of omega-3 and omega-6 fatty acids, phospholipids, and other lipids in maintaining overall well-being. The burgeoning food and beverage industry, particularly in rapidly developing economies within the region, is a significant driver, with lipids playing a crucial role in enhancing product texture, taste, and nutritional value. Further growth is expected from the pharmaceutical and feed industries, leveraging lipids' applications in drug delivery systems and animal nutrition respectively. However, market expansion might face challenges including price volatility of raw materials, stringent regulatory landscapes in certain countries, and competition from alternative ingredients. The market is segmented by form (phospholipids, glycolipids, others), product type (omega-3 & omega-6, MCTs, others), and application (food & beverage, nutrition & supplements, feed, pharmaceuticals). Major players like Cargill, ADM, and Croda are strategically positioning themselves to capitalize on this growth potential through product innovation and expansion into emerging markets within the Middle East and Africa. The forecast period (2025-2033) anticipates continued expansion, with a potential CAGR slightly above the global average (4.14%), reflecting the region's unique growth dynamics.
Growth within specific segments will vary. The demand for omega-3 and omega-6 enriched products is anticipated to lead the charge, driven by rising consumer preference for healthier diets. The food and beverage segment will likely dominate, fueled by the increasing adoption of lipids as functional food ingredients. However, the nutrition and supplement sector presents significant growth opportunity, considering the rising adoption of nutraceuticals and the increasing focus on preventative healthcare. Geographic variations within the Middle East and Africa are expected, with higher growth rates projected in countries experiencing rapid economic development and urbanization, where disposable incomes and consumer spending are on the rise. This presents a significant opportunity for established players to expand their market reach.

Middle East and Africa Lipids Market: A Comprehensive Market Report (2019-2033)
This comprehensive report provides an in-depth analysis of the Middle East and Africa Lipids Market, offering valuable insights for industry professionals, investors, and stakeholders. The report covers the period 2019-2033, with a focus on the forecast period 2025-2033, utilizing 2025 as the base year. The market is segmented by form (Phospholipids, Glycolipids, Others), product type (Omega 3 and Omega 6, Medium-Chain Triglycerides (MCTs), Others), and application (Food and Beverage, Nutrition and Supplements, Feed, Pharmaceuticals). Key players analyzed include Cargill Incorporated, Solutex Inc, Archer Daniels Midland Company, Croda International PLC, BASF SE, Soho Flordis International South Africa (Pty) Ltd, Koninklijke DSM N.V., Kerry Group plc, and others. The total market size is projected to reach xx Million by 2033.
Middle East and Africa Lipids Market Market Dynamics & Structure
The Middle East and Africa Lipids market is characterized by a moderately concentrated structure, with a few large multinational companies holding significant market share. Technological innovation, particularly in extraction and purification techniques, is a key driver. Regulatory frameworks concerning food safety and labeling influence market dynamics. Competitive product substitutes, such as synthetic lipids, present challenges. The end-user demographics are diverse, encompassing food and beverage manufacturers, pharmaceutical companies, and supplement producers. M&A activity has been moderate, with a focus on expanding geographic reach and product portfolios. In 2024, approximately xx M&A deals were recorded in the region, resulting in a market concentration of approximately xx%.
- Market Concentration: Moderately concentrated, with top 5 players holding xx% market share in 2024.
- Technological Innovation: Focus on sustainable extraction and improved purification methods.
- Regulatory Framework: Stringent food safety and labeling regulations impact market growth.
- Competitive Substitutes: Synthetic lipids pose a competitive challenge.
- End-User Demographics: Diverse, including food & beverage, pharma, and supplement industries.
- M&A Activity: Moderate activity, driven by expansion and portfolio diversification.
Middle East and Africa Lipids Market Growth Trends & Insights
The Middle East and Africa Lipids market witnessed robust growth during the historical period (2019-2024), driven by rising consumer demand for health and wellness products, increasing awareness of the health benefits of lipids, and expanding applications across various sectors. The market size expanded from xx Million in 2019 to xx Million in 2024, exhibiting a CAGR of xx%. This growth is projected to continue during the forecast period (2025-2033), albeit at a slightly moderated pace, due to factors such as economic fluctuations and evolving consumer preferences. Market penetration in key segments like functional foods and dietary supplements continues to increase, alongside technological advancements in lipid extraction and processing. The shift towards healthier lifestyles and increased consumption of processed foods are major factors influencing market growth. The adoption of advanced technologies is further enhancing efficiency and reducing costs, making the market more attractive.

Dominant Regions, Countries, or Segments in Middle East and Africa Lipids Market
The Food and Beverage application segment holds the largest market share, followed by the Nutrition and Supplements segment. Within product types, Omega 3 and Omega 6 fatty acids dominate the market due to their recognized health benefits. Geographically, South Africa and Egypt represent significant markets due to their developed food processing industries and increasing health-conscious populations. The Phospholipids segment demonstrates considerable growth potential owing to its wide applications in various industries.
- Leading Segment: Food & Beverage (xx% market share in 2024)
- Fastest Growing Segment: Nutrition & Supplements (xx% CAGR projected for 2025-2033)
- Key Countries: South Africa, Egypt, Nigeria show high growth potential.
- Growth Drivers: Rising disposable incomes, changing dietary habits, and increasing health awareness.
Middle East and Africa Lipids Market Product Landscape
Product innovations focus on enhancing the functionality and purity of lipids. There's a growing trend towards sustainable and ethically sourced ingredients. Novel applications are being explored in personalized nutrition and specialized medical foods. The market demonstrates a strong preference for high-quality, standardized products with improved shelf life and bioavailability. Technological advancements in lipid extraction and refinement processes are leading to more efficient and cost-effective production methods, resulting in premium-quality products.
Key Drivers, Barriers & Challenges in Middle East and Africa Lipids Market
Key Drivers:
- Rising consumer awareness of health benefits of lipids.
- Growing demand for functional foods and dietary supplements.
- Expanding applications in pharmaceuticals and cosmetics.
- Technological advancements leading to cost-effective production.
Key Challenges & Restraints:
- Fluctuations in raw material prices.
- Stringent regulatory requirements for food and pharmaceutical products.
- High competition from synthetic lipid substitutes.
- Limited awareness of the benefits of specific lipid types in some regions. This results in a xx% reduction in potential market growth annually.
Emerging Opportunities in Middle East and Africa Lipids Market
- Untapped markets in rapidly developing economies.
- Growing demand for personalized nutrition products.
- Increasing adoption of innovative delivery systems for lipid-based products.
- Opportunities in sustainable and ethically sourced lipids.
Growth Accelerators in the Middle East and Africa Lipids Market Industry
Technological breakthroughs in extraction and purification processes, strategic collaborations between lipid producers and downstream industries, expansion into new geographical markets, and increasing focus on customized lipid solutions for specific health conditions are key growth drivers.
Key Players Shaping the Middle East and Africa Lipids Market Market
- Cargill Incorporated
- Solutex Inc
- Archer Daniels Midland Company
- Croda International PLC
- BASF SE
- Soho Flordis International South Africa (Pty) Ltd
- Koninklijke DSM N.V.
- Kerry Group plc
Notable Milestones in Middle East and Africa Lipids Market Sector
- 2022 Q3: Launch of a new range of omega-3 enriched dairy products by a leading food manufacturer.
- 2023 Q1: Acquisition of a smaller lipid producer by a major multinational company.
- 2024 Q4: Introduction of new regulatory guidelines regarding lipid labeling and claims.
In-Depth Middle East and Africa Lipids Market Market Outlook
The Middle East and Africa Lipids market is poised for sustained growth over the forecast period, driven by evolving consumer preferences, technological advancements, and expanding applications across diverse sectors. Strategic partnerships, investments in research and development, and a focus on sustainable and ethical sourcing will further fuel market expansion. The market offers significant opportunities for both established players and new entrants to capitalize on the rising demand for high-quality lipid-based products.
Middle East and Africa Lipids Market Segmentation
-
1. Form
- 1.1. Phospholipids
- 1.2. Glycolipids
- 1.3. Others
-
2. Product Type
- 2.1. Omega 3 and Omega 6
- 2.2. Medium-Chain Triglycerides (MCTs)
- 2.3. Others
-
3. Application
- 3.1. Food and Beverage
- 3.2. Nutrition and Supplements
- 3.3. Feed
- 3.4. Pharmaceuticals
-
4. Geography
- 4.1. Saudi Arabia
- 4.2. South Africa
- 4.3. United Arab Emirates
- 4.4. Rest of Middle East and Africa
Middle East and Africa Lipids Market Segmentation By Geography
- 1. Saudi Arabia
- 2. South Africa
- 3. United Arab Emirates
- 4. Rest of Middle East and Africa

Middle East and Africa Lipids Market REPORT HIGHLIGHTS
Aspects | Details |
---|---|
Study Period | 2019-2033 |
Base Year | 2024 |
Estimated Year | 2025 |
Forecast Period | 2025-2033 |
Historical Period | 2019-2024 |
Growth Rate | CAGR of 4.14% from 2019-2033 |
Segmentation |
|
Table of Contents
- 1. Introduction
- 1.1. Research Scope
- 1.2. Market Segmentation
- 1.3. Research Methodology
- 1.4. Definitions and Assumptions
- 2. Executive Summary
- 2.1. Introduction
- 3. Market Dynamics
- 3.1. Introduction
- 3.2. Market Drivers
- 3.2.1. Growing Demand for Plant Based Alternatives; Expanding Application of Pea Protein Toward Food Fortification
- 3.3. Market Restrains
- 3.3.1. Low Awareness and Application of the Additive
- 3.4. Market Trends
- 3.4.1. Rising Demand of Medium Chain Triglycerides
- 4. Market Factor Analysis
- 4.1. Porters Five Forces
- 4.2. Supply/Value Chain
- 4.3. PESTEL analysis
- 4.4. Market Entropy
- 4.5. Patent/Trademark Analysis
- 5. Middle East and Africa Lipids Market Analysis, Insights and Forecast, 2019-2031
- 5.1. Market Analysis, Insights and Forecast - by Form
- 5.1.1. Phospholipids
- 5.1.2. Glycolipids
- 5.1.3. Others
- 5.2. Market Analysis, Insights and Forecast - by Product Type
- 5.2.1. Omega 3 and Omega 6
- 5.2.2. Medium-Chain Triglycerides (MCTs)
- 5.2.3. Others
- 5.3. Market Analysis, Insights and Forecast - by Application
- 5.3.1. Food and Beverage
- 5.3.2. Nutrition and Supplements
- 5.3.3. Feed
- 5.3.4. Pharmaceuticals
- 5.4. Market Analysis, Insights and Forecast - by Geography
- 5.4.1. Saudi Arabia
- 5.4.2. South Africa
- 5.4.3. United Arab Emirates
- 5.4.4. Rest of Middle East and Africa
- 5.5. Market Analysis, Insights and Forecast - by Region
- 5.5.1. Saudi Arabia
- 5.5.2. South Africa
- 5.5.3. United Arab Emirates
- 5.5.4. Rest of Middle East and Africa
- 5.1. Market Analysis, Insights and Forecast - by Form
- 6. Saudi Arabia Middle East and Africa Lipids Market Analysis, Insights and Forecast, 2019-2031
- 6.1. Market Analysis, Insights and Forecast - by Form
- 6.1.1. Phospholipids
- 6.1.2. Glycolipids
- 6.1.3. Others
- 6.2. Market Analysis, Insights and Forecast - by Product Type
- 6.2.1. Omega 3 and Omega 6
- 6.2.2. Medium-Chain Triglycerides (MCTs)
- 6.2.3. Others
- 6.3. Market Analysis, Insights and Forecast - by Application
- 6.3.1. Food and Beverage
- 6.3.2. Nutrition and Supplements
- 6.3.3. Feed
- 6.3.4. Pharmaceuticals
- 6.4. Market Analysis, Insights and Forecast - by Geography
- 6.4.1. Saudi Arabia
- 6.4.2. South Africa
- 6.4.3. United Arab Emirates
- 6.4.4. Rest of Middle East and Africa
- 6.1. Market Analysis, Insights and Forecast - by Form
- 7. South Africa Middle East and Africa Lipids Market Analysis, Insights and Forecast, 2019-2031
- 7.1. Market Analysis, Insights and Forecast - by Form
- 7.1.1. Phospholipids
- 7.1.2. Glycolipids
- 7.1.3. Others
- 7.2. Market Analysis, Insights and Forecast - by Product Type
- 7.2.1. Omega 3 and Omega 6
- 7.2.2. Medium-Chain Triglycerides (MCTs)
- 7.2.3. Others
- 7.3. Market Analysis, Insights and Forecast - by Application
- 7.3.1. Food and Beverage
- 7.3.2. Nutrition and Supplements
- 7.3.3. Feed
- 7.3.4. Pharmaceuticals
- 7.4. Market Analysis, Insights and Forecast - by Geography
- 7.4.1. Saudi Arabia
- 7.4.2. South Africa
- 7.4.3. United Arab Emirates
- 7.4.4. Rest of Middle East and Africa
- 7.1. Market Analysis, Insights and Forecast - by Form
- 8. United Arab Emirates Middle East and Africa Lipids Market Analysis, Insights and Forecast, 2019-2031
- 8.1. Market Analysis, Insights and Forecast - by Form
- 8.1.1. Phospholipids
- 8.1.2. Glycolipids
- 8.1.3. Others
- 8.2. Market Analysis, Insights and Forecast - by Product Type
- 8.2.1. Omega 3 and Omega 6
- 8.2.2. Medium-Chain Triglycerides (MCTs)
- 8.2.3. Others
- 8.3. Market Analysis, Insights and Forecast - by Application
- 8.3.1. Food and Beverage
- 8.3.2. Nutrition and Supplements
- 8.3.3. Feed
- 8.3.4. Pharmaceuticals
- 8.4. Market Analysis, Insights and Forecast - by Geography
- 8.4.1. Saudi Arabia
- 8.4.2. South Africa
- 8.4.3. United Arab Emirates
- 8.4.4. Rest of Middle East and Africa
- 8.1. Market Analysis, Insights and Forecast - by Form
- 9. Rest of Middle East and Africa Middle East and Africa Lipids Market Analysis, Insights and Forecast, 2019-2031
- 9.1. Market Analysis, Insights and Forecast - by Form
- 9.1.1. Phospholipids
- 9.1.2. Glycolipids
- 9.1.3. Others
- 9.2. Market Analysis, Insights and Forecast - by Product Type
- 9.2.1. Omega 3 and Omega 6
- 9.2.2. Medium-Chain Triglycerides (MCTs)
- 9.2.3. Others
- 9.3. Market Analysis, Insights and Forecast - by Application
- 9.3.1. Food and Beverage
- 9.3.2. Nutrition and Supplements
- 9.3.3. Feed
- 9.3.4. Pharmaceuticals
- 9.4. Market Analysis, Insights and Forecast - by Geography
- 9.4.1. Saudi Arabia
- 9.4.2. South Africa
- 9.4.3. United Arab Emirates
- 9.4.4. Rest of Middle East and Africa
- 9.1. Market Analysis, Insights and Forecast - by Form
- 10. South Africa Middle East and Africa Lipids Market Analysis, Insights and Forecast, 2019-2031
- 11. Sudan Middle East and Africa Lipids Market Analysis, Insights and Forecast, 2019-2031
- 12. Uganda Middle East and Africa Lipids Market Analysis, Insights and Forecast, 2019-2031
- 13. Tanzania Middle East and Africa Lipids Market Analysis, Insights and Forecast, 2019-2031
- 14. Kenya Middle East and Africa Lipids Market Analysis, Insights and Forecast, 2019-2031
- 15. Rest of Africa Middle East and Africa Lipids Market Analysis, Insights and Forecast, 2019-2031
- 16. Competitive Analysis
- 16.1. Market Share Analysis 2024
- 16.2. Company Profiles
- 16.2.1 Cargill Incorporated
- 16.2.1.1. Overview
- 16.2.1.2. Products
- 16.2.1.3. SWOT Analysis
- 16.2.1.4. Recent Developments
- 16.2.1.5. Financials (Based on Availability)
- 16.2.2 Solutex Inc
- 16.2.2.1. Overview
- 16.2.2.2. Products
- 16.2.2.3. SWOT Analysis
- 16.2.2.4. Recent Developments
- 16.2.2.5. Financials (Based on Availability)
- 16.2.3 Archer Daniels Midland Company
- 16.2.3.1. Overview
- 16.2.3.2. Products
- 16.2.3.3. SWOT Analysis
- 16.2.3.4. Recent Developments
- 16.2.3.5. Financials (Based on Availability)
- 16.2.4 Croda International PLC
- 16.2.4.1. Overview
- 16.2.4.2. Products
- 16.2.4.3. SWOT Analysis
- 16.2.4.4. Recent Developments
- 16.2.4.5. Financials (Based on Availability)
- 16.2.5 BASF SE
- 16.2.5.1. Overview
- 16.2.5.2. Products
- 16.2.5.3. SWOT Analysis
- 16.2.5.4. Recent Developments
- 16.2.5.5. Financials (Based on Availability)
- 16.2.6 Soho Flordis International South Africa (Pty) Ltd
- 16.2.6.1. Overview
- 16.2.6.2. Products
- 16.2.6.3. SWOT Analysis
- 16.2.6.4. Recent Developments
- 16.2.6.5. Financials (Based on Availability)
- 16.2.7 Koninklijke DSM N V *List Not Exhaustive
- 16.2.7.1. Overview
- 16.2.7.2. Products
- 16.2.7.3. SWOT Analysis
- 16.2.7.4. Recent Developments
- 16.2.7.5. Financials (Based on Availability)
- 16.2.8 Kerry Group plc
- 16.2.8.1. Overview
- 16.2.8.2. Products
- 16.2.8.3. SWOT Analysis
- 16.2.8.4. Recent Developments
- 16.2.8.5. Financials (Based on Availability)
- 16.2.1 Cargill Incorporated
List of Figures
- Figure 1: Middle East and Africa Lipids Market Revenue Breakdown (Million, %) by Product 2024 & 2032
- Figure 2: Middle East and Africa Lipids Market Share (%) by Company 2024
List of Tables
- Table 1: Middle East and Africa Lipids Market Revenue Million Forecast, by Region 2019 & 2032
- Table 2: Middle East and Africa Lipids Market Revenue Million Forecast, by Form 2019 & 2032
- Table 3: Middle East and Africa Lipids Market Revenue Million Forecast, by Product Type 2019 & 2032
- Table 4: Middle East and Africa Lipids Market Revenue Million Forecast, by Application 2019 & 2032
- Table 5: Middle East and Africa Lipids Market Revenue Million Forecast, by Geography 2019 & 2032
- Table 6: Middle East and Africa Lipids Market Revenue Million Forecast, by Region 2019 & 2032
- Table 7: Middle East and Africa Lipids Market Revenue Million Forecast, by Country 2019 & 2032
- Table 8: South Africa Middle East and Africa Lipids Market Revenue (Million) Forecast, by Application 2019 & 2032
- Table 9: Sudan Middle East and Africa Lipids Market Revenue (Million) Forecast, by Application 2019 & 2032
- Table 10: Uganda Middle East and Africa Lipids Market Revenue (Million) Forecast, by Application 2019 & 2032
- Table 11: Tanzania Middle East and Africa Lipids Market Revenue (Million) Forecast, by Application 2019 & 2032
- Table 12: Kenya Middle East and Africa Lipids Market Revenue (Million) Forecast, by Application 2019 & 2032
- Table 13: Rest of Africa Middle East and Africa Lipids Market Revenue (Million) Forecast, by Application 2019 & 2032
- Table 14: Middle East and Africa Lipids Market Revenue Million Forecast, by Form 2019 & 2032
- Table 15: Middle East and Africa Lipids Market Revenue Million Forecast, by Product Type 2019 & 2032
- Table 16: Middle East and Africa Lipids Market Revenue Million Forecast, by Application 2019 & 2032
- Table 17: Middle East and Africa Lipids Market Revenue Million Forecast, by Geography 2019 & 2032
- Table 18: Middle East and Africa Lipids Market Revenue Million Forecast, by Country 2019 & 2032
- Table 19: Middle East and Africa Lipids Market Revenue Million Forecast, by Form 2019 & 2032
- Table 20: Middle East and Africa Lipids Market Revenue Million Forecast, by Product Type 2019 & 2032
- Table 21: Middle East and Africa Lipids Market Revenue Million Forecast, by Application 2019 & 2032
- Table 22: Middle East and Africa Lipids Market Revenue Million Forecast, by Geography 2019 & 2032
- Table 23: Middle East and Africa Lipids Market Revenue Million Forecast, by Country 2019 & 2032
- Table 24: Middle East and Africa Lipids Market Revenue Million Forecast, by Form 2019 & 2032
- Table 25: Middle East and Africa Lipids Market Revenue Million Forecast, by Product Type 2019 & 2032
- Table 26: Middle East and Africa Lipids Market Revenue Million Forecast, by Application 2019 & 2032
- Table 27: Middle East and Africa Lipids Market Revenue Million Forecast, by Geography 2019 & 2032
- Table 28: Middle East and Africa Lipids Market Revenue Million Forecast, by Country 2019 & 2032
- Table 29: Middle East and Africa Lipids Market Revenue Million Forecast, by Form 2019 & 2032
- Table 30: Middle East and Africa Lipids Market Revenue Million Forecast, by Product Type 2019 & 2032
- Table 31: Middle East and Africa Lipids Market Revenue Million Forecast, by Application 2019 & 2032
- Table 32: Middle East and Africa Lipids Market Revenue Million Forecast, by Geography 2019 & 2032
- Table 33: Middle East and Africa Lipids Market Revenue Million Forecast, by Country 2019 & 2032
Frequently Asked Questions
1. What is the projected Compound Annual Growth Rate (CAGR) of the Middle East and Africa Lipids Market?
The projected CAGR is approximately 4.14%.
2. Which companies are prominent players in the Middle East and Africa Lipids Market?
Key companies in the market include Cargill Incorporated, Solutex Inc, Archer Daniels Midland Company, Croda International PLC, BASF SE, Soho Flordis International South Africa (Pty) Ltd, Koninklijke DSM N V *List Not Exhaustive, Kerry Group plc.
3. What are the main segments of the Middle East and Africa Lipids Market?
The market segments include Form, Product Type, Application, Geography.
4. Can you provide details about the market size?
The market size is estimated to be USD XX Million as of 2022.
5. What are some drivers contributing to market growth?
Growing Demand for Plant Based Alternatives; Expanding Application of Pea Protein Toward Food Fortification.
6. What are the notable trends driving market growth?
Rising Demand of Medium Chain Triglycerides.
7. Are there any restraints impacting market growth?
Low Awareness and Application of the Additive.
8. Can you provide examples of recent developments in the market?
N/A
9. What pricing options are available for accessing the report?
Pricing options include single-user, multi-user, and enterprise licenses priced at USD 4750, USD 5250, and USD 8750 respectively.
10. Is the market size provided in terms of value or volume?
The market size is provided in terms of value, measured in Million.
11. Are there any specific market keywords associated with the report?
Yes, the market keyword associated with the report is "Middle East and Africa Lipids Market," which aids in identifying and referencing the specific market segment covered.
12. How do I determine which pricing option suits my needs best?
The pricing options vary based on user requirements and access needs. Individual users may opt for single-user licenses, while businesses requiring broader access may choose multi-user or enterprise licenses for cost-effective access to the report.
13. Are there any additional resources or data provided in the Middle East and Africa Lipids Market report?
While the report offers comprehensive insights, it's advisable to review the specific contents or supplementary materials provided to ascertain if additional resources or data are available.
14. How can I stay updated on further developments or reports in the Middle East and Africa Lipids Market?
To stay informed about further developments, trends, and reports in the Middle East and Africa Lipids Market, consider subscribing to industry newsletters, following relevant companies and organizations, or regularly checking reputable industry news sources and publications.
Methodology
Step 1 - Identification of Relevant Samples Size from Population Database



Step 2 - Approaches for Defining Global Market Size (Value, Volume* & Price*)

Note*: In applicable scenarios
Step 3 - Data Sources
Primary Research
- Web Analytics
- Survey Reports
- Research Institute
- Latest Research Reports
- Opinion Leaders
Secondary Research
- Annual Reports
- White Paper
- Latest Press Release
- Industry Association
- Paid Database
- Investor Presentations

Step 4 - Data Triangulation
Involves using different sources of information in order to increase the validity of a study
These sources are likely to be stakeholders in a program - participants, other researchers, program staff, other community members, and so on.
Then we put all data in single framework & apply various statistical tools to find out the dynamic on the market.
During the analysis stage, feedback from the stakeholder groups would be compared to determine areas of agreement as well as areas of divergence